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Intermittent turbulent suspension events over sand dunes on the bed of the Fraser River, near Mission,… Lapointe, Michel F. 1990

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INTERMITTENT TURBULENT SUSPENSION EVENTS OVER SAND DUNES ON THE BED OF THE FRASER RIVER, NEAR MISSION, BRITISH COLUMBIA. MICHEL F. LAPOINTE B.Sc, McGill University, 1975 M.Sc, McGill University, 1983 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF THE FACULTY OF GRADUATE STUDIES (Department of Geography) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1990 © Michel F. Lapointe, 1990 By DOCTOR OF PHILOSOPHY in In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Geography  The University of British Columbia Vancouver, Canada Date October 24. 1990  DE-6 (2/88) i i I ntermittent turbulent suspension events over sand dunes on the bed of the Fraser River, near Mission, B r i t i s h Columbia. ABSTRACT The purpose of t h i s study i s to gain some f i r s t i n s i g h t s into the r o l e of b u r s t - l i k e turbulent motions i n sediment suspension over a sandy channel bed, during t y p i c a l conditions of strong sediment transport with active bedforms. The focus i s the suspension mechanism that maintains sizeable sediment concentrations away from the bed, where much of the downstream transport occurs, rather than entrainment at the sediment boundary i t s e l f . Flow components downstream and normal to the mean boundary, along with the output of an o p t i c a l suspended sediment sensor, were monitored 1 m above the bed. The main study data were c o l l e c t e d i n a 10 m deep channel of the F r a s e r R i v e r near Mission, B r i t i s h Columbia, Canada. V e l o c i t i e s averaged 1.4 m/s at the surface and 0.9 m/s at the sensors, where mean suspended sediment concentrations were 500 mg/1; decimetre height small dunes on the backs of la r g e r , metre amplitude dunes covered the channel bed. Many hours of data were recorded at 5 Hz, allowing multi-second scale turbulent motions as w e l l as multi-minute o s c i l l a t i o n s to be resolved i n both the v e l o c i t y and t u r b i d i t y records. B u r s t - l i k e " e j e c t i o n and inrush" motions were i d e n t i f i e d , producing a high degree of intermittency i n momentum exchange: 80% of the mean Reynolds stress at the 1 m l e v e l i s produced during 12% of the record duration. The burst recurrence period appears to be s i g n i f i c a n t l y greater than predicted by applying the conventional outer flow s c a l i n g i n t h i s environment. I t i s hypothesised that the non-uniform shear and pressure gradient conditions over the various scales of bedforms on the r i v e r f l o o r may somehow a f f e c t mean burst p e r i o d i c i t y , modifying the recurrence s c a l i n g developed over f l a t boundaries. The determination of a burst recurrence timescale from one-point data i s inherently imprecise however and, as elsewhere, a i i i continuous variation of return periods with relative magnitude of extreme (u'v') events is observed. The optical turbidity (OBS) time series reveals that these intermittent burst-like motions are, as expected, very important in ver t i c a l l y mixing sediments across the 1 m level in the flow; for example v i o l e n t ejections, occurring only 1% of the time and contributing some 10% to mean turbulent momentum flux, appear to account for 6% of the total vertical sediment flux. The s t a t i s t i c a l association between the momentum and sediment mixing efficiencies of any ejection appears to be only moderately strong, however; very intense suspension can be associated with rather "weak" ejections (in terms of stress), and vice-versa. Differences between momentum and sediment mixing effects of a given ejection may partly be r e l a t e d to the "crossing t r a j e c t o r i e s e f f e c t " ; sand grains continually f a l l out of the eddies that bear them, so the momentum and sediment "contents" of an eddy at 1 m off the bed are not perfectly linked. Turbulent sediment suspension i s , like momentum exchange, a highly intermittent process in i t s e l f . After selecting turbulent events only for suspension efficiency, the largest ones, occupying only 5% of the time, contribute approximately one half of the total v e r t i c a l sediment flux. There is no indication that the conventional scaling of burst recurrence corresponds to the occurrence of any distinctive event level for suspension. Interestingly, burst-like turbulent motions are not the only flow oscillations contributing to suspension in the high flow conditions of the study. Multi-minute period flow perturbations at 1 m off the bed significantly assist burst-scale turbulent motions in driving the upward sediment mixing. In summary, turbulent mixing of both momentum and sediment at 1 m over a typical sandy river bed is dominated by intermittent, i n t e n s e " b u r s t - l i k e " events. However, the extrapolation of intermittent "bursting" concepts and structural constants from small-scale laboratory flows to the larger f l u v i a l environment may be misleading. i v CONTENTS Page Abstract i i Contents i v L i s t of Tables v i i L i s t of Figures v i i i 1 Introduction 1 1.1 Bursting i n laboratory and large-scale flows 2 1.2 Bursting and sediment transport 6 1.3 Sedimentary bedforms and bursting 7 1.4 The objectives of t h i s study 8 1.4.1 General study d e f i n i t i o n 8 1.4.2 Study o u t l i n e and s p e c i f i c objectives 11 2 Methodology 15 2.1 Sensor deployment methods 15 2.2 Sensor c h a r a c t e r i s t i c s and frequency losses 22 2.2.1 Electromagnetic current meter and high frequency losses 22 2.2.2 O p t i c a l Backscatter Sensor 26 2.2.3 Other apparatus 28 2.2.4 Low frequency losses 30 2.3 Sensor output contamination by organic debris 31 2.4 Study s i t e s and near-bed flow records 32 2.5 From frame based to boundary layer based v e l o c i t y coordinates 40 2.6 Low frequency flow o s c i l l a t i o n s i n r i v e r s 45 V Page 3 Momentum fluxes and turbulent bursting events 51 3.1 The frequency d i s t r i b u t i o n of momentum exchange 51 3.1.1 U and V spectra 54 3.1.2 The UV cospectrum 60 3.2 Intermittent contributions to momentum exchange 64 3.2.1 Intermittence of (u'v') time seri e s at sensor l e v e l 65 3.2.2 Mean burst recurrence period 70 3.3 Modulation of bursting over bedwaves: a speculative i n t e r p r e t a t i o n of the above r e s u l t s 77 3.4 I s o l a t i n g purely turbulent contributions to momentum exchange 81 3.5 Summary of main findings 82 4 Turbulent sediment suspension events 85 4.1 OBS output as a measure of suspended sediment concentration 85 4.2 V e r t i c a l v e l o c i t y and sediment concentrations f l u c t u a t i o n s at the 1 m l e v e l 94 4.2.1 S t a t i s t i c a l analysis of the r e l a t i o n between v and OBS signals 95 4.2.2 High frequency t u r b i d i t y f l u c t u a t i o n s : a p h y s i c a l i n t e r p r e t a t i o n 103 v i page 4.3 Recurrence analysis of high suspended sediment concentrations 107 4.4 Horizontal and v e r t i c a l suspended sediment fluxes at sensor l e v e l 110 4.4.1 An analysis of the v e r t i c a l sediment f l u x 110 4.4.2 The frequency contributions to net v e r t i c a l mixing f l u x 115 4.4.3 Intermittent high sediment f l u x events 117 4.4.4 Resultant downstream suspended sediment transport 129 5 Conclusions 131 5.1 Summary of research question 131 5.1.1 Momentum exchange: main findings 132 5.1.2 Sediment suspension: main findings 134 5.2 Further implications of the findings and avenues fo r research 135 References 138 LIST OF TABLES Conditions during the various 1987-1988 study deployments. Moment s t a t i s t i c s f o r u', v' and (u'v') d i s t r i b u t i o n s . S t a t i s t i c a l data on OBS c a l i b r a t i o n suspended sediment samples. V I 1 1 LIST OF FIGURES Page Fi g . 1: (top) Side view of the bare sensor support frame. (bottom) Close-up of the two main sensors on the frame support arms. 17 Fi g . 2: Work platform used to deploy the submersible frame. 19 F i g . 3: Frame being lowered to the channel bed from the back of the f l o a t i n g platform. 21 Fi g . 4: EM meter c a l i b r a t i o n data. 24 Fi g . 5 : The study s i t e s (*). Fraser River near Mission and Barnston Is., B.C., Canada. 35 F i g . 6: A 160 m long streamwise bed p r o f i l e taken on June 13, 1988 i n the area where the sensors were deployed. 37 F i g . 7: Stage record at the Mission gauge of Water Survey of Canada, June 12 to 14, 1988. 39 F i g . 8: 7 hour-long time seri e s of flow speed, angle and OBS output 1 m above the channel bed, June 13, 1988. 42 F i g . 9: The same flow v a r i a b l e s as i n F i g . 8, t h i s time smoothed with a 40 s running mean. 43 ix Page F i g . 10: Schematic diagram of streamline perturbations with time at 1 m o f f r i v e r bed. 49 Fi g . 11: A 10 min time seri e s of U and V flow components as w e l l as OBS output. 53 Fi g . 12: U, V and OBS power spectra, June 13, 1988. 56 Fig . 13: U spectra from two deployments, superimposed. 58 Fi g . 14: V spectra from two deployments, superimposed. 59 F i g . 15 a): TJ, V Coherence 2 b): (U, V) cospectra from two deployments, superimposed. 62 F i g . 16: A 14 min time s e r i e s of (U'V) along with simultaneous low-frequency f l u c t u a t i o n s i n U. 66 Fi g . 17: Percent of time and percent of mean kinematic stress associated with periods when the -(U'V) time s e r i e s exceeds various threshold values, 68 Fi g . 18: Histogram of (U'V) values compared with that of a normal d i s t r i b u t i o n with same mean and standard deviations. 71 X pages F i g . 19: Mean recurrence periods of intense " e j e c t i o n s " during which the -(U'V) s i g n a l exceeds various threshold values. 72 Fig . 20: Same as F i g . 19, f o r 3 deployments. 74 Fi g . 21: Same as F i g . 19, f o r wind tunnel data, Willmarth and Lu, 1974. 75 Fi g . 22: A 14 min time seri e s of the high-frequency contributions to momentum exchange at sensor l e v e l , along with simultaneous low-frequency h o r i z o n t a l v e l o c i t y o s c i l l a t i o n s . 83 Fi g . 23: Grain s i z e analysis and concurrent OBS response f o r 27, 7 second duration suspended sediment samples. 87 Fi g . 24: Scatter p l o t and l e a s t square regression l i n e e s t a b l i s h i n g a c a l i b r a t i o n of OBS output i n terms of t o t a l sample suspended sediment concentration. 90 Fi g . 25: same as F i g . 24, f o r a c a l i b r a t i o n of OBS output i n terms of the concentration of the sand f r a c t i o n s coarser than 0.09 mm. 93 Fi g . 26: Concurrent time s e r i e s of 1 min means of U, V and OBS output, based on 80 minutes of data. 97 xi pages F i g . 27: Concurrent 18 min time seri e s of OBS output and v e r t i c a l v e l o c i t i e s . 99 F i g . 28: Coherence 2 function analyzing the degree of l i n e a r r e l a t i o n between OBS output and V f l u c t u a t i o n s over d i f f e r e n t frequencies. 101 F i g . 29: Smoothed surface through (hp-OBS) response l e v e l s to 2 s periods with various i n t e n s i t y of r a p i d (turbulent) U and V f l u c t u a t i o n s (hp-U' and h p - V ) . 106 F i g . 30: A 100 min s e r i e s of OBS events over 2100 mV (dashed l i n e s forming spikes), along with simultaneous records of low-frequency U and V f l u c t u a t i o n s . 109 F i g . 31: OBS, V cospectrum. 116 F i g . 32: A 22 min seri e s of high-frequency contributions to v e r t i c a l sediment mixing (hp-0BS*hp-V) and momentum exchange (hp-U'*hp-V), along with simultaneous low frequency f l u c t u a t i o n s i n V. 118 x i i pages F i g . 33: Scatter p l o t comparing the high-frequency stress bearing and sediment mixing e f f i c i e n c i e s of i n d i v i d u a l 2 s periods chosen during turbulent e j e c t i o n s . 120 Fi g . 34: Aggregate duration as well as percentages of the high-frequency contributions to both momentum and v e r t i c a l sediment fluxes associated with e j e c t i o n periods exceeding various thresholds of (hp-U'*hp-V ) . 121 Fig . 35: Aggregate duration as well as percentages of the t o t a l contributions to both momentum and v e r t i c a l sediment fluxes associated with e j e c t i o n periods exceeding various thresholds of (U' * V ) . 123 Fi g . 36: Aggregate duration as well as percentage of mean v e r t i c a l sediment f l u x associated with periods when (hp-0BS*hp-V) exceeded various threshold values. 125 Fi g . 37: Same as F i g . 39, superimposed curves f o r two deployments. 126 Fi g . 38: Mean recurrence periods between " p o s i t i v e " turbulent mixing events (defined i n the text) exceeding various thresholds of (hp-0BS*hp-V). 127 Fi g . 39: Same as F i g . 41, curves superimposed f o r two two deployments. 128 1 CHAPTER 1 INTRODUCTION The i n v e s t i g a t i o n over recent decades of coherent bursting structures i n wall bounded shear flows has brought a new perspective to the study o f a l l u v i a l sediment t r a n s p o r t . A l t h o u g h long parameterized by mean boundary shear s t r e s s , bed material transport p r o c e s s e s are known to depend on near-bed turbulent v e l o c i t y f l u c t u a t i o n s and r e s u l t a n t instantaneous drag and l i f t forces. Turbulent b u r s t i n g i s a prevalent working model to understand and q u a n t i f y l a r g e near-bed turbulent motions. The d e t a i l s of the sto c h a s t i c b u rsting events and t h e i r dependence on the parameters of the o v e r a l l flow are however complex and s t i l l i m p e r f e c t l y understood. Moreover the i n t e r a c t i o n of these turbulent structures with deformable sediment boundaries constitutes a vast area for future research. Sediments on natural stream beds d i s p l a y a range of p a r t i c l e s i z e s and f a l l v e l o c i t i e s a f f e c t i n g t h e i r s u s c e p t i b i l i t y to entrainment by eddy motions. They also become arranged into a v a r i e t y o f bedforms that themselves modify the shear flow and turbulence generation. A b r i e f c r i t i c a l review of t h i s research context w i l l be presented. I t w i l l be shown that, to date, only preliminary i n s i g h t s i n t o the broad s i g n i f i c a n c e of turbulent b u r s t i n g to a l l u v i a l sediment transport have been gained, e s s e n t i a l l y f o r lack of d i r e c t observations of these phenomena i n strong r i v e r flows. The study reported here aims i n p a r t i c u l a r to investigate a long-standing c o n j e c t u r e i n the f l u v i a l l i t e r a t u r e about the importance f o r suspended sand transport of "macroturbulent" v e r t i c a l eddy motions ( v i s u a l i s e d i n " b o i l s " and now often i d e n t i f i e d with bursting; Matthes, 1947; Coleman, 1969; Jackson 1976). Casual observation of 2 sands brought v i o l e n t l y to the surface i n " b o i l s " suggests to some that b u r s t - l i k e motions may dominate o v e r a l l sediment suspension. Conceptual models l i n k i n g turbulent bursting, suspended sediment transport and a l l u v i a l bedforms have found t h e i r way into textbooks (e.g. A l l e n , 1985), despite not having been d i r e c t l y tested i n the f l u v i a l environment. This study w i l l focus on turbulent suspension processes i n a sandy f l u v i a l environment, as they occur over a c t i v e dune bedforms. The main emphasis of the study w i l l be on the timing and the con t r i b u t i o n to momentum exchange as well as sediment suspension of inter m i t t e n t " b u r s t - l i k e " events, monitored at 1 m from the bed, i n a large r i v e r channel with active dune f i e l d , and under high flow conditions. The key objective w i l l be to assess the importance to suspension ( r e l a t i v e to the mean v e r t i c a l sediment flux ) of the " b u r s t - l i k e " turbulent events at that height i n a 10 m deep r i v e r flow. A thorough study of the r e l a t i o n of such b u r s t - l i k e events to " c l a s s i c " laboratory b u r s t i n g w i l l not be attempted here; i t would require a more extensive set of flow data than could be generated i n t h i s study. 1.1 Bursting i n laboratory and large-scale flows. S t a r t i n g i n the 1960s with eddy v i s u a l i z a t i o n studies of motions i n the n e a r - w a l l zone, where much of the turbulence production i n boundary layers was known to occur (e.g.: Kli n e et a l . , 1967), much research on turbulent bursting has been conducted i n the l a s t decades. Cantwell (1981) provides a survey of the general f i e l d of coherent motions i n turbulent flows that developed from these e a r l y f i n d i n g s . In o u t l i n e , a c h a r a c t e r i s t i c sequence of events i s observed to occur i n the near-wall zone of boundary layers i n laboratory flows: i t involves deformation of streamwise, low-speed " s t r e a k s " i n the v i s c o u s s u b l a y e r and eventual v i o l e n t " e j e c t i o n s " of these r e l a t i v e l y slow parcels away from the wall, as part of "bursting" motions reaching t y p i c a l l y as f a r as the outer 3 zones of the boundary layer. Completing the bursting sequence (and maintaining c o n t i n u i t y of mass) are "sweeps" of f a s t e r f l u i d that move down towards the w a l l . Such intermittent, v i o l e n t motions are seen to account f o r much of the momentum exchange and turbulence production i n the boundary layer. Although a coherent sequence of events i s observed, these occur randomly i n space and time. There appears to be however an average recurrence period for strong bursting events at any point i n the flow, and t h i s period i s f a i r l y constant across much of the boundary l a y e r . U n f o r t u n a t e l y , e s t i m a t i o n of burst recurrence s t a t i s t i c s remains a vexed issue (Bogard and Tiederman, 1986); i t depends on the type of s i g n a l a v a i l a b l e (whether flow v i s u a l i z a t i o n movies or simple E u l e r i a n v e l o c i t y r e c o r d s ) and on various procedures of f i l t e r i n g or c o n d i t i o n a l sampling. I t also depends s t r o n g l y on s u b j e c t i v e decisions as to event thresholds. Such complications mar the i n t e r p r e t a t i o n of burst recurrence data from la r g e - s c a l e geophysical flows (such as are studied here) . There i s some agreement however that the burst recurrence period "T^" appears to scale with the "outer v a r i a b l e s " : free-stream v e l o c i t y U s and boundary layer thickness H (Rao et a l . , 1971; Willmarth and Lu, 1974). (1) T D= a*(H/U s), where a i s i n the range 3 to 7 Much of the subsequent f l u i d mechanics research i n t h i s area has concentrated on e l u c i d a t i n g the r e l a t i o n s between the near-w a l l i n s t a b i l i t i e s and "outer flow" events such as turbulent bulges or " b o i l s " i n free surface flows (e.g.: Falco, 1977; Brown and Thomas, 1977; Nakagawa and Nezu, 1981). In p a r t i c u l a r , p h y s i c a l models have been proposed to explain the t r i g g e r i n g of minute inner flow i n s t a b i l i t i e s at a rate set by bulk flow events and parameters (as suggested by (1)) and, conversely, the controls that seem to allow only c e r t a i n of these i n s t a b i l i t i e s to grow to the scale of the flow thickness. 4 Streaks i n the viscous sublayer were seen to play a large r o l e i n the genesis of bursting over smooth, f l a t boundaries i n the laboratory. Yet i n most natural f l u i d flows the viscous layer i s severely disrupted by the large scale of boundary roughness. Hence i t was n a t u r a l to ask whether bursting also occurred over rough, non-planar surfaces, i n p a r t i c u l a r sedimentary beds. Grass (1971) demonstrated that burst/sweep motions occurred over rough, sandy or g r a v e l l y , as well as smooth surfaces i n the laboratory. In the absence of a viscous sublayer, ejections were observed to o r i g i n a t e from the i n t e r s t i c e s of the sediment bed. Natural r i v e r flows have, however, Reynolds numbers based on flow depth that are t y p i c a l l y 2 orders of magnitude higher than those encountered i n the laboratory studies, where bu r s t i n g events have been i n v e s t i g a t e d extensively. River boundaries are often marked by complex bedform arrangements, that can modulate the flow through most of i t s f u l l depth. Detailed confirmation, through flow v i s u a l i z a t i o n , o f the e x i s t e n c e o f 3D " b u r s t i n g s t r u c t u r e s " analogous to those studied i n the laboratory, i s s t i l l l a c k i n g i n high Reynolds number geophysical flows. Such v i s u a l i s a t i o n may have to wait f o r new remote-monitoring techniques of the 3D turbulent f i e l d (e.g. by acoustic Doppler techniques) to be developed for these environments. Rood and H i c k i n (1989) speculate that eddy shedding i n the lee of bed dunes, rather than b u r s t i n g - r e l a t e d disturbances, may be mainly responsible f o r l a r g e - s c a l e suspension motions r e s u l t i n g i n surface b o i l s i n sand bed r i v e r s . A number of f i e l d studies have suggested, nonetheless, that b u r s t - l i k e processes are active at geophysical scales. Turbulence measurements, conducted at 1 to 2 m from the bed i n benthic and t i d a l b o u n d a r y l a y e r s , r e v e a l i n t e r m i t t e n t e v e n t s w i t h c h a r a c t e r i s t i c s akin to those of laboratory bursting, at l e a s t as f a r as observations at one p o s i t i o n within the flow can d i s c l o s e (Gordon, 1975; Gordon and Witting, 1977; Heathershaw, 1974, 1979; Anwar, 1981; Anwar and Atkins, 1982). These studies e s s e n t i a l l y r e l y 5 on recorded (u'v') signals (u' i s the f l u c t u a t i o n i n streamwise v e l o c i t y and v' that i n the v e l o c i t y normal to the boundary) ; t h i s (u'v') product i s often interpreted as an instantaneous c o n t r i b u t i o n to h o r i z o n t a l momentum exchange (shear stress) across the layer. In most cases i t was found that, as i n laboratory bursting, much of the mean str e s s was produced by b r i e f but intense (thus "intermittent") " e j e c t i o n and inrush" events. This type of analysis i s at the heart of my study. C l e a r c o n f i r m a t i o n , f o r such " b u r s t - l i k e " events i n g e o p h y s i c a l f l o w s , o f the r e c u r r e n c e s c a l i n g observed i n the l a b o r a t o r y (1) has not always been p o s s i b l e however: w h i l e laboratory research has pointed out the s e n s i t i v i t y of burst counts to the s e l e c t i o n of the event-defining threshold (Willmarth and Lu, 1974), i n many f i e l d s t u d i e s of (u'v') events no e x p l i c i t j u s t i f i c a t i o n of the choice of event threshold was provided. Results can be hard to i n t e r p r e t unless great care i s taken to set the "event"-defining threshold o b j e c t i v e l y and c o n s i s t e n t l y . C o n s i d e r a b l e s o p h i s t i c a t i o n i s involved i n d e f i n i n g and counting bursts i n c o n t r o l l e d laboratory conditions and using multi-point data (e.g. Rao et a l . , 1971; Lu and Willmarth, 1973; Willmarth and Lu, 1974; Bogard and Tiederman, 1986). One-point (u'v') seri e s from large scale flows do not appear to be easier to i n t e r p r e t . McLean and Smith (1979) claim not to have been able to i d e n t i f y conspicuous b u r s t - l i k e (u'v') events l i a b l e to such a recurrence analysis near the bed of the Columbia River (no c l e a r threshold was perceived between the d i f f e r e n t l e v e l s of intense events and the lower i n t e n s i t y background). Heathershaw (1979) d i d not produce d i r e c t counts of bursting events i n I r i s h Sea t i d a l flows, but i n f e r r e d return periods through derived estimates of intermittency and burst duration. Gordon (1974, 1975) defined a burst counting t h r e s h o l d l e v e l equal to twice the median (u'v') , but d i d not otherwise j u s t i f y t h i s choice. Anwar (1981) also f a i l e d to discuss h i s choice of threshold and a r r i v e d at a burst recurrence period i n a t i d a l flow much below the values predicted by outer flow s c a l i n g . 6 1.2 Bursting and sediment transport. The p o t e n t i a l e f f e c t i v e n e s s i n terms of sediment entrainment of energetic "sweeps" bringing high v e l o c i t i e s to the bed, as well as that of ejections of near bed f l u i d i n suspending sediment, are both immediately obvious. Early d e t a i l e d observations of sediment motion by Sutherland (1967) had revealed the r o l e of eddies impinging on a sand bed i n both entraining and suspending p a r t i c l e s . Later flow v i s u a l i z a t i o n work by Grass (1970, 1971, 1974) c l e a r l y suggested a complementarity of sweeps and ej e c t i o n s i n transporting sands. These l a s t studies elucidated the r o l e played by instantaneous peaks i n boundary shear stresses due to sweeps i n i n i t i a l l y e n t raining sand grains from stable bed p o s i t i o n s , as well as the suspension of entrained sands "trapped" i n ejected f l u i d p a r c e l s . Sumer and Oguz (1978) and Sumer and Deigaard (1981) c a r e f u l l y tracked the suspension t r a j e c t o r i e s of r e l a t i v e l y heavy sand p a r t i c l e s and found a close correspondence with the kinematics of b u r s t motions. In the case of the h e a v i e r p a r t i c l e s , a manifestation of the " c r o s s i n g - t r a j e c t o r i e s e f f e c t " (Yudine, 1959) was i n evidence: i n i t i a l upward p a r t i c l e t r a j e c t o r i e s from the boundary were interrupted before the ejected eddies l o s t t h e i r i d e n t i t y , the p a r t i c l e s i n e f f e c t f a l l i n g out of the ejected f l u i d p a r c e l s . More recently, acoustic monitoring of "self-generated noise" due to gravel motion i n a t i d a l boundary layer confirmed that inrush or "sweep"-like events were those responsible f o r most of the sediment transport when p a r t i c l e s are too heavy to be suspended (Heathershaw and Thome, 1985; Thome et a l . , 1989). Use of f a s t response o p t i c a l or dynamic suspended sediment sensors has s i m i l a r l y allowed Soulsby et a l . (1984, 1985) and West and Oduyemi (1989) to b e g i n the study of turbulent f l u c t u a t i o n s i n near-bed sediment concentration and the suspension e f f e c t s of b u r s t - l i k e intermittent 7 motions i n open channel flows. The l a t t e r p a r t i c u l a r issues w i l l be c e n t r a l to the present study, as we l l . 1.3 Sedimentary bedforms and bursting The tendency f o r sandy flow boundaries to develop into r i p p l e or dune bedforms produces perturbations of the near-bed streamlines and thus modulation of l o c a l shearing conditions. In t u r n t h i s m o d u l a t i o n has the p o t e n t i a l to a f f e c t l o c a l burst g e n e r a t i o n and sediment t r a n s p o r t , and thus bedform evolution i t s e l f . A c r u c i a l l i n k i n t h i s hypothetical feedback e f f e c t may be the s e n s i t i v i t y of l o c a l burst generation to downstream pressure g r a d i e n t s . There i s evidence of enhanced b u r s t i n g i n adverse gradients (e.g.: Klin e et a l . , 1967), while l o c a l l y adverse pressure gradients are known to occur over much of the lee side of bedforms, where they often lead to flow separation (e.g.: Raudkivi, 1964; Buckles et a l . , 1984). S p a t i a l modulation of bed surface pressures, as w e l l as that of turbulence parameters such as Reynolds stresses, are w e l l documented from laboratory experiments over a r t i f i c i a l waviness introduced into flow boundaries (Kendal, 1970; Hsu and Kennedy, 1971; Z i l k e r and Hanratty, 1979; Buckles et a l . , 1984). Comparatively few d e t a i l e d data are a v a i l a b l e on bursting-r e l a t e d sediment transport patterns along the surface of bedforms, however. Ikeda and Asaeda (1983) observed i n the laboratory p r e f e r e n t i a l b u r s t - l i k e a c t i v i t y and r e l a t e d sand suspension near the reattachment point on the lee side of r i p p l e s . A peak i n the power spectrum of suspended concentration was used to confirm the outer flow s c a l i n g of burst recurrence, suggesting that the events near the reattachment point might be somewhat more p e r i o d i c than the b u r s t i n g reported near f l a t boundaries. High-speed movie camera o b s e r v a t i o n s by Itakura and K i s h i (1980) of eddy motions over s o l i d i f i e d sand dunes i n the laboratory s i m i l a r l y revealed more intense b u r s t i n g near the reattachment point. I 8 I n t e r e s t i n g l y , these l a s t researchers found that burst frequency near the reattachment point followed a Strouhal s c a l i n g i n which the dune height replaced t o t a l boundary layer depth, the l a t t e r being the usual length scale i n the outer flow s c a l i n g of bursts. Along with the i n d i c a t i o n s of event p e r i o d i c i t y mentioned e a r l i e r , t h i s f i n d i n g suggests that vortex shedding along separated shear layers i n the lee of bedforms may also have been involved i n these c a s e s . The r e l a t i o n between such turbulent "events" over bedforms and " c l a s s i c " f l a t boundary b u r s t i n g remains to be investigated. Consideration has also been given i n the l i t e r a t u r e to p o s s i b l e l i n k s between burst mechanics and sedimentary i n s t a b i l i t i e s l e a d i n g to the development of bedforms. Ripples are thought to r e f l e c t i n s t a b i l i t i e s i n sediment transport i n the streaky, viscous sublayer, i n v o l v i n g grain pile-up and flow separation (Williams and Kemp, 1971; Y a l i n , 1972). As both dune wavelength and burst scales appear to depend on flow depth, a few authors have suggested a d i r e c t i n t e r a c t i o n between them (e.g.: Y a l i n , 1972; Jackson, 1976). Due to lack of data these l a s t models, however i n t e r e s t i n g , are s p e c u l a t i v e and the d e t a i l s of the proposed i n t e r a c t i o n s remain sketchy. 1.4 The objectives of t h i s study. 1.4.1 General study d e f i n i t i o n As e x p l a i n e d above, t h i s study w i l l f o c u s on the importance of b u r s t - l i k e motions i n v e r t i c a l l y suspending sands above an a c t i v e r i v e r dune f i e l d . This issue i s of fundamental i n t e r e s t to students of r i v e r mechanics: f o r example, e s t a b l i s h i n g that d i s t i n c t b u r s t - l i k e events of known recurrence were responsible 9 for the bulk of suspended sediment transport might, eventually, lead to improved parameterisations of sediment transport, as well as po s s i b l y shed l i g h t on bedform genesis. To the author's knowledge, no such study has been conducted to date i n a large r i v e r at high flow. P a r t i c u l a r d i f f i c u l t i e s i n gathering the required data i n such environments w i l l be discussed i n the next chapter. The object of t h i s study i s thus to analyse i n d e t a i l r e l a t i o n s between turbulent s t r e s s and sediment s u s p e n s i o n "events" i n a t y p i c a l f l u v i a l c o n t e x t . Given the t e c h n i c a l d i f f i c u l t i e s encountered i n data g a t h e r i n g , i n v e s t i g a t i o n of the e f f e c t s on these r e l a t i o n s of changing flow and bed conditions and sensing height, w i l l be l e f t to furthe r studies. B e f o r e i n t r o d u c i n g s p e c i f i c r e s e a r c h q u e s t i o n s and o b j e c t i v e s , an o u t l i n e of the type of data c o l l e c t e d w i l l be presented next. The key data f o r t h i s study were provided by a f a s t response o p t i c a l t u r b i d i t y sensor, monitoring f l u c t u a t i o n s i n suspended sand l e v e l s , deployed at 1 m from the bed alongside a b i d i r e c t i o n a l electromagnetic flow meter sensing v e l o c i t y components both streamwise (u) and normal to the boundary (v). Eddy c o r r e l a t i o n methods applied to these 3 signals w i l l shed l i g h t on v e r t i c a l f l u x e s through sensor l e v e l of both h o r i z o n t a l momentum (the Reynolds shear stress) and suspended sediment, and the uv quadrant method (e.g. Willmarth and Lu, 1974) w i l l be used to detect burst-l i k e motions. This type of data i s akin to that r e c e n t l y gathered by Soulsby et a l . (1984, 1985) and West and Oduyemi (1989), i n a t i d a l (rather than f l u v i a l ) environment and, as w i l l be seen i n the next section, with somewhat d i f f e r e n t objectives. Given the complexity of turbulent flow f i e l d s , the p h y s i c a l i n s i g h t s obtainable from E u l e r i a n data on momentum and sediment fluxes at one point i n the flow i s of course l i m i t e d . Sediment d i s p e r s a l from the bed would be bett e r described i n a Lagrangian (flow p a r c e l tracking) framework. Because of the severe problems of interference generated by multiple probes aligned to track events, i t was t h o u g h t t h a t , at t h i s e x p l o r a t o r y stage, extended 10 observations at one point could nonetheless throw u s e f u l l i g h t on intermittent momentum exchange and suspension. A number of factors were involved i n the s e l e c t i o n of a 1 m sensing height f o r t h i s study. The l a t t e r corresponds to the general area of the flow where the greatest bed material (sand) f l u x occurs, w i t h both sediment concentrations i n suspension and downstream v e l o c i t i e s s i m u l t a n e o u s l y h i g h . Indeed, under t y p i c a l freshet conditions near Mission approximately h a l f the t o t a l sand load of the 10 m deep Fraser River i s transported within 2 m of the r i v e r bed (McLean and Church, 1986). However turbulent events c o n t r o l entrainment at the sedimentary bed i t s e l f (processes not d i r e c t l y observed i n t h i s study) , the suspension mechanisms that have an influence at the 1 m l e v e l , and are studied here, have a strong bearing on downstream suspended sediment transport, and as such are worthy of a t t e n t i o n i n t h e i r own r i g h t . Other t e c h n i c a l reasons for choosing the 1 m sensing height w i l l be discussed i n the next chapter. A number of data sets were gathered i n 1987 and 1988, i n d i f f e r e n t f l u v i a l and t i d a l environments wi t h i n the Fraser V a l l e y area. The data sets c o l l e c t e d and deployment, sensor malfunction and data c o r r u p t i o n problems encountered i n these e f f o r t s w i l l be summarised i n the next chapter. The main findings reported i n t h i s study are based on the highest q u a l i t y data set a v a i l a b l e , c o l l e c t e d June 13, 1988 on the Fraser River near Mission, B.C., Canada; during t h i s run a l l sensors functioned properly, flow conditions were re a s o n a b l y steady, and s i g n a l corruption by water-borne organic debris was l e s s p e r s i s t e n t than i n any of the other runs. These data were gathered over a 7 hour period above a f i e l d of mostly small dunes, 8-30 cm i n amplitude, i n a 10 m deep flow with a 1.4 m/s s u r f a c e v e l o c i t y . Further d e t a i l s on flow conditions and data gathering methodology w i l l also be found i n chapter 2. Because of the length of usable records gathered i n the June 13 run near Mission, these data provide the best estimates of the s t a t i s t i c s of f l u x intermittence and spectra under steady f l u v i a l conditions that 11 could be obtained over the 2 f i e l d seasons. The June 13 r e s u l t s are nonetheless further substantiated i n the thesis by more l i m i t e d data sets gathered at other r i v e r s i t e s and times. 1.4.2 Study ou t l i n e and s p e c i f i c o bjectives. As discussed i n s e c t i o n 1.1, i t has commonly been assumed that i n t e r m i t t e n t b u r s t - l i k e (u'v') events i n t i d a l flows are the signature, as they advect past the sensor l o c a t i o n away from the bed, of 3D bursting structures s i m i l a r to those observed i n simpler laboratory flows. Two c r i t e r i a have often been considered to be, i n e f f e c t , diagnostic of turbulent bursting when analysing such records (e.g. Gordon, 1975; Anwar, 1981): a) A high l e v e l of "intermittence" i n the (u'v') s i g n a l ; that i s , r e l a t i v e l y b r i e f record segments i d e n t i f i e d as intense "ejections" (u'<0, v'>0) and "inrushes" (u'>0, v'<0) dominate the o v e r a l l <u'v'> covariance. b) Mean recurrence periods of intense (u'v') events that appear to conform to the outer flow s c a l i n g (1) of laboratory bursting. T h i s "u, v q u a d r a n t " method has been used almost e x c l u s i v e l y to a n a l y s e r e c o r d s from d i f f i c u l t g e o p h y s i c a l environments, because i t does not require multi-point observations, v e r y h i g h - f r e q u e n c y sensor response or s u b j e c t i v e f r e q u e n c y f i l t e r i n g procedures. The above two c r i t e r i a w i l l be applied to the (u'v') r e c o r d s i n the f l u v i a l environment to determine whether b u r s t - l i k e events s i m i l a r to those o c c a s i o n a l l y reported i n benthic and t i d a l flows can be i d e n t i f i e d . I t must be kept i n mind however that the burst signature j u s t described (based on (u'v') records w e l l away from the wall) has only been v a l i d a t e d i n studies of lower Reynolds number laboratory flows over f l a t boundaries (e.g. Lu and 12 Willmarth, 1973). In addi t i o n to in v o l v i n g s u b j e c t i v i t y i n counting "events" (cf. s e c t i o n 1.1), the above c r i t e r i a may not be e n t i r e l y s u f f i c i e n t or necessary to diagnose the presence of bu r s t i n g motions i n d e e p e r / f a s t e r flows over complex boundary geometries. There, other mechanisms may produce " b u r s t - l i k e " u'v' events, or c l a s s i c burst p e r i o d i c i t y may not s t r i c t l y apply. In the absence of f u l l e r flow v i s u a l i z a t i o n data to s e r i o u s l y address these l a r g e r questions, the most that can be done i n t h i s study i s to inv e s t i g a t e whether b u r s t - l i k e (u'v') events conforming to the two above c r i t e r i a occur i n the study conditions. 1. A f i r s t objective of t h i s study w i l l thus be to i n v e s t i g a t e intermittent (u'v') "events" 1 m above r i v e r dunes i n strong sediment transport conditions i n the l i g h t of these two conventional c r i t e r i a f o r bursting . Of i n t e r e s t here i s whether (u'v') events i n the study conditions conform to, or deviate from the c l a s s i c properties of boundary layer b u r s t i n g often assumed to apply i n f l u v i a l environments as well (e.g. Jackson, 1976; A l l e n , 1985). The study data cannot resolve the more fundamental question: how are these "events" i n r i v e r s fundamentally r e l a t e d to c l a s s i c b u r s t i n g ? T h i s f i r s t o b j e c t i v e w i l l be pursued i n chapter 3, devoted to momentum exchange. Chapter 2 deals with methodology. The main aim of t h i s study however i s not to define more appropriate s c a l i n g f o r momentum exchange "events" i n the f l u v i a l environment, but r a t h e r to assess the importance to sediment suspension and transport of those large-scale momentum "events" that are present. This question w i l l be pursued i n chapter 4. whatever t h e i r ultimate r e l a t i o n to the c l a s s i c b u r s t ing phenomenon (an issue that cannot be s e t t l e d i n t h i s study), intense 13 ( u ' v ' ) e v e n t s a r e n o n e t h e l e s s i n t e r e s t i n g to the proc e s s geomorphologist i n t h e i r own r i g h t . They reveal the occurrence of strong turbulent disturbances i n the near-bed flow and these are l i k e l y t o have i m p l i c a t i o n s f o r sediment entrainmnent and suspension. However, many fewer data are a v a i l a b l e on turbulent s u s p e n s i o n events than on momentum exchange i n natural channel flows. Investigations to date have been conducted i n t i d a l flows and have mostly focused on the v a r i a t i o n of v e r t i c a l sediment eddy d i f f u s i v i t y and fluxes with t i d a l phase. Soulsby et a l . (1984, 1985) monitored h o r i z o n t a l suspended sand fluxes as well as h o r i z o n t a l and v e r t i c a l flow f l u c t u a t i o n s within 33 cm of the c r e s t of a large sand wave i n a t i d a l estuarine flow. West and Oduyemi (1989) report s i m i l a r types of observations wi t h i n 1.25 m of the bed i n t i d a l channels from which they a l s o derive information on frequency c o n t e n t o f the suspension processes. These l a s t authors also describe large intermittent contributions to the v e r t i c a l suspended sediment f l u x i n t h e i r near-bed records. Their a n a l y s i s however f a i l e d to indic a t e to what extent these events corresponded to the i n t e n s e s t r e s s bearing episodes, i . e . b u r s t - l i k e (u'v') events. Pursuit of t h i s question i s the second and p r i n c i p a l objective of t h i s study: 2. An analysis w i l l be conducted of the "suspension e f f i c i e n c y " of strong stress-bearing " e j e c t i o n s " and "inrushes" ( i d e n t i f i e d i n (u'v') records), as well as the r e c u r r e n c e p e r i o d i c i t y of dominant suspension e v e n t s . In p a r t i c u l a r the f o l l o w i n g " n a t u r a l " conjecture w i l l be investigated: that those ejections c o n t r i b u t i n g most to momentum exchange v e r t i c a l l y through the sensor l e v e l (and studied i n chapter 3) play a comparably large r o l e i n sediment suspension. 14 A range of issues w i l l thus be addressed, based mainly on o b s e r v a t i o n s from one s p e c i f i c g e o p h y s i c a l flow context. The u n d e r l y i n g motivation for t h i s study i s to gain i n s i g h t , using conventional a n a l y t i c a l techniques, into the usefulness of the burst concept i n u n d e r s t a n d i n g sediment suspension i n a large-scale f l u v i a l context. CHAPTER 2 METHODOLOGY This chapter w i l l f i r s t l y discuss sensor deployment methods and sensor c h a r a c t e r i s t i c s , high and low frequency losses, as well as a n c i l l a r y apparatus used during data c o l l e c t i o n . Then, study s i t e conditions w i l l be presented as well as the q u a l i t y of the various data sets c o l l e c t e d during the 1987 and 1988 f i e l d seasons. Various procedures of preliminary data q u a l i f i c a t i o n and transformation w i l l also be introduced. F i n a l l y some comments w i l l be made on problems of data analysis s p e c i f i c to a f i e l d (as opposed to laboratory) study of t h i s kind. 2.1 Sensor deployment methods. The f i r s t problem to be solved i n t h i s study was that of deploying the flow and t u r b i d i t y sensors, from a f l o a t i n g platform i n a strong and deep r i v e r flow, so that they would l i e stably i n the d e s i r e d p o s i t i o n 1 m o f f the bed. In c o n t r a s t to t i d a l deployments, i n t h i s study the sensors could not be lowered, o r i e n t e d and w e l l s e c u r e d d u r i n g n e a r l y s l a c k f l o w s . As a consequence i t was f i r s t necessary to design a sensor support frame that would s e l f - a l i g n into the strong mean flow when approaching the bed and remain stable a f t e r touchdown, as well as a surface work platform that could handle the required loads. Over the f i r s t months of the study, a streamlined s t e e l frame was conceived and tested that could deploy the t u r b i d i t y and b i d i r e c t i o n a l flow sensors with the proper o r i e n t a t i o n into f a i r l y unobstructed near-bed flow. A major co n s t r a i n t i n doing so was to minimise the t o t a l weight and d r a g o f the frame without compromising i t s s t a b i l i t y ; bed 16 disturbance near the frame had to be minimised and the frame had to be deployed from a r e l a t i v e l y l i g h t f l o a t i n g platform (for reasons described below). F i g . 1 (top) shows the frame that was eventually developed (without the sensors). The frame consists of a weighted rounded base supporting a l i g h t superstructure made up of 3 sections of s t e e l pipe. The v e r t i c a l front pipe i s 2.5 cm i n diameter and serves as support f o r two s t e e l arms p r o j e c t i n g forward from the pipe to hold the sensors i n the flow. F i g . 1 (bottom) i s a close-up of the arrangement of the two main sensors on these support arms: the b i d i r e c t i o n a l electromagnetic current meter on the l e f t and the O p t i c a l Backscatter Sensor (OBS) measuring suspensate r e f l e c t i o n s on the r i g h t (the pipe intake behind the OBS head i s part of the suspended sediment sampling apparatus, d e s c r i b e d i n the next s e c t i o n ) . Once clamped onto the support arms, the sensors l i e well above and s l i g h t l y upstream of the base of the frame. The sensor support arms can also s l i d e on the v e r t i c a l front pipe to vary the height of sensor deployment above the bed. The two pipes r i s i n g v e r t i c a l l y from the back of the frame (Fi g . 1) hold a p a i r of f i n s (interchangeable i n size) that o r i e n t the frame into the flow during deployment. The base of the frame measures 1.25 m by 1.1 m, and s t a b i l i t y of the frame on the bed i s assured by a t o t a l b a l l a s t of 90 kg of lead, h a l f of which i s cast into the base while the other h a l f i s b o l t e d on to adjust h o r i z o n t a l trim. The t o t a l height of the frame i s 1.2 m, and t o t a l weight with sensors approximately 120 kg. Except f o r the front pipe and sensors themselves, the main drag producing elements are at the back of the frame, more than 1 m downstream from the sensor l o c a t i o n . The large gap between the f i n s , as w e l l as the use of smaller f i n s than those depicted i n F i g . 1 i n the f a s t flows during the main data runs i s expected to have produced only minor disturbance of the mean streamlines at the s e n s o r s . Any such d i s t u r b a n c e was corrected by the coordinate t r a n s f o r m a t i o n of v e l o c i t i e s d e s c r i b e d i n s e c t i o n 2.5. Rapid d i s t o r t i o n e f f e c t s on Reynolds shear stresses due to streamline 17 F i g . 1: (top): Side view of the bare sensor support frame. (bottom) : Close-up of the two main sensors on the frame support arms: the b i d i r e c t i o n a l EM flow meter i s on the l e f t , the Optical Backscatter Sensor (OBS), on the r i g h t . The pipe intake behind the OBS u n i t i s used to sample suspended sediments. 18 perturbation (e.g. Wyngaard et a l . , 1985) are also expected to have been small, given the l i m i t e d high frequency response of the flow sensors (only large eddies are monitored) and the l o c a t i o n of the sensors w e l l upstream from the main sources of flow d i s t o r t i o n . The disturbance to advancing bedforms close to the base of the frame i s harder to quantify. Disturbances to l o c a l bedform geometry near the frame have to be minimised since, i f large enough, they could a f f e c t the v e l o c i t y signals monitored at the sensors. As the main drag producing elements were high on the frame and i t s base i t s e l f was r e l a t i v e l y unobtrusive as well as p a r t i a l l y buried, the disturbance to dune-scale bedforms should, i n any case, have been l i m i t e d . Smaller and higher c e l e r i t y bed " r i p p l e s " occupying the s t o s s s i d e s of dunes, however, are more l i k e l y to have been disturbed as they a r r i v e d close to the frame base. The focus of the an a l y s i s , however, i s on large turbulent eddy motions; these are convected by the strong mean flow to the sensor p o s i t i o n and for the most part depend on shear conditions meters upstream from the frame. Such eddies are thus u n l i k e l y to be a f f e c t e d by small disturbances to bedforms near the base of the frame, l y i n g 1 m v e r t i c a l l y under the sensors. This study was conceived as the f i r s t component i n a longer term s e r i e s of i n v e s t i g a t i o n s of suspended sediment transport conditions i n a v a r i e t y of r i v e r environments. To allow f o r eventual deployment of t h i s sensor frame i n a range of stream environments (often remote and unsuitable to launching or maneuvering a large boat), major e f f o r t s were also dedicated at the s t a r t of the study to designing a strong, yet l i g h t weight and mobile, f l o a t i n g work platform. The platform was designed and constructed by the w r i t e r i n c o l l a b o r a t i o n with J . Skapski, Eng. Technician i n the Department of Geography at U.B.C. I t incorporates a cutout deck at the back, over which a DC powered winch i s mounted on an A structure ( F i g . 2), and an outboard engine set at f r o n t . The two 0.6 m diameter and 4 m long c y l i n d r i c a l h u l l s are constructed of f i b e r g l a s s , and provide ample buoyancy to l i f t the frame from the bed unless the l a t t e r i s badly 19 F i g . 2: frame. Work platform used to deploy the submersible 20 snagged on r i v e r bottom d e b r i s . The r e s t of the p la t form s t r u c t u r e and decking i s made up of b o l t e d aluminum segments; these can be r a p i d l y disassembled in to a few components weighing each under 50 kg for t r a n s p o r t , then reassembled at a remote r i v e r bank and launched without need for a boat ramp. A two person crew can, i f necessary, t ransport the disassembled work p la t form on the roof of a small van to a remote r i v e r s i t e and then c a r r y the pieces through rough bush to stream bank for assembly. Once the p l a t f o r m i s motored and then anchored at the s e l ec t ed s i t e , the frame and sensors are g r a d u a l l y lowered down through the opening at the back of the deck, d r i f t i n g somewhat downstream i n the p r o c e s s ( F i g . 3 ) . In a l l f l ow v e l o c i t i e s encountered the s t a b i l i t y of the frame when suspended j u s t under the flow surface was e x c e l l e n t , with no tendency for yaw o s c i l l a t i o n . Lowering of the frame to the r i v e r bed i s i n t e r r u p t e d for some moments when the frame l i e s a few decimeters above the bed, to assure that the frame axis i s approximately a l i g n e d with the mean flow d i r e c t i o n at the bed. The frame and sensors are then deposi ted onto the bed. The existence of apprec iable mul t i - second turbulent f l u c t u a t i o n s i n the l a t e r a l v e l o c i t y component impl ies that the frame o r i e n t a t i o n at touchdown may s t i l l deviate from the long-term mean flow azimuth by as much as 15 degrees; t h i s f a c t o r cou ld l ead to , at most, a 4% uncer ta in ty i n the f l u x covariances i n v o l v i n g the h o r i z o n t a l flow component (Pond, pers . comm., 1990). The p r e c i s e o r i e n t a t i o n of flow sensor coordinates i n the v e r t i c a l plane i s of much greater consequence: the procedures to a l i g n these with the mean shear flow are d iscussed i n sect ions 2 .2 .1 and 2.5 . A f t e r deployment and throughout data logg ing , a constant check i s kept that the s t e e l support cable remains loose and the s i g n a l cables f r e e , thus assur ing that the frame i s not s lowly dragging on the bottom. The p o s s i b i l i t y of f o u l i n g of the sensors was minimised by running the sensor cables towards a support loop at the back of the frame and then upward to the work p la t form. 21 F i g 3: Frame being lowered to the channel bed from the back of the f l o a t i n g platform. Note that smaller f i n s than shown here were used i n the stronger flows on June 13, 1988, near Mission. 22 By v a r y i n g the s i ze and drag of the t a i l f i n s and the amount of l ead b a l l a s t on the frame i t was p o s s i b l e to eventua l ly f u l l y s t a b i l i s e t h e f r a m e i n a range o f deployment c o n d i t i o n s . O c c a s i o n a l l y deployments had to be i n t e r r u p t e d , the frame l i f t e d and relowered or data d i scarded i f boat waves from r i v e r t r a f f i c exerted undue heave on the frame support cab le s . A more p e r s i s t e n t and p r o b l e m a t i c source o f data c o r r u p t i o n was in ter ference of suspended organic debr is with the sensors; t h i s important problem w i l l be d i scussed i n s e c t i o n 2.3 . 2.2 Sensor c h a r a c t e r i s t i c s and frequency losses 2 .2 .1 Electromagnet ic current meter and h igh frequency losses . V e l o c i t i e s were monitored with a Marsh McBirney (Inc) model 524 b i d i r e c t i o n a l e lectromagnetic (EM) current meter with 10 cm sensing sphere and 0.2 s time constant , adapted for 12 VDC power supply . Such sensors are qui te commonly used i n benth ic and t i d a l boundary l ayer s tud ies , f or which they d i s p l a y reasonably good flow d i r e c t i o n and frequency responses. The v e l o c i t y channel that had the best noise and zero d r i f t c h a r a c t e r i s t i c s ("Y") was set to sense flow normal to the base of the frame (c f . F i g . 1, bottom), while the other ("X") sensed flow along the frame a x i s . Because the f o r e - a f t t i l t of the frame depends on the l o c a l geometry of the bed at touchdown, there i s no guarantee that i n a g iven deployment the base of the frame p a r a l l e l s the l o c a l mean boundary o r i e n t a t i o n , and hence that v e l o c i t i e s normal to the base (the Y component) i n the long term average to zero . The good cosine ( d i r e c t i o n a l ) response of the sensor to the two orthogonal flow components (as documented by Marsh McBirney Inc . ) a l lows , however, the frame of reference of the v e l o c i t y components to be ro ta ted at 23 the data analysis stage, to compensate f o r t h i s t i l t of the frame. Thus the v e l o c i t y component normal to the mean boundary (v, with zero mean and defined as p o s i t i v e upwards), as well as the component i n the downstream (mean s t r e a m l i n e ) d i r e c t i o n (u, p o s i t i v e downstream) can be r e t r i e v e d . The importance of t h i s data t r a n s f o r m a t i o n w i l l be d i s c u s s e d f u r t h e r i n se c t i o n 2.5. Its accuracy depends d i r e c t l y on the p r e c i s i o n of zero flow readings on the EM flow meter. S t i l l water output noise and zero d r i f t were f i r s t t ested i n the laboratory i n March 1987. Both channel outputs were monitored over 7 hours with the sensor on DC power immersed i n a large p a i l of tap water on the UBC campus. Observed long term zero d r i f t was under 0.5 cm/s, rms noise of X and Y channel outputs were of the order of 0.7 and 0.8 cm/s, r e s p e c t i v e l y and zero o f f s e t trim potentiometers were adjusted to bring the mean output to zero. In June 1987 the s t i l l water output s t a b i l i t y was furth e r tested i n the f i e l d i n a large p a i l of Fraser River water from the study area near Barnston Island (then well upstream from the estuary s a l t -wedge; see F i g . 5): X and Y channel rms f l u c t u a t i o n s based on two hours of monitoring were comparable to the laboratory r e s u l t s , at 0.9 and 1.0 cm/s, r e s p e c t i v e l y and the mean d r i f t against laboratory zero was under 0.6 cm/s. These t e s t s i n d i c a t e that the zero s t a b i l i t y o f the EM meter i s good both i n UBC tap and study c o n d i t i o n freshwaters. EM v e l o c i t y meter c a l i b r a t i o n s were checked separately f o r each channel against a recently c a l i b r a t e d Ott type meter at r i v e r s i t e s . Comparisons were done i n 3 flow strengths (4 with the s t i l l water tests) by deploying side by side the Ott meter and c a r e f u l l y o riented EM meter and noting 4 minute average v e l o c i t i e s . The r e s u l t s f o r both channels are p r e s e n t e d i n F i g . 4. The Ott c a l i b r a t i o n e r r o r i n a towing tank i s of the order of 0.3 cm/s. In turbulent flows with i n t e n s i t y below 0.2, such as i n the study conditions, t h i s e r r o r i s estimated at under 1% (thus under 1.1 cm/s for a l l values i n F i g . 4) . The EM meter r e s u l t s of F i g . 4 suggest that sensor l i n e a r i t y i s roughly w i t h i n the manufacturers 24 > 3 C L o a; 8 o o o CM o o. in O O . o o o in H X channel Y channel O f I I I I I I I I M I I I I I I I I I | I I I I I I I I I | I I I I I I I I I | I I I I I I I I I | I I I I I I I I I | 0 20 40 60 80 Flow vel. ( c m / s ) 100 120 Fig.4: Calibration data for EM current meter. Reference v e l o c i t i e s are based on 4 minute readings by Ott meter i n r i v e r flows (+/- 1 cm/s). 25 s p e c i f i c a t i o n s (2%) . The EM output c a l i b r a t i o n constant f o r each channel was computed based on the data of F i g . 4. Some of the factors determining the height above bed at which a flow sensor i s to be deployed are i t s frequency response and the f r a c t i o n of the high-frequency turbulent spectrum that needs to be recorded to s a t i s f y the study objectives. This i s because the f r a c t i o n of the t o t a l turbulent energy above any given frequency tends to decrease away from the immediate boundary. The 0.2 s low-pass f i l t e r constant on the Marsh McBirney u n i t cuts o f f 98% of the power of v e l o c i t y f l u c t u a t i o n s at 5 Hz (T=0.2 s ) , h a l f the power at approximately 0.8 Hz (1.25 s) and only 10% of the power at 0.25 Hz (4 s) . Using the half-power f i g u r e as nominal c u t o f f frequency (f=0.8 Hz), t h i s t r anslates into a non-dimensional c u t o f f frequency n=fz/U of 0.8-0.9 f o r sensors deployed at z =1 m from the boundary, where the mean v e l o c i t y (U) i n the main study runs was 0.8-0.9 m/s. Use of the s i m i l a r i t y s c a l i n g f requency n, c o n v e n t i o n a l i n atmospheric surface layer studies, i s also common i n t i d a l boundary layer studies (e.g. Soulsby, 1977; Heathershaw, 1979; Anwar, 1981). This non-dimensional frequency can be int e r p r e t e d as the r a t i o of sensor height to streamwise dimension of an eddy, assuming frozen turbulence behaviour. Panofsky and Dutton (1984) state that n values i n the range 1 to 10 mark the upper l i m i t of the energy containing range and the s t a r t o f the i n e r t i a l subrange i n atmospheric s u r f a c e layer turbulence. A nominal flow sensor high frequency c u t o f f (half-power) of 0.8-0.9 i n t h i s study would thus imply that a l l but the smallest " e n e r g e t i c e ddies" should have been monitored. "Macroturbulent" eddies that are considered important i n sediment suspension (e.g. Matthes, 1947) as well as bursting motions are generally taken to be included i n the energy containing range. Soulsby (1980) states that a high-frequency c u t o f f of n=l s t i l l excludes between 20 and 30% of the t o t a l variance of the v e r t i c a l turbulent f l u c t u a t i o n s i n near-bed t i d a l flows, but only about 5% of the h o r i z o n t a l variance and the Reynolds shear stress covariance, which both are dominated by 26 l a r g e r eddies. Had the v e l o c i t y sensors been deployed much c l o s e r than 1 m to the boundary, a s u b s t a n t i a l f r a c t i o n of the energy containing eddies (and p o t e n t i a l l y some of the bursting motions themselves) might have been f i l t e r e d out due to the l i m i t e d sensor response. The combination of a 1 m sensing height and 0.2 s flow response-constant i s generally comparable to that used i n previous b u r s t i n g studies i n benthic or f l u v i a l boundary layers (e.g. Heathershaw, 1979; McLean and Smith, 1979) . In a d d i t i o n to the frequency response, such flow sensors a l s o have a l i m i t e d wavenumber response. S p a t i a l averaging of v e l o c i t y over the u n i t ' s sensing volume, by smoothing out the response to smaller eddies, can become a l i m i t when the bed i s approached. Based on the manufacturer's s p e c i f i c a t i o n s the 10 cm diameter sphere averages the flow i n a 30 cm diameter volume and would thus s i g n i f i c a n t l y damp the response to eddies smaller than some 50 cm (see also discussion i n Soulsby, 1980). While the dynamic response of the current meter precluded observations much c l o s e r to the bed than 1 m, the maximum.practical distance of deployment o f f the bed was determined by the d i f f i c u l t y of ensuring s t a b i l i t y of a larger submersible frame. The 1 m sensing h e i g h t i s a compromise based on the exploratory nature of the research and the l i m i t s of a v a i l a b l e equipment and budgets. I t also corresponds to the general area of the flow where the greatest suspended bed material (sand) transport tends to occur. 2.2.2 O p t i c a l Backscatter Sensor To monitor suspended sediment f l u c t u a t i o n s at a rate comparable to that provided by the v e l o c i t y sensor, a f a s t response concentration sensor i s required. Both dynamic impact (Soulsby et a l . , 1984) and o p t i c a l sensors have been used (West and Oduyemi, 1989, and t h i s study). Both types of sensors can produce very good l i n e a r c a l i b r a t i o n s of output against sediment concentration i n 27 laboratory conditions, when i n the presence of p a r t i c l e s of uniform s i z e ( i n the case of the dynamic Sand Transport Probe used by Soulsby et a l . (1984), concurrent f a s t response measurements of v e l o c i t y are a l s o r e q u i r e d ) . Unfortunately, c a l i b r a t i o n i n the presence of v a r i a b l e sediment mixtures remains a problem with both sensor types. The s e n s i t i v i t y of the o p t i c a l units peaks f o r s i l t -c l a y p a r t i c l e s while, i n the case of the dynamic STP u n i t t h i s can be set to zero by varying response thresholds. However, even for the l a t t e r sensor, s e n s i t i v i t i e s to the d i f f e r e n t sand f r a c t i o n s are n o t c o n s t a n t , and f i e l d c a l i b r a t i o n s a g a i n s t t o t a l sand concentrations display s u b s t a n t i a l s c a t t e r (Soulsby et a l . , 1984). F u r t h e r r e s e a r c h i s required to develop a t r u l y accurate f a s t r e s p o n s e s e n s o r f o r s u s p e n d e d sand c o n c e n t r a t i o n s i n the environment. Errors introduced i n estimates of suspension fluxes and s p e c t r a through the use of the p r e s e n t l y i m p e r f e c t sensor c a l i b r a t i o n s remain poorly q u a n t i f i e d at t h i s stage. In t h i s study, the O p t i c a l Backscatter Sensor developed at the U n i v e r s i t y of Washington (Downing et a l . , 1981) was used to monitor concentration f l u c t u a t i o n s (cf. F i g . 1, bottom). I t detects the i n t e n s i t y of b a c k - r e f l e c t i o n o f i n f r a - r e d l i g h t from the suspended p a r t i c l e s i n a small volume of flow passing by the sensor head. Because of the r a p i d attenuation of IR l i g h t i n water the sensing volume i s only of the order of a cm^. Laboratory t e s t s have shown that the response to increasing concentrations of a given sediment d i s t r i b u t i o n i s l i n e a r over a considerable range (e.g. up to 100 ppt f o r a medium sand; Downing et a l , 1981). However, as noted above, the response c o e f f i c i e n t s vary with sediment s i z e , shape, mineralogy etc., and c a l i b r a t i o n of the output to actual concentrations i n the f i e l d environment i s necessary. Apparatus to t h i s end i s discussed l a t e r i n t h i s section. C a l i b r a t i o n tests ( s e c t i o n 4.1) w i l l show that, despite the high s e n s i t i v i t y to the s i l t / c l a y f r a c t i o n s , the response to the much la r g e r f l u c t u a t i o n s of sand concentration i s c l e a r l y detected i n the records produced by the OBS i n the study conditions. 28 The inherently high dynamic response of the optics and e l e c t r o n i c s of the OBS as well as the small s i z e of i t s sensing volume require that i t s output be low-passed f i l t e r e d to match the dynamic response of the flow meter. The output was thus run through a low pass f i l t e r adjusted to a frequency c u t o f f s i m i l a r to that of the v e l o c i t y meter. This procedure was also important to introduce a phase l a g at the higher frequencies of OBS output, to roughly match the l a g introduced i n v e l o c i t y output by the l a t t e r ' s RC f i l t e r . F a i l u r e to do so would bias v e l o c i t y - c o n c e n t r a t i o n covariances (sediment fluxes) at higher frequencies (mostly i n the range f>0.5 Hz). Although the phase s h i f t spectra of the v e l o c i t y and OBS f i l t e r s may not have been i d e n t i c a l , the remaining bias i s thought to be unimportant, as the higher frequencies w i l l be seen to make a minor c o n t r i b u t i o n to the covariances. 2.2.3 Other apparatus A v a r i a b l e speed p e r i s t a l t i c pump on deck was connected to a 20 m long p l a s t i c pipe (1 cm i n t e r n a l diameter), with intake 30 cm behind the OBS sensing volume on the frame (cf. F i g . 2). Pipe output was at a sampling s t a t i o n on deck. This apparatus allowed p h y s i c a l sampling of suspended sediments at the sensor and a degree of c a l i b r a t i o n of the OBS output. The intake speed was adjusted to match the mean h o r i z o n t a l flow v e l o c i t y at the time of sampling, to avoid b i a s i n g the sand content i n the c o l l e c t e d sample. The time of sampling was c a r e f u l l y synchronised (to 1 s accuracy) with the OBS record, allowance being made f o r the time of t r a v e l of the sample f r o m OBS sensor to sampling s t a t i o n . L a b o r a t o r y t e s t s had demonstrated t h a t sands t r a v e l l e d the l e n g t h of the pipe at e s s e n t i a l l y the intake v e l o c i t y (generally of the order of 0.8-0.9 m/s) and that sample t r a v e l time (to 1 s) could be pre d i c t e d on the b a s i s o f t h i s v e l o c i t y and p i p e l e n g t h . C o l l e c t e d samples corresponded to 5 to 10 s of flow at the OBS sensor and c a l i b r a t i o n 29 was l i m i t e d to corresponding mean values of the OBS record. The r e s u l t s of the c a l i b r a t i o n are presented i n chapter 4. A mostly unsuccessful attempt was made to document the passage of any bedforms underneath the sensors. A Raytheon DE719 echo sounding transducer (-200 KHz acoustics) was mounted on the frame. The transducer was supported by an extension arm (not shown on F i g . 1) located somewhat upflow and 25 cm to the r i g h t of the OBS unit; thus the transducer pointed s l i g h t l y upstream and near the r i g h t margin of the base of the frame. Event marks were made every minute on the c h a r t recorder on deck, synchronised (with 1 s accuracy) with those on the v e l o c i t y and t u r b i d i t y records. Possibly due to disturbance of the smaller bedforms, as w e l l as t i l t of the sensor frame and consequent improper acoustic beam o r i e n t a t i o n , bed h e i g h t o s c i l l a t i o n s c o u l d be d e t e c t e d o n l y b r i e f l y and i n t e r m i t t e n t l y d u r i n g most deployments. I t was not generally p o s s i b l e to c l e a r l y r e l a t e these intermittent s i g n a l s to known bedform scales present i n the study conditions. V e l o c i t y components and OBS output were sampled, d i g i t i s e d and stored on magnetic tape, along with s t a t i s t i c a l summaries, time and date marks, using a Campbell S c i e n t i f i c Inc. 21X data logger. A 5 Hz sampling rate was selected. This rate l e d to negligeable a l i a s i n g ; e.g. only 9% of the r e l a t i v e l y small power present i n v e l o c i t y f l u c t u a t i o n s at the c u t o f f frequency of 2.5 Hz, and 2 % at 5 Hz, pass the v e l o c i t y meter's low-pass f i l t e r . Power spectra p r e s e n t e d l a t e r w i l l show that the r e s u l t a n t v e l o c i t y / t u r b i d i t y power at the c u t o f f frequency i s negligeable compared to that at the lower frequencies i n t h i s study. Use of a f a s t e r sampling rate l e d to data overflow problems, given the minimum computing required to c o n t r o l the logging process. 30 2.2.4 Low frequency losses. In t h i s study the d i f f i c u l t i e s i n assessing s i g n i f i c a n t low-frequency contributions to the fluxes, w i t h i n an achievable t o t a l record length, are greater than that posed by the better documented high-frequency instrument losses ( s e c t i o n 2.2.1, above). A q u a l i t a t i v e d i s c u s s i o n of the importance of the low-frequency f l u c t u a t i o n s to momentum and sediment fluxes w i l l be presented i n the l a s t s e c t i o n of t h i s chapter. Preliminary surveys i n d i c a t e d the presence i n the v e l o c i t y and OBS records of strong multi-minute f l u c t u a t i o n s (many with periods over 10 minutes) i n nominally steady r i v e r f l o w s . Examples of these are given i n s e c t i o n 2.5. This i n d i c a t e d that the longest records p r a c t i c a b l e should be c o l l e c t e d i n the study environment, to help resolve the r o l e of these very low frequencies i n momentum and sediment exchange. Possible generating mechanisms f o r such low-frequency flow cycles w i l l be b r i e f l y considered i n sec t i o n 2.6. In the presence of low-frequency f l u c t u a t i o n s not us u a l l y important i n benthic studies, the us e f u l nomogram presented by Soulsby (1980, h i s F i g . 3) for low-frequency losses as a function of reco r d length may be assumed to underestimate the low-frequency contributions to variances i n t h i s study. Long-term mean v e r t i c a l sediment and momentum fluxes i n such an environment may be extremely d i f f i c u l t to assess accurately. However, the complete evaluation of these int e g r a t e d fluxes i s not necessary to the e l u c i d a t i o n of burs t - s c a l e v e r t i c a l momentum and sediment mixing, the aim of t h i s study. 31 2.3 Sensor output contamination by organic debris. Serious and p e r s i s t e n t data corruption i n t h i s environment r e s u l t s from the passage very close to, or contact with the sensors of large pieces of organic debris such as leaves and bark. Due to erosion of vegetated banks, such debris i n general i s an i n t e g r a l part of the material transported i n t r a c t i o n and suspension by r i v e r flows. The presence of log booms along many large r i v e r s i n the lower Fraser V a l l e y may have amplified t h i s problem i n the study environment. This type of data corruption t y p i c a l l y produces b r i e f , unusually large v e l o c i t y or OBS sign a l s ; since t h i s study i t s e l f focuses on extreme stress and suspension events, e l i m i n a t i n g record segments corrupted by organic debris was c r u c i a l before the study objectives could be pursued. Fortunately a f a i r l y c h a r a c t e r i s t i c signature allowed corrupted segments to be i d e n t i f i e d and deleted. Much of the t o t a l records c o l l e c t e d over the various deployments had to be r e j e c t e d because of frequent periods of intense corruption. During data logging major corruption events were e a s i l y noticed, as they l e d to overrange values of e i t h e r v e l o c i t y or t u r b i d i t y output l a s t i n g tens of seconds. In these cases logging was interrupted, the frame l i f t e d o f f the bed, and i f necessary the sensors brought to the surface f o r cleaning. T y p i c a l l y a l e a f would be found draped onto the sensors. A f t e r removal and inspection, the frame would be redeployed on the channel bed. B r i e f e r or more subtle corruption events were i d e n t i f i e d at the data q u a l i f i c a t i o n stage. In a d d i t i o n to momentary overrange or c l e a r l y u n r e a l i s t i c values of any s i g n a l , i d e n t i f i c a t i o n i n the case of the v e l o c i t y records was based on a recognizable signature f o r organic corruption. I t had been noted, when the frame was c l o s e to the s u r f a c e , t h a t o c c a s i o n a l l y a l e a f draped onto the v e l o c i t y sensing sphere tended to o s c i l l a t e with vortex shedding, a l t e r n a t i v e l y touching X and Y flow electrodes. This c h a r a c t e r i s t i c a l l y produced large synchronous 32 o s c i l l a t i o n s of both v e l o c i t y outputs that were strongly p o s i t i v e l y c o r r e l a t e d . The e n t i r e v e l o c i t y r e c o r d was thus inspected by computing 2 minute v e l o c i t y variances and covariances. Periods when corruption had occurred stood out c l e a r l y i n t h i s a n a l y s i s , with exaggerated v e l o c i t y variances along with negligeable or p o s i t i v e covariances, instead of the negative values of u and v covariances t y p i c a l o f boundary l a y e r t u r b u l e n c e . The corrupted 2 minute segments tended to c l u s t e r together and d e t a i l e d s c r u t i n y could pinpoint s p e c i f i c corruption events within them. Such periods were then deleted from the a n a l y s i s . Record segments d e l e t e d on the basis of the v e l o c i t y s i g n a l s u s u a l l y included overrange OBS returns and were assumed to be also u n r e l i a b l e as records of suspension events. In the case of the OBS s i g n a l s however, i t can be expected that minute organic debris forming part of the normal f l u v i a l suspended load may have also frequently a f f e c t e d the sensor output, but i n a way that cannot be i d e n t i f i e d separately from the bulk sediment signature. The l a t t e r events simply contribute to the random err o r i n c a l i b r a t i n g OBS output to mineral sediment concentrations which i s assessed i n s e c t i o n 4.1. The q u a l i t y of the c a l i b r a t i o n r e l a t i o n s w i l l i n d i c a t e that, outside of the periods of intense organic corruption, the OBS si g n a l s e s s e n t i a l l y r e f l e c t e d the suspended sediment load. 2.4 Study s i t e s and near-bed flow records. Table 1 l i s t s l o c a t i o n s , dates and main problems encountered during deployments i n 1987 and 1988 f o r t h i s study. P r i o r to June 19 88 when the OBS u n i t became a v a i l a b l e , t u r b i d i t y sensing was accomplished with an older o p t i c a l transmissometer u n i t which was eventually found to be u n r e l i a b l e i n the f i e l d . Deployments that 33 TABLE 1 FRASER RIVER DATA SETS SITE DATE D(ra) V l m(m/s) V s(m/s) T (hr) REMARKS BARNSTON ISLAND 07.14.87* 07.15.87 07.16.87 0.85 0 .75 0 . 6 1. 3 1 . 1 0 . 8 2 . 5 3 . 5 transmissometer m a l f u n c t i o n ; much org a n i c c o r r u p t i o n ti it MISSION 06.08.88* 8 06.13.88* 10 0.85 0 . 9 1.1 5.1 1.4 7.0 frequent boat t r a f f i c ; o rgan.corrupt ti • ti D: l o c a l depth *^lm: v e l o c i t y at 1 m o f f bed V s: s u r f a c e v e l . T: t o t a l d u r a t i o n of deployments *: r e s u l t s presented i n t h i s study 34 produced r e s u l t s of s u f f i c i e n t q u a l i t y to be reported i n t h i s study are marked by a s t e r i s k s i n Table 1. F i g . 5 locates the various study s i t e s discussed. In a d d i t i o n to the June 13, 1988 data from the Fraser River near Mission, which provide the main evidence discussed i n t h i s t h e s i s , more r e s t r i c t e d r e s u l t s from deployments on June 8, 1988 near Mission and on J u l y 14, 1987, near Barnston Island are presented i n the next chapters to confirm the main f i n d i n g s . As discussed i n s e c t i o n 2.3, s i g n a l corruption by organics marred most of the deployments, and only b r i e f record segments could be used i n the f i n a l a n a l y s i s . Not l i s t e d i n Table 1 are 5 deployments conducted between March and May 1988 i n strongly t i d a l conditions on the lower P i t t River near the j u n c t i o n with the Fraser R. These t i d a l surveys were d i r e c t e d at c l a r i f y i n g the onset o f s u s p e n s i o n i n gradually increasing flow conditions, a secondary objective not discussed i n t h i s study. Unfortunately the P i t t River study was not successful because of very intense s i g n a l corruption by organic debris as well as u n r e l i a b i l i t y of the t u r b i d i t y sensors used at the time. The f o l l o w i n g d i s c u s s i o n presents d e t a i l s on the study environments, w i t h main emphasis on the key deployments near Mission. This s i t e l i e s i n a channel of the Fraser River to the south of Matsqui Island, i n the Lower Mainland of B r i t i s h Columbia, Canada ( F i g . 5, see blow-up map). The Fraser basin (area 228,000 km at Mission) drains a large part of the i n t e r i o r and the Coast Mountains of B r i t i s h Columbia. Mean annual discharge at Mission i s 3410 m?/s. The f a i r l y s t r a i g h t and uniform reach of the r i v e r where the sensors were deployed i s located 5 km downstream of Mission, and 2 km downstream of a moderately sharp bend on the channel. The channel c r o s s - s e c t i o n i s approximately trapezoidal over t h i s reach, with a width of 250-280 m and depths ranging from 9 to 11 m during the survey period. Bed materials are f a i r l y uniform medium sands (D5o=0.38 mm near Mission). Approximately 7 km upstream of Mission l i e s the zone where sand succeeds to gravel on the bed of the Fraser River. Further upstream there i s an anastomosed-"wandering" gravel F i g . 5: The study s i t e s (*) . Fraser R i v e r at Matsqui I s l a n d , near M i s s i o n (main s i t e ) , and secondary s i t e at. Burnaton I s l and , B . C . , Canada. 36 reach of the r i v e r , which extends to the head of the Fraser Valley-lowlands . The main study data at Mission were c o l l e c t e d during a period of smowmelt-fed high runoff on June 13, 1988. The discharge at Mission was 6500 m^/s and had been gradually i n c r e a s i n g over the previous week. Such a discharge i s exceeded on average 13% of the time at the s i t e . Surface v e l o c i t i e s at the June 13 deployment s t a t i o n 80 m from the r i g h t bank, i n 10 m depths, were 1.4 m/s and mean v e l o c i t i e s over the v e r t i c a l 1.1 m/s. The flow Reynolds number (based on flow depth) i n the study reach was about 8 X 10°; t h i s i s approximately 2 orders of magnitude higher than most of the values encountered i n laboratory studies of bursting events. Bedforms i n the study channel during t h i s period generally consisted of small dunes (8-12 cm scale amplitudes) o v e r r i d i n g l a r g e r ones (30-150 cm amplitudes). F i g . 6 presents a surface p r o f i l e of bedforms i n the immediate v i c i n i t y of the sensors during the June 13 deployment. The decimeter scale forms have wavelengths i n the range 1.5-2 m, the l a r g e r dunes have lengths of 5-11 m. Smaller scale r i p p l e s (15-30 cm l e n g t h s ) , p o s s i b l y a l s o p r e s e n t would probably not have been resolved from the surface i n 10 m depths. During the June 13 deployment mean suspended sediment c o n c e n t r a t i o n s at sensor l e v e l were 500 mg/1. The decreasing concentration of suspended sediment (and r e s u l t a n t flow density) away from the bed produced a very weak degree of stable density s t r a t i f i c a t i o n i n the flow 1 m over the bed. The degree of t h i s s t a b i l i t y i s estimated to have corresponded to a f l u x Richardson number Rf of 0.02 i n the June 13 conditions, based on a mean upward sediment exchange due to turbulent mixing of 3 g/mz s (estimated i n / 0 0 s e c t i o n 4.4), a kinematic Reynolds stress of -28 x 10 m z/s z (cf s e c t i o n 3.1) and a mean v e r t i c a l v e l o c i t y gradient of 0.22 m/s/m, a l l at sensor height. Heathershaw (1979) considers that turbulence i s completely suppressed at Richardson numbers of 0.25, while values l e s s than 0.03 would represent e s s e n t i a l l y neutral conditions (no measurable damping of turbulence due to the s t r a t i f i c a t i o n being F i g . 6: A 160 m long streamwise bed p r o f i l e showing dune bedforms taken on June 13, 1988 i n the area where the s e n s o r s were deployed, southern channel of the Fraser River, near Mission. 38 discernable). The l a t t e r appears to apply to the study conditions. The flow conditions at Mission were only approximately steady during the extended period of data logging on June 13, 1988 (7 hours, from 13:30 to 20:30 hrs, P a c i f i c Standard Time). F i g . 7 presents a record of stage height ( r e l a t i v e to an a r b i t r a r y datum) at the Mission gauge for a 3 day period i n c l u d i n g the 7 hours of data gathering (Water Survey of Canada, 1988, pers. com.). A 12 hour cycle i n stage, of peak amplitude 15 cm (1.5% of depth at the study s i t e ) , i s the backwater e f f e c t of the t i d a l cycle at the mouth of the Fraser River i n the S t r a i t of Georgia, 85 r i v e r km downstream. The tides on the S t r a i t were almost d i u r n a l on these days, with one deep (4 m range) and a second very shallow cycle (0.5 m range). These are c l o s e l y mimicked i n the stage at Mission, where they occurred with a delay of some 4 hours. These damped f l u c t u a t i o n s were superimposed on a trend of increasing stage, of the order of 8 cm/day, r e f l e c t i n g gradually r i s i n g t r i b u t a r y inflow due to snowmelt i n the mountainous Fraser R. basin. Over the t o t a l of 7 hours of data logging on June 13, t h i s trend r e f l e c t s a 0.6% increase i n discharge at Mission. In the author's experience, a 1-2% f l u c t u a t i o n i n flow depth during one d a y l i g h t p e r i o d i s , i n p r a c t i c e , c l o s e to the l i m i t of flow steadiness that can be expected even i n large n a t u r a l streams. The e f f e c t s of such s l i g h t non-steadiness i n o v e r a l l flow conditions on near-bed v e l o c i t i e s at the study s i t e w i l l be discussed l a t e r i n t h i s chapter. Only minor corruption events were detected, and no redeployment took place, during a continuous 2.7 hr period s t a r t i n g at 17:00 hrs on June 13. The d e t a i l e d analysis i n the subsequent chapters i s l a r g e l y based on t h i s segment of the record. 39 F i g . 7: Stage record at the Mission gauge of Water Survey of Canada, June 12 to 14, 1988. The study period on June 13 l i e s between the v e r t i c a l l i n e s . L i n e a r trend indicated by dashed l ine . 40 The June 8 deployment near Mission (Table 1) occurred i n only s l i g h t l y weaker o v e r a l l discharge conditions, somewhat upstream and across the channel from the June 13 deployments and i n shallower flow. Hydraulic conditions were less intense: l o c a l depth was 8 m, surface v e l o c i t i e s averaged 1.1 m/s and the bed near the sensor was mainly covered with 5-10 m length, 0.3 m height dunes. The June 8 deployment was marred by frequent i n t e r r u p t i o n s due to boat t r a f f i c and p e r s i s t e n t organic corruption of records. Analysis of 35 minutes of good q u a l i t y OBS, u and v data (19:22 to 19:57 h PST) w i l l be reported i n coming chapters. The surveys of J u l y 1987 (Table 1) were also conducted on the Fraser River, approximately 40 km downstream from the Mission s i t e i n the s o u t h e r n channel at Barnston Island (cf F i g . 5). Deployments occurred at d i f f e r e n t stations i n the reach i n hydraulic and sediment transport conditions broadly comparable to those during the M i s s i o n deployments (5-10 m depths, 0.9-1.2 m/s surface v e l o c i t i e s , dune bedforms). O p t i c a l transmissometer problems prevented e x t r a c t i n g precise r e s u l t s on sediment transport events. Analysis of 57 minutes of uncorrupted u, v data (July 14, 1987, 12:30-13:27 h PST) f o r stress intermittence w i l l be presented i n chapter 3 along with the main 1988 r e s u l t s from Mission on that subj ect. 2.5 From frame based to boundary layer based v e l o c i t y coordinates. No t i l t m e t e r data were a v a i l a b l e to monitor frame motions on the channel bed, although the weight of the frame made such motion u n l i k e l y . I t was important however to v e r i f y whether s h i f t s i n the v e l o c i t y coordinate system caused by any occasional motions of the frame might have produced spurious f l u c t u a t i o n s i n the r e c o r d s of near-bed flow. To e s t a b l i s h that recorded v e l o c i t y 41 f l u c t u a t i o n s were genuine, and not the r e s u l t of any frame rocking, t o t a l flow speed and angle (the l a t t e r p o s i t i v e upward r e l a t i v e to frame base) were pl o t t e d , instead of the separate X and Y flow components i n the frame system of reference. While flow angle ser i e s may be a f f e c t e d by frame r o t a t i o n , speed (the r e s u l t a n t of the X and Y flow components) as well of course as OBS return are i n v a r i a n t to rotations of the frame of reference. F i g . 8 presents the e n t i r e 7 hours of flow speed, angle and t u r b i d i t y (OBS) records for June 13, 1988, h e a v i l y smoothed with a 5 minute running mean, and d i s c l o s i n g long period f l u c t u a t i o n s i n these s i g n a l s . As pointed out above, the strong f l u c t u a t i o n s i n speed and OBS output cannot be explained by frame r o t a t i o n . F i g . 9 i s a s i m i l a r p l o t f o r an 80 minute excerpt from the record of F i g . 8, t h i s time smoothed with a 40 s running mean and thus d i s p l a y i n g strong higher frequency f l u c t u a t i o n s , that again cannot be due to frame rocking. Some obvious r e l a t i o n s among these signals w i l l be discussed i n the next section. A l l v e l o c i t y f l u c t u a t i o n s discussed i n t h i s study, in c l u d i n g those at even higher frequencies (0.05 Hz<f<2.5 Hz) that have been l a r g e l y f i l t e r e d out from Figs. 8 and 9, s i m i l a r l y involved both speed and angle changes and thus could not have been produced by frame r o t a t i o n . I t i s concluded that frame motions, i f present, d i d not a f f e c t the flow s e r i e s i n a s i g n i f i c a n t way. The system of coordinates r e l a t i n g to the frame base used above i s not s u i t a b l e to computations of v e r t i c a l momentum and sediment flu x e s . The o r i e n t a t i o n of the frame-based X and Y v e l o c i t y coordinates discussed i n s e c t i o n 2.2.1 depends on the bed slope i n the immediate area on which deployment happens to be established. They are thus of l i t t l e relevance, i n themselves, to understanding the flow. In p a r t i c u l a r , any time that the frame was l i f t e d o f f the bed and redeployed the e x i s t i n g frame coordinate system was l o s t and a somewhat d i f f e r e n t one established. The n a t u r a l coordinate system f o r v e r t i c a l exchange of momentum and sediment from near-bed to the outer parts of the flow i s one i n which u, the downstream flow Fig. 8 13 14 15 16 17 18 19 20 21 Time (hrs , Pac i f i c S tanda rd Time) F i g . 8: 7 hour-long time s e r i e s of flow speed, angle and OBS output 1 m above the channel bed on June 13, 1 9 8 8, near Mission. The data have been h e a v i l y smoothed with a 5 min running mean. The flow angle i s measured v e r t i c a l l y from the multi-hour mean streamline o r i e n t a t i o n . P o s i t i v e angles are upward. FLOW SPEED ( c m / s ) OBS OUTPUT (mv) in (D l-l 0 era I-1- o • O rt a -ed rt O s H re rt sr he < fl> B> in B> 0> i-1 3 tt> 3" o r+i CO I - 1 3* O er rui •1 e 3 o 3 O CO p i O 3 (->• a. 3 £ $ w <* • 3 K " OP Pi £ M CO I-1' =T 3 -75 95 115 ."^ | ' i i i i i i i i i i b 3 CD to TJ 00 _ d p. ID. b 1850 1950 2050 I i i i_i i_i i i i I FLOW ANGLE (deg. from horiz.) - 5 - 3 0 3 5 i i i i i i i t i i i i i i i I i i i i i €7 44 component, i s p a r a l l e l w i t h the l o c a l mean boundary ( i t s e l f perturbed by the large scale roughness of moving bedforms) and v i s the component normal to the mean boundary. Turbulent Reynolds shear stresses, i n p a r t i c u l a r , are known to be very s e n s i t i v e to the proper o r i e n t a t i o n of the flow coordinates r e l a t i v e to the mean shear w i t h i n a boundary layer (e.g. Pond, 1968; Kaimal and Haugen, 1969) . Improper o r i e n t a t i o n produces contamination of the v' flow component by u', and hence the (u'v') covariance (or kinematic st r e s s ) by the strong (u')^ term. Appreciable misalignment can also introduce spurious (u'v') events and a f f e c t the an a l y s i s of event recurrence. I t can be estimated that an i n s t a b i l i t y of (+/-) 1 cm/s i n sensor zero (approximating the performance of the study u n i t as discussed i n s e c t i o n 2.2.1) w i l l lead to a 0.6 degree uncertainty i n flow c o o r d i n a t e s , and hence a 8% u n c e r t a i n t y i n the (u'v') covariance (Pond, 1990, person, comm.). In p r a c t i c e , the mean shear coordinates were approximated by r o t a t i n g the raw, frame-based X and Y v e l o c i t y components to compensate f o r frame t i l t , to y i e l d u and v values such that the long-term mean v e r t i c a l v e l o c i t y v during any deployment period i s zero. The coordinate r o t a t i o n i s given by: u = X cos 9 + Y s i n 9 v = Y cos 9 - X s i n 9 The r o t a t i o n angle 9 can compensate f o r the t i l t of the frame i n a g i v e n deployment; i t was generally le s s than 3 degrees i n our s t u d i e s . I t must be noted t h a t t h i s common, and g e n e r a l l y unavoidable procedure f o r d e f i n i n g " i n t e r n a l l y " the boundary layer coordinates, based on the observed flow data i t s e l f , has drawbacks. Among others, i t leaves the observer unaware of any mixing across the layer caused by the presence of "secondary" c e l l s i n the mean flow. Sets of weak, streamwise r o l l v o r t i c e s , superimposed on the much stronger primary flow, have been documented i n some channels. In the presence of such c e l l s , mean shear coordinates defined at 1 m 45 from the bed, as above, may l o c a l l y diverge from the "true mean boundary", towards or away from i t depending on which side of a c e l l the sensors might be located. Assuming the c e l l s were f i x e d r e l a t i v e to the sensor l o c a t i o n d u r i n g a l l of a deployment, only the turbulent v e r t i c a l momentum and sediment mixing fluxes across the l o c a l mean flow c o o r d i n a t e s would be computed. However i t i s p r e c i s e l y the turbulent mixing that i s of primary i n t e r e s t i n t h i s study. Further problems of d e f i n i t i o n and s t a t i s t i c a l v a r i a b i l i t y of Reynolds stress estimates based on t h i s approach w i l l be discussed i n chapter 3. 2.6 Low frequency flow o s c i l l a t i o n s i n r i v e r s The importance of low-frequency components i n the data has already been seen i n the f i l t e r e d records presented above. Figs. 8 and 9 documented the existence of strong f l u c t u a t i o n s of flow speed, angle and t u r b i d i t y with periods of many minutes to hours at the Mission study s i t e . There i s i n p a r t i c u l a r a multi-hour f l u c t u a t i o n i n the June 13, 1988 records, with a peak i n speed corresponding to a trough i n angle around 17.5 hrs (Fig. 8). This long cycle at 1 m from the bed may have been caused by the s l i g h t t i d a l backwater cycle (of stage amplitude le s s than 2% of l o c a l depth) documented i n F i g . 7. However, the delay of near-bed flow d e c e l e r a t i o n a f u l l 2 hours beyond the s t a r t of t i d a l stage r i s e at Mission, as well as the coincidence of flow angle and speed changes suggests that the s l i g h t t i d a l e f f e c t s may have been overshadowed by a multi-hour cycle p o s s i b l y r e l a t e d to the advance of some large bedform. The f i l t e r e d r e c o r d s ( F i g s . 8, 9) a l s o suggest the existence of approximately 20 minute period flow f l u c t u a t i o n s , most noticeably i n the speed record of F i g . 8 a f t e r 17.0 hrs, when the cycles have peak to peak amplitudes of as much as 15 cm/s. The same 46 "20 min" cycles are s t i l l v i s i b l e i n the less f i l t e r e d speed record of F i g . 9. The existence of approximately 3 to 5 minute-period cycles "on the backs" of the 20 minute ones can also be detected i n F i g . 9, most c l e a r l y i n the speed record before 18.5 hrs. Similar multi-minute flow speed and angle f l u c t u a t i o n s were detected at a l l study s i t e s . Although the f i l t e r i n g of records that l e d to Figs 8 and 9 cannot i n i t s e l f introduce low-frequency v a r i a b i l i t y where none e x i s t s , i t may have a r t i f i c i a l l y enhanced the r e l a t i v e importance of these long period o s c i l l a t i o n s . The r e l a t i v e weight of these multi-minute o s c i l l a t i o n s w i l l be estimated s p e c t r a l l y i n chapter 3. The nature of these p a r t i c u l a r f l u c t u a t i o n s i s of more than p e r i p h e r a l i n t e r e s t to t h i s study. Slow turbulent flow o s c i l l a t i o n s f o r the most part do not f i g u r e i n present conceptual models of a l l u v i a l sediment transport mechanics. The records presented i n Figs. 8 and 9 suggest however that the multi-minute f l u c t u a t i o n s are s i g n i f i c a n t l y involved i n v e r t i c a l momentum and sediment fluxes through the sensor l e v e l . A strong tendency f o r the flow to veer upwards (angle increases) as i t slows down (speed decreases) i s indeed noticeable i n the records. As the flow angles are small, the h o r i z o n t a l component e s s e n t i a l l y dominates the t o t a l speed and so the observed p a t t e r n i s f o r s m a l l e r downstream v e l o c i t i e s to coincide with more upward flow, and vice-versa. At the same time, h i g h e r t u r b i d i t y l e v e l s are a l s o associated with the slower and more upward d i r e c t e d flow, and lower t u r b i d i t y l e v e l s with downward flow, most noticeably i n the 2-5 min cycles i n F i g . 9. This, for now apparent, s t a t i s t i c a l a s s o c i a t i o n of more upward d i r e c t e d flow with a d e f i c i t i n h o r i z o n t a l momentum, as w e l l as with higher sediment contents (and vice-versa) i n low-frequency cycles w i l l be q u a n t i f i e d i n coming chapters. I t suggests t h a t t h e p r o c e s s ( e s ) r e s p o n s i b l e f o r these low-frequency f l u c t u a t i o n s i n f a c t also contribute to both sediment and h o r i z o n t a l momentum transport, v e r t i c a l l y through the sensor l e v e l . M u l t i - m i n u t e c y c l e s i n flow speed have been reported 47 previously i n other r i v e r s (e.g. T i f f a n y , 1963; Ishihara and Yokosi, 1967), but with l i t t l e i n s i g h t into t h e i r o r i g i n and s i g n i f i c a n c e . I s h i h a r a and Y o k o s i (1967) suggest t h a t such m u l t i - m i n u t e f l u c t u a t i o n s simply r e f l e c t l arge-scale turbulence. The issue of whether "turbulence" can explain such low-frequency o s c i l l a t i o n s i n the F r a s e r R i v e r , or whether other process(es) might be also involved, i s a complex one that cannot be completely resolved on the basis of the one point study data. A phenomenological approach w i l l c o n s i s t i n comparing the u, v and uv spectra from the Fraser records with t y p i c a l turbulent spectra i n geophysical flows. The conclusions of t h i s analysis w i l l be presented i n the next s e c t i o n (s. 3.1). A few general comments on the o r i g i n of low-frequency r i v e r flow o s c i l l a t i o n s can be made here. I f one understands the concept of turbulent eddy i n i t s usual sense, as an evolving 3D flow disturbance convected with the mean flow, the often made hypothesis of f l u v i a l " t u r b u l e n c e " at multi-minute scales has troublesome implications that should be noted. The hypothesis of Ishihara and Yokosi (1967) would imply advection past the sensors (at e.g. 1 m/s mean flow speeds) of hig h l y two dimensional eddies, measuring many hundreds of meters i n length (to produce multi-minute periods). The s i z e of energetic turbulent eddies i s known however to scale with the dimensions of the mean shear layer ( i . e . the thickness of the boundary layer) from which they extract t h e i r energy. In r i v e r flows, they should scale with channel depth. The above authors did not suggest an energy generating mechanism f o r many hundreds of m long "two-dimensional" eddies, t r a v e l l i n g contained w i t h i n 1-10 m deep boundary layers between the r i v e r bed and the flow surface. T h i s simple " f r o z e n t u r b u l e n c e " i n t e r p r e t a t i o n may not be appropriate to describe such slow o s c i l l a t i o n s . I t w i l l be seen that l e s s extreme i n t e r p r e t a t i o n s are possi b l e . D i f f e r e n t generating mechanisms f o r multi-minute near-bed flow cycles i n r i v e r s can also be suggested, although lack of data w i l l p r e v e n t p u r s u i n g the i s s u e f u r t h e r i n t h i s t h e s i s . F l u c t u a t i o n s i n time s e r i e s of flow at only one point can be 48 v i s u a l i s e d i n d i f f e r e n t ways, i n a s p a t i a l sense. Rather than being produced by extremely elongated turbulent eddies t r a v e l l i n g at bulk flow v e l o c i t y , i t i s also possible to i n t e r p r e t the multi-minute speed and angle f l u c t u a t i o n s i n the Fraser records (Figs. 8, 9) as slow f l u c t u a t i o n s of the mean flow streamline at thes sensor p o s i t i o n (schematised i n F i g . 10), over which f a s t e r turbulent motions are superimposed. Note i n F i g . 10 the a s s o c i a t i o n between f a s t e r and downward d i r e c t e d flow (and vice-versa) seen i n Figs. 8, 9. Note also that streamline curvature i n t h i s schematic i s quite exaggerated; while multi-minute f l u c t u a t i o n s i n mean speed i n the study records are important (of the order of 10 cm/s), hypothesized streamline angle o s c i l l a t i o n s would be very subdued, of the order of 1-3 degrees over periods of minutes (Figs. 8, 9). What processes might produce gentle multi-minute streamline f l u c t u a t i o n s at a given p o s i t i o n i n the flow? One process was alluded to i n sec t i o n 2.5. Large, streamwise v o r t i c e s may be present In the "mean flow", and i f t h e i r amplitude or l o c a t i o n r e l a t i v e to the f i x e d sensor were to s h i f t , f o r example i n response to slowly changing bed conditions, slow changes i n the mean flow at the sensor would be recorded. A more d i r e c t l i n k with changing bed conditions i s also p o s s i b l e . Bedforms advance during a c t i v e sediment transport conditions, and some passages of f a s t e r , smaller bedforms under a f i x e d sensor frame can be expected during multi-hour records. In p r i n c i p l e such passages d i r e c t l y produce, through pressure e f f e c t s , l o c a l perturbations of flow streamlines (which may or may not be e a s i l y p e r c e p t i b l e at sensor l e v e l , 1 m o f f the bed). Could t h i s obvious source of streamline perturbation underlie some of the observed multi-minute (1-3 deg amplitude) flow o s c i l l a t i o n s ? Lack of data on small scale bed a c t i v i t y near the sensor frame p r e v e n t e d i n v e s t i g a t i n g t h i s h y p o t h e s i s i n the study environments. For t h i s s p e c u l a t i o n to be p l a u s i b l e , f a s t e r advancing, low amplitude bedforms (for example, 8-15 cm height, 1-2 m l e n g t h "dunes" known to be p r e s e n t i n the June 13, 1988 conditions, F i g . 6, or yet even smaller r i p p l e s ) would have had to 49 TIME Fig. 10: Schematic diagram of multi-minute streamline oscillations, with time, at sensor level in the study conditions. Angular deviations are much exaggerated. At any instant, turbulent flow parcels arrive at sensors from a range of directions spread around this mean streamline. 50 pass under the sensors as o f t e n as every few minutes (or as infrequently as every 20 min, F i g . 8). This could imply bedform c e l e r i t i e s of the order of a few mm/s i f , f o r example, passage of the smaller length dunes present on June 13, 1988 near Mission were to cause streamline perturbations of 3-5 min period (as i n F i g . 9). I t i s unclear whether such bedform c e l e r i t i e s are po s s i b l e . There are unfortunately few data a v a i l a b l e on c e l e r i t i e s of very small bedforms i n such f a s t , and deep flows, where these small forms advance over the backs of the l a r g e r , e a s i e r tracked dunes. A v a i l a b l e laboratory data on c e l e r i t i e s of small bedforms may not be e a s i l y extrapolated to conditions i n deep flows with multiple scales of bedforms and considerable s p a t i a l v a r i a t i o n i n bed s t r e s s . Since very l i t t l e s p e c i f i c a l l y i s known about the movement of small bedforms i n deep flows and that some disturbance to these forms i s expected near the base of the sensor frame, a d e t a i l e d and unambiguous (almost v i s u a l ) record of the nature of the bed a c t i v i t y would be r e q u i r e d to c o n v i n c i n g l y e s t a b l i s h the l i n k between bedforms and multi-minute streamline perturbations at 1 m. Possibly because of sonar beam t i l t , the depth sounder mounted on the sensor frame i n t h i s study f a i l e d to d i s c l o s e unambiguous information on bedform passage events (cf. section 2.2.3). In any case such depth sounder records (even at two points) cannot d i r e c t l y d i s c l o s e the nat u r e , form and length (and hence c e l e r i t y ) of i n d i v i d u a l bed disturbances near the frame, c r u c i a l information to s o l i d l y confirm the hypothesis l i n k i n g streamline o s c i l l a t i o n s to bedform passages. High suspended sediment concentrations near the bed make video m o n i t o r i n g v i r t u a l l y i m p o s s i b l e . A compact s i d e - s c a n sonar transducer with high s p a t i a l r e s o l u t i o n would probably need to be developed to allow d e t a i l e d documentation of small-scale bedform a c t i v i t y near such a frame, and i t s r e l a t i o n to long flow c y c l e s . In coming chapters, estimates w i l l also be made of the importance of these multi-minute flow o s c i l l a t i o n s to momentum and sediment fluxes, before they are f i l t e r e d out to leave the burst-scale turbulent motions of main i n t e r e s t to t h i s study. CHAPTER 3 MOMENTUM FLUXES AND TURBULENT BURSTING EVENTS The simultaneous time s e r i e s of h o r i z o n t a l and v e r t i c a l v e l o c i t y f l u c t u a t i o n s 1 m o f f the channel bed provide a means of e s t i m a t i n g , through "eddy c o r r e l a t i o n " s t a t i s t i c s , the rate of exchange of h o r i z o n t a l momentum (the Reynolds shear stress) through that height i n the water column. In t h i s chapter, the s p e c t r a l contributions to momentum exchange w i l l f i r s t be discussed. Then, objective 1 (cf. s e c t i o n 1.4.2) w i l l be pursued: to describe "burst-l i k e " stress events i n a f l u v i a l environment during high flows and contrast them to those reported i n other geophysical flows. The ro l e and timing of large intermittent contributions to momentum exchange w i l l be analysed, and t h e i r p ossible r e l a t i o n to the "bursting" events i d e n t i f i e d i n laboratory flows w i l l be discussed. In the next chapter, the key objective of t h i s study i s pursued: an analysis i s conducted of the effectiveness of the intermittent b u r s t - l i k e events i n terms of sediment suspension. 3.1 The frequency d i s t r i b u t i o n of momentum exchange. Here the usual convention f o r f l u c t u a t i o n s i s followed: u' = u - <u> v' = v - <v> where O denotes a long-term mean, and <v> = 0. Inspection of simultaneous u and v reco r d s d i s c l o s e s that momentum exchange p r o c e s s e s occur over a wide range of frequencies. Q u a l i t a t i v e evidence was p r e s e n t e d i n the previous chapter of a negative 52 c o r r e l a t i o n between multi-minute period f l u c t u a t i o n s of the v e r t i c a l (v') and downstream (u') v e l o c i t y components (see Figs. 8, 9). As discussed i n sec t i o n 2.6, these very low frequency flow f l u c t u a t i o n s at the sensor tend to associate f a s t e r (u'>0) with downward (v'<0) flow, while slower flow tends to be d i r e c t e d away from the bed. On average such motions would produce a v e r t i c a l exchange of h o r i z o n t a l momentum through the sensor height; s p e c i f i c a l l y a retar d i n g stress on the outer flow. Although low-frequency processes are not of c e n t r a l i n t e r e s t to t h i s study, t h e i r importance to momentum exchange i n the study conditions w i l l be assessed as an element of general i n t e r e s t . A stress bearing a s s o c i a t i o n of u and v f l u c t u a t i o n s i s also detectable i n the f a s t e r turbulent components, superimposed on these multi-minute o s c i l l a t i o n s . This can be seen i n F i g . 11, which shows 10 minute long time s e r i e s , s t a r t i n g at 16:57 hrs PST on June 13, 1988, of OBS output along with v and u flow components. To extend the time base of the p l o t , minor f l u c t u a t i o n s with periods le s s than some 2 s have been f i l t e r e d out, using a 0.8 s running mean. F i g . 11 can be viewed as the l a s t stage of a "magnification" of the records begun with Figs. 8 and 9; on i t can be r e a d i l y observed f a s t e r (multi-second-scale) turbulent motions, superimposed on the multi-minute v e l o c i t y f l u c t u a t i o n s . Notice that the 2 to 5 min "cycles" are strong enough to remain conspicuous i n these l a r g e l y u n f i l t e r e d records, e s p e c i a l l y i n the u and OBS s e r i e s , despite the presence of the strong shorter period turbulent f l u c t u a t i o n s . The tendency of upwelling motions (v'>0) to mostly b r i n g r e l a t i v e l y slower near-bed water parcels into the f a s t e r flow above sensor l e v e l , and v i c e -versa, can be detected over the f u l l range of frequency components seen i n F i g . 11, incl u d i n g the multi-second scale turbulence. Spectral techniques w i l l help i n quantifying the r e l a t i v e c o n t r i b u t i o n to o v e r a l l momentum exchange of the various frequencies of flow f l u c t u a t i o n s d i s c u s s e d above. An issue r a i s e d e a r l i e r ( s e c t i o n 2.6) w i l l be considered i n t h i s l i g h t : are the multi-minute flow cycles near the bed of the Fraser River unusually intense to - 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 • • 1 1 1 1 1 I • I 1 1 1 0 1 2 3 4 5 6 7 8 9 1( Time (min, from 16:57 hr PST) F i g . 11: A 10 min time ser i e s o f U and V flow components w as w e l l as OBS output , r e v e a l i n g seconds-scale t u r b u l e n t f l u c t u a t i o n s s u p e r i m p o s e d on m u l t i - m i n u t e f l o w o a c i l l a L l o n a . June 13, 1988 deployment neur M i s s i o n . 54 represent simple boundary layer turbulence. Before presenting the cospectrum of momentum exchange through the sensor l e v e l , i n d i v i d u a l u and v power spectra w i l l also be introduced and b r i e f l y compared to those encountered i n other geophysical boundary layer flows. 3.1.1 U and V spectra. In p r a c t i c e s p e c t r a l estimates based on a given record can analyse the whole underlying process only i f a large number of the lowest frequency cycles involved are included i n the record, to average out t h e i r properties. The approach taken here was to analyse only the low-frequency cycles with periods under approx. 14 minutes, of which there was a reasonable number i n the uncorrupted records of June 13, 1988 near Mission. Spectral estimates of longer period o s c i l l a t i o n s would have been marred by unacceptable sampling error. Less w e l l resolved spectra from another deployment w i l l also be presented that broadly corroborate the June 13, 1988 f i n d i n g s . I n d i v i d u a l 13.65 minute time segments ( 2 ^ data points sampled at 5 Hz) were i d e n t i f i e d i n the June 13, 1988 records during which no apparent corruption of e i t h e r v e l o c i t y record by organic debris could be recognised. In t o t a l , 2.7 hours of data were thus retained, recorded between 16:57 and 20:00 hr. The variances of h o r i z o n t a l and v e r t i c a l flow components (3.3 minute averages) were t r e n d l e s s during t h i s period, despite a slowly r i s i n g stage at M i s s i o n (about 2 cm/hr) due to t i d a l backwater; t h i s weak s t a t i o n a r i t y i n the records i s the usual requirement f o r s p e c t r a l decompos i t i o n . To reduce the random error i n the s p e c t r a l estimates as much as possible within t h i s l i m i t e d record length, 23 such 2 ^ point time segments were delimited, allowing f o r 50% overlapping of segments where possible (Bendat and P i e r s o l , 1986). Each of these segments was detrended by l i n e a r regression, tapered with a Hanning type window, and f a s t - F o u r i e r transformed. Thus, contamination of the spectra by cycles longer than 13.65 minutes was i n h i b i t e d . Power 5 5 spectral density estimates from the 23 records were then averaged, and further bin averaging of adjacent frequency bands was done where desirable to reduce the random variance of the estimates. Even in laboratory flows, under the most steady conditions practically realisable, turbulent velocity spectra often show the greatest power density (per Hz unit of frequency) at the lowest frequencies studied (I. Gartshore, pers. comm, January 1987). There is typically however a frequency at which peak power per frequency  decade occurs and this value provides a useful scale for the turbulence (Panofsky and Dutton, 1984). This peak is displayed in the standard area-preserving form of the spectrum, in which ( f * s p e c t r a l density) i s plotted against the log of frequency. Because of record length limitations, the peak may or may not be reached in observed u spectra. "Internal" adjustment of mean v to zero (section 2.5) w i l l always produce a peak in the v spectrum. Fig. 12 contrasts these forms of the horizontal and v e r t i c a l spectra for the June 13, 1988 data, smoothed by" averaging 10 adjacent estimates. The OBS output spectrum for this run is also superimposed on the velocity spectra for later reference (section 4.2.1). Soulsby (1977) documented the usefulness of scaling eddy wavenumber by sensor height (as a f i r s t approximation u n t i l further work defines other scaling length(s) reflecting complex bedform geometries) to compare among them benthic and t i d a l turbulence spectra, as well as atmospheric surface layer spectra. This scaling is implicit in the commonly used non-dimensional frequency n = f * z/U, where f is frequency in Hz, z is sensor height in m and U is local flow velocity in m/s. In the June 13, Mission data the non-dimensional and dimensional frequencies are approximately numerically equal, when the latter is expressed in Hz: n = (fz/U) ~ f as the sensor height z was 1 m, where the mean flow velocity U was 0.9 m/s. 56 Frequency resolution: 0.0122 Hz Standard error of u.v densities:»7« OBS densities: "12» i i i | 0.01 -1—I—I I I I I I 0.1 Frequency (Hz) o o o-o • 00 • o • o • CD-CD • CO • O ' O ' CD-CO • O ' o • CD-CD • CN • > E CD O CO c CD a o CL) 0 0 cr F i z 12- U V and OBS output power spectra i n area preserving form. June 13, 1988 deployment near Mission. 57 Figs 13 and 14 compare the U and V spectra obtained on June 13, 1988 near Mission to those extracted from 57 minutes of data c o l l e c t e d i n s l i g h t l y weaker flow conditions near Barnston Island ( c f s e c t i o n 2.4) on J u l y 14, 1987, ( i n 9 m depths and with v e l o c i t i e s of 0.85 m/s at 1 m from the bed). The s c a l i n g f a c t o r to non-dimensionalise frequencies (z/U) was approximately the same f o r both records, and again f ( i n Hz) can be e s s e n t i a l l y taken as n on these p l o t s . Because of shorter a v a i l a b l e records, the Barnston spectra have more sampling v a r i a b i l i t y . Despite somewhat weaker U, V turbulent i n t e n s i t i e s i n the Barnston flow, the shape of the spectra appear to be broadly s i m i l a r to those near Mission. Turbulence s t a t i s t i c s are n o t o r i o u s l y v a r i a b l e and the g e n e r a l i t y of conclusions that can be drawn here i s severely l i m i t e d by the small number of a v a i l a b l e spectra, a consequence of the d e a r t h of uncorrupted data runs i n the Fraser deployments. The l o c a t i o n of the u, v s p e c t r a l peaks i n the Fraser data w i l l nonetheless be compared with those of b e t t e r documented atmospheric surface layer turbulence under s i m i l a r conditions of near neutral ( s l i g h t l y stable) density s t r a t i f i c a t i o n ( cf. s e c t i o n 2.4). Panofsky and Dutton (1984) summarise some ea r l y atmospheric r e s u l t s i n t h e i r engineering textbook ( r e l y i n g strongly on J.C. Kaimal's work). They r e p o r t t h a t f o r purely mechanical turbulence i n the atmosphere (neutral s t a b i l i t y conditions) the peak i n the v e r t i c a l v e l o c i t y spectrum appears to occur at a non-dimensional frequency n=0.5, i . e . f o r eddies as large as twice the sensing height. The v a r i a b i l i t y i n turbulent spectra however i s considerable. Pond et a l . (1971) for example present surface layer v spectra based on numerous records over the ocean i n only s l i g h t l y unstable conditions that tend to peak nearer n = 0.2. Peaks around n= 0.2-0.3 were also obtained by Anderson and Verma (1985) and Smith and Chandler (1987) i n atmospheric surface layer flows over, r e s p e c t i v e l y , f i e l d crops and the ocean, under near-neutral conditions. 58 0.01 0.1 i Frequency (Hz) F i g . 13: U power spectra, superimposed, f o r main June 13, 1988 deployment near Mission and J u l y 14, 1987 deployment at Barnston Island. See s e c t i o n 2.4 f o r flow conditions. 59 F i g . 14: V power s p e c t r a , s u p e r i m p o s e d , f o r main June 13, 1988 deployment near M i s s i o n and J u l y 14, 1987 deployment a t B a r n s t o n I s l a n d . See s e c t i o n 2.4 f o r f l o w c o n d i t i o n s . 60 The peaks i n the Fraser v e r t i c a l spectra i n F i g . 14 are centered around n = 0.1. However, the l o c a t i o n of the peak i n these spectra i s somewhat af f e c t e d by damping of f a s t e r flow o s c i l l a t i o n s due to the r e l a t i v e l y slow frequency response of the electromagnetic flowmeter. As discussed i n Chapter 2, the 0.2 s time constant has l e d to a 30% power loss by f = 0.5 Hz (n = 0.5) for both components, so that most of the i n e r t i a l range (at approx n>3-10, Panofsky and Dutton, 1984) and a small f r a c t i o n of the f a s t e r energy-bearing components were not recorded. This accelerated r o l l - o f somewhat s h i f t s the v e r t i c a l peak to a lower frequency. Compensating for frequency response one obtains a peak around n = 0.3. This i s within the range reported above for v component turbulence i n the near-ne u t r a l atmosphere. Less c o n s t r a i n e d by p r o x i m i t y to the boundary, the h o r i z o n t a l eddy component t y p i c a l l y produces a s p e c t r a l peak at longer wavelengths. While Panofsky and Dutton (1984) report t h i s peak around n=0.05 i n neutral conditions i n the atmosphere, Pond et a l . (1971) observed peaks around n = 0.01 - 0.02 based on t h e i r numerous runs. The l a t t e r range of values also applies to the Anderson and Verma (1985) and Smith and Chandler (1987) studies reported above. There i s thus no evidence that the peak i n the u spectrum f o r the Fraser River data, i n the range n = 0.02 - 0.05 (F i g . 13) i s s i g n i f i c a n t l y s h i f t e d from t h i s expected range for u turbulence. 3.1.2 The uv cospectrum. The mean kinematic stress (-<u'v'>) about the long-term streamline, c a l c u l a t e d f o r a 2.33 hr period between 17:40 and 20:00 hours i n the June 13, 1988 records i s 28 cm 2/s 2. This i s equivalent to a shear stress (-p<u'v'>) of 2.8 Pa (p i s water density). At the approximately 10 m flow depths i n the study reach near Mission such a shear stress would be t y p i c a l of a steady flow with an energy gradient of 3 x 10" . No data are a v a i l a b l e on energy gradient on the side-channel of the Fraser River, at t h i s precise stage of runoff and phase of t i d a l backwater. Such an energy gradient however i s of the r i g h t order of magnitude given what i s known of the t y p i c a l o v e r a l l slope of the Fraser R. at Mission, at 5 x 10"^. The cospectrum of u'and v' f l u c t u a t i o n s breaks down the t o t a l Reynolds st r e s s reported above into component contributions over the range of frequencies of v e l o c i t y o s c i l l a t i o n . Cospectral estimates were computed from 21 time segments (with 50% overlaps) of uncorrupted flow data, each of 13.65 min ( 2 ^ 2 data points) length f o r the June 13, 1988 record. The l e v e l of coherence between the two s e r i e s i s l i m i t e d ( Fig. 15 a): coherence squared reaches a l e v e l of 0.5 o n l y a t lowest f r e q u e n c i e s (although these low frequency e s t i m a t e s have more random v a r i a b i l i t y than the r e s t ) . Mostly, coherence i s around the t y p i c a l turbulent value of 0.3 up to the instrumental r o l l - o f f above 0.5 Hz. Coherences under 1 generate even more sampling v a r i a b i l i t y i n the cospectrum than was present i n the i n d i v i d u a l v e l o c i t y spectra (Bendat and P i e r s o l , 1986). To b r i n g down the sampling v a r i a b i l i t y , mean estimates from the 21 sets were f u r t h e r smoothed by averaging 20 adjacent frequency bins: t h i s procedure degraded the frequency r e s o l u t i o n to (20/13.65 min) or 0.0244 Hz. The r e s u l t s are presented i n F i g . 15 b) i n the conventional area preserving form. Also displayed i s the U,V cospectrum extracted from the 57 minutes of records from Barnston Island described above, with mean stress somewhat lower than i n the June 13, 1988 Mission conditions. For the Mission data, the integrated c o s p e c t r a l density between 0.0012 Hz and 2.5 Hz i s 29 cm 2/s 2 (20 cm 2/s 2 f o r the Barnston data). This i s the same, within sampling v a r i a b i l i t y , as the 2.33 hr long mean kinematic stress from the Mission record reported e a r l i e r . The contributions to stress between 0.0012 Hz (T=13.65 min) and 0.00012 Hz (T=2.33 hrs) thus appear minor o v e r a l l . Because the lowest frequency estimate averages a l l the cospectral content between f=0.00122 (T-13.65 min) and f=0.0244 Hz (T=41 s) 62 F i g . 15: (A, t o p ) : Coherence spec trum between the U and V s i g n a l s , based on 2.2 hrs o f records from June 13, 1988. Low frequency est imates are l e f t unsmoothed. 20 est imate b loc means beyond 0.02 Hz. (B, bottom): UV cospec tra , superimposed, for main June 13, 1988 deployment near M i s s i o n and J u l y 14, 1987 deployment at Barnston I s l a n d . See s e c t i o n 2.4 for flow c o n d i t i o n s . E r r o r bars represent s tandard dev ia t ions of c o s p e c t r a l d e n s i t i e s . 63 i t appears r e l a t i v e l y high. The raw, unaveraged s p e c t r a l estimates trend downward towards the longest period sampled (13.65 min). Panofsky and Dutton (1984) report that the peak c o n t r i b u t i o n to the uv cospectrum, per frequency decade, i n the n e u t r a l atmospheric surface layer occurs near a non-dimensional frequency n=0.08. As seen above, i n these surveys the non-dimensional and dimensional frequencies are numerically approximately the same, and so the l o c a t i o n of the peak i n F i g . 15 b) approximately conforms to t h i s atmospheric standard. More noteworthy i n F i g . 15 b) i s the o v e r a l l importance of the lower frequencies to t o t a l s t r e s s . In the Mission data, the r e l a t i v e c o n t r i b u t i o n of motions between 0.0012 Hz (T=13 min) and 0.08 Hz (T=12.5 s) i s 80% of the t o t a l stress (75% f o r the Barnston data). (Note that the abscissa i s truncated at 0.01 Hz on F i g . 15 b) , but the lowest s p e c t r a l density represents o s c i l l a t i o n s down to 0.0012 Hz). T y p i c a l r e s u l t s f o r turbulent stress are again varied. Panofsky and Dutton (1984; t h e i r f i g . 8.26) state that approximately 50% of the stress occurs below t h i s value n = 0.08 i n the neutral atmospheric surface layer. Soulsby (1980) reports a s i m i l a r value from t i d a l boundary layer data. Large and Pond however (1981) present atmospheric uv cospectra i n s l i g t h l y unstable conditions over the ocean i n which t h i s c o n t r i b u t i o n i s 60% of the t o t a l . To see i f the multi-minute flow o s c i l l a t i o n s on the Fraser River produce a c o n t r i b u t i o n to momentum exchange unusually large f o r turbulence, i t i s best to consider the cospe c t r a l contributions below n = 0.01, corresponding to o s c i l l a t i o n periods greater than 1.7 min. The Mission cospectrum includes 27% of the t o t a l below t h i s value and t h i s proportion i s 21% f o r the Barnston data. Thus close to a fourth of the t o t a l momentum exchange i n the study data i s caused by slow flow o s c i l l a t i o n s of period over 1.7 minutes. Both Panofsky and Dutton (1984; atmospheric data) and Soulsby (1980; t i d a l data) report a lower turbulent c o n t r i b u t i o n to shear stress below n=0.01: between 5 and 10% of the t o t a l . Other near-neutral flows have been reported to contain low-frequency contributions of 64 the same scale as those found on the Fraser River, however. The Large and Pond (1981) records from the surface layer above the ocean include some 17% of the stress below n = 0.01, e s s e n t i a l l y the same as the Barnston Island r e s u l t on the Fraser River. The uv cospectra over f i e l d crops i n near neutral conditions reported by Anderson and Verma (1985) include roughly a quarter of t h e i r area below n = 0.01. Because of the v a r i a b i l i t y i n turbulence s t a t i s t i c s and the small number of study spectra, the above comparisons are preliminary and t e n t a t i v e . In summary, the a v a i l a b l e r e s u l t s do not point to a l e v e l of c o n t r i b u t i o n to stress by multi-minute o s c i l l a t i o n s that i s c l e a r l y unusually large f o r boundary layer turbulence. The absence of a s p e c t r a l "gap" i n u, v or uv spectra (Figs. 13, 14, 15 b) , around periods of the order of a minute (f=0.017 Hz), further suggests that turbulent processes may occupy the whole range of frequency content i n the Fraser data. The cospectral peak at f=0.07-0.1 Hz i n F i g . 15 b) nonetheless indicates that the most important contributions to s t r e s s correspond to 10 to 15 s scale turbulent events. Large turbulent motions i n t h i s c l a s s w i l l be analysed further i n what follows. 3.2 Intermittent contributions to momentum exchange. Complex turbulent "bursting" structures are best perceived through flow v i s u a l i z a t i o n (e.g. K l i n e et a l , 1968) and the study of simultaneous flow records at d i f f e r e n t heights above the wall (e.g. Nakagawa and Nezu, 1981). Nonetheless various attempts have also been made to detect the passage of these structures from flow s e r i e s at one point, such as were gathered i n t h i s study (cf s e c t i o n 1.1). Unfortunately, whether they are i d e n t i f i e d through pulsations i n high-frequency turbulence i n t e n s i t y at one point (e.g. Rao et a l , 1971) or high magnitudes of (u'v') (e.g. Lu and Willmarth, 1973), considerable l a t i t u d e remains i n d e f i n i n g and counting such (u'v') 65 "events", as well as i n r e l a t i n g them to the c l a s s i c b u r s t ing process. In the next two sections the Fraser River (u'v') records w i l l be analysed i n the l i g h t of two c r i t e r i a conventionally used to i d e n t i f y turbulent bursting i n geophysical (u'v') records: high intermittence of stress contributions and mean "event" recurrence conforming to the "outer s c a l i n g " i d e n t i f i e d i n the laboratory. The aim o f t h i s a n a l y s i s i s to compare p r o p e r t i e s (degree of intermittence, recurrence p e r i o d i c i t y ) of b u r s t - l i k e s t r e s s "events" i n the Fraser River to those reported i n laboratory as well as t i d a l and benthic boundary laye r s . 3.2.1 Intermittence of (u'v') time s e r i e s at sensor l e v e l . B u r s t s are known to account f o r most of the turbulence production and momentum exchange i n a boundary layer and the l a t t e r property can produce a signature i d e n t i f i a b l e on (u'v') records. Between a d j a c e n t zero c r o s s i n g s of the (u'v') time s e r i e s , i n d i v i d u a l "events" are c l a s s i f i e d as "e j e c t i o n s " (u'<0, v'>0), " i n r u s h e s " (u'>0, v'<0), and "negative s t r e s s " producing inward (u'<0, v'<0) and outward (u'>0, v'>0) " i n t e r a c t i o n s " . The f i r s t two event types dominate the records and lead to p o s i t i v e mean momentum exchange. Larger burst structures are t y p i c a l l y associated with a p a i r of strong ejection/inrushes i n the u'v' record. T y p i c a l l y , the recurrence of such large events leads to an inte r m i t t e n t (u'v') record: although occupying only a small f r a c t i o n of time the intense events account f o r much of the mean s t r e s s . F i g . 16 presents 14 minutes of the (u'v') time s e r i e s on June 13, 1988 near Mission along with the low-frequency component of h o r i z o n t a l v e l o c i t y f l u c t u a t i o n s (low-passed with half-power at T= 30 s) . The p l o t t e d s e r i e s s t a r t at 16:57 hr, as i n F i g . 11. One second means of (u'v') have been p l o t t e d i n F i g . 16 to allow the di s p l a y of a longer time segment and la r g e r events are l a b e l l e d as ejections or inrushes. The 1 s mean produces very l i m i t e d smoothing as f l u c t u a t i o n s f a s t e r than 1 Hz contribute l i t t l e to the t o t a l I I II I I I N I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I M I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 T i m e ' (min, f rom 16:57 hr "PST) F i g . 16: A 14 min time series of (U'V), i n d i c a t i n g instantaneous momentum exchange through the sensor l e v e l , a l o n g w i t h s i m u l t a n e o u s 1 o w - f r e q u e n c y f l u c t u a t i o n s i n U. June 13, 1988 deployment near Mission. Large events marked E and I are respectively "ejections" (U'<0, V>0) and "inrushes" (U'>0, V'<0). 67 s t r e s s ( c f . F i g . 15 b) ; a l l subsequent (u'v') s t a t i s t i c s w i l l nonetheless be based on the recorded v e l o c i t y f l u c t u a t i o n s at 5 Hz. Immediately apparent are large negative spikes i n (u'v') of 5-10 s duration; many of these events reach or exceed a l e v e l equal to 5 times (-150 cm 2/s 2) and a few even 10 times (-300 cm 2/s 2) the mean <u'v'>. The aggregate c o n t r i b u t i o n of these b r i e f events i s considerable; thus the momentum exchange i s int e r m i t t e n t . Gordon and W i t t i n g (1977) found t h a t s t r o n g events occupying only 25% of the record time accounted f o r e s s e n t i a l l y a l l the momentum exchange 2 m from the bed of a t i d a l channel. Although conventional by now, such s t a t i s t i c s are somewhat misleading: events o t h e r than those t a l l i e d i n t h i s 25% may not be of minor s i g n i f i c a n c e to momentum exchange, as implied; rather t h e i r p o s i t i v e and negative contributions might simply cancel each other. Despite t h i s q u a l i f i c a t i o n , such s t a t i s t i c s nonetheless o f f e r a ready measure of intermittency that can be compared to previous f i n d i n g s . On the Fraser River near Mission the intermittency can be i l l u s t r a t e d by a s i m i l a r comparison of the f r a c t i o n of time versus f r a c t i o n of t o t a l momentum exchange due to (u'v') values below a c e r t a i n threshold ( Fig. 17, based on 2.2 hr of data on June 13). As i n Gordon and Witting's (1977) data, (u'v') values exceeded only 25% of the time (here below -50 cm 2/s 2) "account" f o r a l l the mean st r e s s . Analysis of more extreme (u'v') l e v e l s i n d i c a t e s that, while values below -100 cm 2/s 2 account f o r close to 80% of the exchange, they only occupy 12% of the time, while more than 30% of momentum exchange can be thought of as occurring during 3% of the time (values below -200). Intermittency, i n the sense used here, i s r e l a t e d to the h i g h degree of k u r t o s i s i n the (u'v') p r o b a b i l i t y density; i f extreme amplitude events are r e l a t i v e l y frequent i n a skewed d i s t r i b u t i o n they tend to dominate o v e r a l l averages (here of course average u'v' i s the stress) . Table 2 presents summary s t a t i s t i c s f o r u', v' and (u'v') d i s t r i b u t i o n s based on the 2.2 hr of data f o r June 13, 1988. By subtracting the value 3, ku r t o s i s here was defined as 3* ca CO i-( (D rt ca M re <JQ O to co M l u co 1—1 a D> (6 Ca fro x ca Ca fro ceeds SOCl Perc 5 ceeds tn CD rt 3 t-. < CO rt g Co p. 3 H o CD (-•• o < M) ca r t r t cr H ' B l - 1 VO r t D " d (D 00 n (tl Co oo (D l-t 3 ca H - P-dep 3* 0 dep old ds pe la-old £ rc 's < 3- CD B CD (D 3 I—1 3 r t 3 C r t 3 n (a th of (0 B P> H fia • (D P> Mi ca <D <=i 3 SS P- <S ki o ' ^ 3 on. 3 r t ema ro H-B ti t o CD o Percent of t ime or stress-TABLE 2 MOMENT STATISTICS FOR u ' , v ' AND (u 'v ' ) DISTRIBUTIONS p e r i o d 17:42-19:56 hr PST, June 13, 1988 v e l o c i t i e s i n cm/s u' v ' u 'v ' N 40266 40266 40266 MEAN 0.0 0.0 -27.9 STAND. DEV. 12.5 5.5 73.6 SKEWNESS(Gl) 0.2 -0.1 -1.9 KURT0SIS(G2) -0.4 0.2 7.4 70 being zero f o r a normal d i s t r i b u t i o n . While both u' and v' are near normal, (u'v') i s negatively skewed and has quite heavy t a i l s . The product of two near normal v a r i a t e s that are cor r e l a t e d , such as u' and v', i s generally expected to have "heavy t a i l s " ( i . e . p o s i t i v e k u r t o s i s ; Kennedy and Corrsin, 1961; Antonia and Atkinson, 1973); however the precise degree of ku r t o s i s can vary, and i t i s one measure of degree of intermittence. What i s of i n t e r e s t here i s thus how the degree of kurtos i s (and hence intermittence) i n the study conditions compares to that reported i n other flows. The f l u v i a l r e s u l t s i n Table 2 are t y p i c a l of those obtained i n laboratory and large-scale flows (Antonia and Atkinson, 1973; Anwar, 1981). Notably, the ku r t o s i s of (u'v') near the bed of the Fraser was of the same order (7.4 at Mission, 6.9 f o r the Barnston data) as values found by others at comparable distances from the bed i n l a r g e - s c a l e flows (McLean and Smith, 1979; Heathershaw, 1979). To g r a p h i c a l l y i l l u s t r a t e the degree of ku r t o s i s i n play here, F i g . 18 compares a histogram of (u'v') values recorded on June 13 and a normal d i s t r i b u t i o n of same mean and standard deviation. The frequencies of occurrence of values of (u'v') below -200 cm 2/s 2 are orders of magnitude higher than "normal". 3.2.2 Mean burst recurrence period Momentum exchange i s thus dominated by repeated intense but b r i e f events and t h i s i s a known c h a r a c t e r i s t i c of bu r s t i n g structures investigated i n the laboratory. The usual way of further e s t a b l i s h i n g a l i n k between such one-point (u'v') "events" and near-wall b u r s t i n g i s to compare the mean recurrence period f o r these events, T D , with the l a b o r a t o r y outer flow s c a l i n g f o r burst r e c u r r e n c e . Do t h e F r a s e r R i v e r o b s e r v a t i o n s c o n f i r m the conventional outer flow s c a l i n g of burst recurrence? As i n much p r e c e d i n g work ( c f . s e c t i o n 1.1), i t i s d i f f i c u l t to define completely o b j e c t i v e l y a mean recurrence period f o r these intense b u r s t - l i k e events i n the Fraser data. F i g . 19 71 O f J I o i — 1 — 1 — 1 — ' — 1 — 1 — 1 — i — 1 — 1 — 1 — i — 1 — 1 — 1 — I — 1 — 1 — 7 1 — i — 1 1 1 I — - 8 0 0 - 6 0 0 - 4 0 0 - 2 0 0 0 2 0 0 4 0 0 U ' V ( c m / s ) * Fig. 18: Histogram of observed (U'V) values compared with that of a normal distribution with same mean and standard deviations. Ordinates are expressed as percent time. Based on 2.2 hrs of data from June 13, 1988 deployment near Mission. 72 CM , _ _ | , ! , ! , ! 1 1 1 1 - 5 0 0 - 4 0 0 - 3 0 0 - 2 0 0 - 1 0 0 0 U'V" ( c m / s ) 1 F i g . 19: Observed mean recurrence periods of intense " e j e c t i o n s " d u r i n g which the -(U'V) s i g n a l exceeds various threshold values. Based on 2.2 hrs of data, June 13, 1988. 73 presents the s t a t i s t i c mean time between strong ejections against the threshold (u'v') value used to separate these events from background, based again on the 2.2 hr of main study data (June 13, 1988). The recurrence periods are i n the minutes range and increase continuously as threshold i s set further from the mean. Although t h i s increase i s most r a p i d at more extreme values of threshold, there i s no apparent "natural" mean recurrence period, T D, i n the sense of being s u b s t a n t i a l l y independent of threshold l e v e l . F i g . 20 superimposes burst recurrence curves from the June 13, 1988 records with those of two other study deployments ( cf. s e c t i o n 2.4). To a l l o w comparison, the stress threshold has been scaled by mean stress applicable to each deployment. The curves are rather s i m i l a r and i n rough agreement for higher stress l e v e l s . In a d e t a i l e d i n v e s t i g a t i o n of the (u'v') event-counting procedure, Willmarth and Lu (1974) had already pointed out the continuous v a r i a t i o n of burst period with u'v' threshold l e v e l , even i n simpler laboratory flows. F i g . 21 presents the dependence of r e c u r r e n c e p e r i o d on t h r e s h o l d s e t t i n g i n t h e i r wind tunnel experiments. I t can be seen that the absence of a natural plateau i n the curve on which to base a threshold s e t t i n g i s not a feature unique to our f l u v i a l data; i t also occurs f o r c l a s s i c b u r s t i n g i n lower Reynolds number f l a t w all flows. The observed burst recurrence period on the Fraser River w i l l thus depend, as i n a l l such studies, on the j u d i c i o u s s e l e c t i o n of a threshold value to separate bursts from background st r e s s a c t i v i t y . W i l l m a r t h and Lu (1974) argued f o r s e t t i n g the event-defining t h r e s h o l d at about 10 times the mean k i n e m a t i c s t r e s s , as contributions of events other than ejections gradually disappeared above t h i s value i n the outer parts of the flow. Furthermore, they showed t h i s 10X threshold to be consistent and u s e f u l even into the middle and outer portions of the boundary layer (which corresponds to the study conditions) and to produce recurrence periods matching those of Rao et a l (1971). To date, t h e i r s would appear to be the best documented threshold s e t t i n g f o r the uv quadrant method applied 74 Fig. 20: Superimposed curves of ejection recurrence periods for -(U'V) events exceeding various threshold v a l u e s . D e t a i l s on f l o w c o n d i t i o n s during three deployments can be found i n s e c t i o n 2.4. S t r e s s thresholds are normalised by mean stress during each deployment. 75 500 200 " 100 50 . 20 10 10 Hole Size, H Fig. 21: Mean recurrence periods of intense " e j e c t i o n s " as a function of u'v' threshold setting and distance from wall ( s o l i d and open symbols) i n wind tunnel experiments. From Willmarth and Lu, 1974 (their Fig. 18). Ordinate i s r e c u r r e n c e p e r i o d T 0 non-dimensionalised by outer variables. Abscissa i s threshold stress normalised by the product of rms of u and v. Hole size of 4.5 corresponds to 10 times mean stress. 76 to outer flow observat ions , and w i l l thus be used here . Apply ing Wi l lmarth and L u ' s c r i t e r i o n to the June 13, 1988 M i s s i o n data ( F i g . 19) i t i s found that e jec t ions with (u 'v ' ) below approximately -290 c m 2 / s 2 (ten times the mean) recur every 8 minutes on average (based on 2.2 hr of data ) . F i g . 20 suggests that i n general on the Fraser River t h i s p e r i o d v a r i e s between 5 and 10 minutes. How do these values compare with p r e d i c t i o n s based on convent ional outer flow sca l ing? The boundary l a y e r thickness (or momentum displacement thickness i n some s tudies) i s a key parameter i n t h i s s c a l i n g . No study has been conducted on whether the b u r s t s c a l i n g i n an open c h a n n e l boundary l a y e r i s a f f ec ted by the presence of a free sur face , which i n e f f e c t imposes a l i m i t , i r r e s p e c t i v e of f e t c h , on the depth of the l a y e r . U n t i l t h i s matter i s c l a r i f i e d , and to avoid confus ion , the usual assumption for r i v e r flows i s best fo l lowed. Thus the boundary l ayer thickness w i l l be taken to correspond to the f u l l flow depth. In the June 13 study c o n d i t i o n s , with 10 m flow depth H and 1.4 m/s s u r f a c e ("free stream") v e l o c i t y U s , the convent ional Rao et a l (1971) s c a l i n g : T b U s / H = 3 to 7 p r e d i c t s a mean burs t recurrence p e r i o d T D between 20 and 50 s. This i s an order of magnitude below the value (8 min) computed from the June 13 data us ing the Wi l lmarth and Lu (1974) thresho ld s e t t i n g . As d i s c u s s e d p r e v i o u s l y , the bas i s and v a l i d i t y of these authors thresho ld was e s tab l i shed i n laboratory comparisons o f flow s igna l s over a range of dis tances from the w a l l (and thus cannot be fur ther v e r i f i e d h e r e ) . I t was claimed by the authors however to produce T D values cons i s tent with the outer flow s c a l i n g i n such f lows, and as such i s one of the few objec t ive and documented thresho ld c r i t e r i a a v a i l a b l e f o r (u 'v ' ) records away from the w a l l l a y e r . In a l l c o n d i t i o n s r e p o r t e d i n F i g . 20, outer flow s c a l i n g would have p r e d i c t e d r e c u r r e n c e p e r i o d s w e l l under 1 minute, much below 77 observed periods. 3.3 Modulation of turbulent bursting over bedwaves: a speculative i n t e r p r e t a t i o n of the above r e s u l t s . The previous analysis revealed the existence of intermittent and intense (u'v') events i n the study data. These events however appear to be l e s s frequent than expected according to conventional views of b u r s t i n g i n t h i s environment. In t h i s section, the possible r e l a t i o n between these events and c l a s s i c laboratory-scale b u r s t i n g w i l l be discussed. As explained i n chapter 1, the s p a t i a l l y l i m i t e d (one point) f i e l d data cannot c o n c l u s i v e l y s e t t l e t h i s issue. Since the usefulness of the bursting "model" to a l l u v i a l flows i s of basic i n t e r e s t to s t u d e n t s of r i v e r mechanics, speculation w i l l be attempted, based on the study data, on p o s s i b l e l i n k s between the study events and conventional bursting. Possible i n t e r p r e t a t i o n s of the stress events i n F i g . 16 that l a r g e l y deny the r o l e of c l a s s i c b u r s t i ng w i l l f i r s t be considered. I t could be argued that the presence of multi-scale boundary deformation (small bedforms over larger) i n t y p i c a l r i v e r flows may e f f e c t i v e l y drown out any d i s t i n g u i s h a b l e b u r s t i n g s i g n a l w i t h i n multiple scales of flow perturbations, eddy shedding i n the lee of bedforms, e t c . I f such were the case, i t might not even be a p p r o p r i a t e to t a l k of " i d e n t i f i a b l e b u r s t - l i k e events" i n the f l u v i a l context. The study observations do not p a r t i c u l a r l y support t h i s extreme view, however. Stress "events" i n the study data do not appear to be l e s s " d i s t i n c t " , i n a t e c h n i c a l sense, than those i d e n t i f i e d over simpler boundaries i n the laboratory. Very intense (u'v') events are quite i d e n t i f i a b l e i n the record from the Fraser River (Fig. 16). Moreover, the m u l t i p l i c i t y of scales of (u'v') events i n f l a t w a l l l a b o r a t o r y flows themselves must not be underestimated. I f two populations of (u'v') values (background 78 values and much less numerous Intense values) were c l e a r l y more d i s t i n c t (better separated) i n the laboratory than i n the r i v e r flows, a much higher kurt o s i s i n the (u'v') d i s t r i b u t i o n might be expected i n the former than i n the l a t t e r . However k u r t o s i s values i n laboratory flows (e.g. Antonia and Atkinson, 1973) were seen to be roughly comparable to those i n the study data (table 2) . A very g r a d u a l change i n b u r s t counts (and mean period) with (u'v') threshold, s i m i l a r to that documented on the Fraser ( F i g . 20), was also reported i n a lower Reynolds number, laboratory flow ( F i g . 21). In summary, s i g n i f i c a n t (u'v') "events" i n the study records appear neither c l e a r l y more nor le s s "conspicuous" or i d e n t i f i a b l e than they are i n laboratory flows. The parameters of t h e i r intermittence are quite s i m i l a r to those reported from other flows, even i f they appear to recur le s s frequently than expected. Could simple eddy shedding from the lee faces of dunes on the bed, a possible alternate generating mechanism f o r large scale eddies i n r i v e r flows (e.g. Rood and Hickin, 1989), be responsible f o r the s i g n a l s i n F i g . 16 ? Based on a s t r i c t d e f i n i t i o n of eddy shedding, the proposal seems u n l i k e l y . On the one hand, "shed" eddies t y p i c a l l y t r a v e l along the separation bubbles i n the lee of dunes, towards flow reattachment points; they are thus u n l i k e l y to be ejected upward away from the dune wake layer into the outer parts of the flow (and even appear as surface " b o i l s " , as argued by Rood and Hickin, 1989). I t i s possible rather that true burst structures, themselves propagating away from the bed, may t r i g g e r ( v i a pressure e f f e c t s ) eddy shedding as they t r a v e l from t h e i r i n c e p t i o n on the dune stoss side over the following dune separation zone. More t e l l i n g l y , i n d i v i d u a l b u r s t - l i k e events i n F i g . 16 have durations of 5 to 10 seconds, roughly matching the peak i n stress spectrum ( F i g . 15 b). I f due to turbulent e f f e c t s , such periods are w e l l w i t h i n the e n e r g e t i c turbulent range f o r which "Taylor's s c a l i n g h y p o t h e s i s " may be u s e f u l . I f , as hypothesised, the disturbances are indeed "shed" into the mean flow, given t h e i r periods they would represent structures of considerable streamwise 79 extent (5-10 s * 1 m/s = 5-10 m) convecting past the sensor at near mean flow v e l o c i t y . However, eddies shed from o b s t a c l e s by d e f i n i t i o n scale with the dimensions of the obstacles, and the l a r g e s t dunes present i n the Mission reach have heights of order 1 m only; such dune-shed eddies would l i k e l y be much smaller than the b u r s t - l i k e structures of length 5-10 m i d e n t i f i e d i n F i g . 16. Could bursting be responsible f o r the observed signals? I t appears to be accepted i n the f l u i d dynamics l i t e r a t u r e that burst structures are i d e n t i f i a b l e (despite d i f f i c u l t i e s ) and that t h e i r recurrence conforms to the outer s c a l i n g at l e a s t over 2 orders of magnitude of flow Reynolds numbers (Rao et a l . , 1971). Grass (1971) a l s o documented the existence of bursting over f l a t sedimentary boundary layers i n the laboratory, even when roughness disrupts the viscous sublayer. For lack of c l e a r evidence to the contrary, i t i s reasonable to assume that the bursting phenomenon may not be t o t a l l y repressed i n even higher Reynolds number r i v e r flows (the d e t a i l s of the process may be modified, of course). I f these assumptions hold, then one can t e n t a t i v e l y associate bursting with the large events i n F i g . 16. I t would remain to be seen, then, why burst passage at the sensors might be less frequent than i n laboratory conditions. I t can be argued that burst recurrence should be s i g n i f i c a n t l y a f f e c t e d by the presence of bedforms on the flow boundary. Busting a c t i v i t y i s s e n s i t i v e to downstream pressure gradients (Kline et a l . , 1967) and these are s p a t i a l l y v a r i e d near r i v e r dunes (e.g. Raudkivi, 1964). On t h e o r e t i c a l grounds, a degree of modulation of turbulent stress a c t i v i t y might be expected as bedforms advance r e l a t i v e to the f i x e d s ensor. T h i s m o d u l a t i o n would r e f l e c t the v a r i a b l e amount of b u r s t i n g a c t i v i t y that occurs on the area of bedform, whether stoss or lee, that happens to l i e j u s t upstream and generates most of the large motions passing the sensor at any moment. These t h e o r e t i c a l ideas f i n d some support i n published observations. Buckles et a l . (1984) document the superposition of eddy motions convected from the intense shear on the stoss side of 80 s i n u s o i d a l bedwaves and the wavy streamline f i e l d away from the bed. They show i n p a r t i c u l a r how any v e r t i c a l p r o f i l e of turbulence i n t e n s i t y over such a b e d f i e l d i s marked by successive maxima, corresponding to the free-shear layers detached from successive bedforms upstream, each r i s i n g o b l i q u e l y into the flow. Given advancing bedwaves and a f i x e d sensor, the existence of these layers of v a r i a b l e t u r b u l e n t i n t e n s i t y would modulate i n time the turbulence at the sensor, and presumably large burst passages. Other studies of the turbulent flow i n the v i c i n i t y of beds formed into pure s i n e waves have documented c y c l i c s p a t i a l v a r i a t i o n s i n turbulence i n t e n s i t i e s and Reynolds stresses i n the flow over these waves (e.g. McLean and Smith, 1979; Hsu and Kennedy, 1971). Iseya (1984) observed peaks i n v e r t i c a l turbulence i n t e n s i t y (variance of v') over the stoss sides of laboratory sand dunes when the flow sensor was j u s t over the l e v e l of wave c r e s t s . Itakura and K i s h i (1980) observed that bursting structures over laboratory sand waves occurred p r e f e r e n t i a l l y near the reattachment point on the stoss side and then convected outward, eventually passing over the back of the next waves. In t h i s way, a f i x e d sensor over advancing bedwaves might well be a f f e c t e d by c y c l i c modulations of turbulent burst a c t i v i t y . This p o s s i b i l i t y implies that mean burst p e r i o d i c i t y at a f i x e d sensor p o s i t i o n i n the f l u v i a l context could depend on r e l a t i v e l o c a t i o n of the sensors within the bedform geometry, bedform advance rates, i n a d d i t i o n to those outer flow parameters i d e n t i f i e d i n f l a t w a l l boundary l a y e r s . Such an outcome may e x p l a i n the a p p a r e n t l y anomalous recurrence periods observed on the Fraser River. The l o c a t i o n and movement of small bedwaves r e l a t i v e to the sensors could not be resolved with s u f f i c i e n t accuracy i n the study conditions to address these issues. 81 3.4 I s o l a t i n g purely turbulent contributions to momentum exchange There i s another p a r t i c u l a r i t y of the time s e r i e s of burst-l i k e motions above the Fraser River bed that i s worth reporting. The strong multi-minute flow cycles on which are superimposed the f a s t e r turbulent motions (cf. F i g . 11) impose a c h a r a c t e r i s t i c modulation of e j e c t i o n / i n r u s h motion which has not, to the author's knowledge, been reported elsewhere. During the multi-minute phases when the mean s t r e a m l i n e at the sensors i s downward, turbulent (higher f r e q u e n c y ) v' f l u c t u a t i o n s c onvected p a s t the sensor are superimposed on a negative minute-scale-average v' . The res u l t a n t measured v' f l u c t u a t i o n s are as a consequence biased negatively: upward motions are uncommon and downward ones are p r o p o r t i o n a l l y exaggerated. The opposite holds during minute scale periods when the average streamline points upward. The e f f e c t of t h i s modulation can be well seen i n F i g . 16. The low-passed u s i g n a l i s a v e r y good i n d i c a t o r of average streamline o r i e n t a t i o n i n a given period; t y p i c a l l y the flow i s a c c e l e r a t e d when o r i e n t e d towards the bed (nega t i v e v') and decelerated when i t tends to be oriented upwards ( p o s i t i v e v') (cf. F i g s 8, 9). While normally i n a boundary layer e j e c t i o n s and inrushes tend to occur i n rough sequence, strong inrushes i n F i g . 16 are sy s t e m a t i c a l l y grouped during periods of high u' (negative v') , and strong ejections during ones of low u' ( p o s i t i v e v ' ) . This modulating e f f e c t of the multi-minute flow cycles on the d i s t r i b u t i o n of ejec t i o n / i n r u s h events can be p a r t l y f i l t e r e d out, i n e f f e c t c o n c e n t r a t i n g a t t e n t i o n on the " b u r s t - s c a l e " turbulent v e l o c i t y f l u c t u a t i o n s and t h e i r c o n t r i b u t i o n to s t r e s s . To t h i s end, the u' and v' records were d i g i t a l l y high-passed (hp) f i l t e r e d , with a f i l t e r half-power point set at a period of 30 s to exclude most of the multi-minute flow o s c i l l a t i o n s . 82 The chosen f i l t e r of course cuts o f f much of the lower frequency turbulence (below n = 0.033) along with any longer non-turbulent o s c i l l a t i o n s . Nonetheless, ejections u s u a l l y documented at 1-2 m distances from the bed i n t i d a l flows have time-scales i n the 5-15 s range (Gordon and Witting, 1977; Heathershaw, 1979) and would thus "pass through" the f i l t e r . A smooth Gaussian f i l t e r was employed to extract the low frequencies. The instantaneous high-frequency c o n t r i b u t i o n to momentum exchange was then computed as the product of high-passed u' and v' signals (hp-u'*hp-v'). Fig . 22 presents a 14 minute time s e r i e s on June 13, 1988 of t h i s high frequency turbulent stress (1 second means) against l p -u' , the low-passed h o r i z o n t a l v e l o c i t y f l u c t u a t i o n s at the sensor p r e v a i l i n g at the same time. The mean kinematic stress due to these high frequencies i s 7.5 cm 2/s 2 approximately (down from 29 f o r the u n f i l t e r e d record). Intermittence of momentum exchange i s s t i l l o b vious, as i t i s co n c e n t r a t e d i n the burst-s c a l e high-passed components. While c l e a r l y much of the stress bearing frequencies have been f i l t e r e d out, the i n t e r e s t here i s not i n the t o t a l stress but o n l y i n the arrangement of the 5-15 s period intermittent "events", already v i s i b l e i n F i g . 16, once they have been extracted from the s t r o n g low-frequency flow o s c i l l a t i o n s . The e f f e c t i v e removal of the multi-minute u'v' f l u c t u a t i o n s from the v e l o c i t y r e c o r d s has s h a r p l y reduced the se g r e g a t i o n of ejections and inrushes discussed previously with reference to F i g . 16; these are more evenly mixed i n F i g . 22. Such an e f f e c t has not, to the writer's knowledge, been reported previously. 3.5 Summary of find i n g s . In summary i t can be stated that momentum exchange at 1 m o f f the bed i n the study conditions i s dominated by b r i e f but intense events, not unlike those seen i n laboratory and other F i g . 22: A 14 min time s e r i e s o f the h i g h - f r e q u e n c y c o n t r i b u t i o n s to momentum exch a n g e at s e n s o r l e v e l , a l o n g w i t h s i m u l t a n e o u s 1 o w - £ r o q ue nc y h o r i z o n t a l v e l o c i t y o s c i l l a t i o n s . Juno 1.3, 1988 d e p l o y m e n t . D a s h e d l i n e a t 10 t i m e s mean h i - f r e q u e n c y ' s t r e s s component <(hp - u '*hp-v')>. 84 l a r g e - s c a l e channel flows. In what way these events are r e l a t e d to b u r s t i n g i s d i f f i c u l t to e s t a b l i s h simply from event counts at one sensor l e v e l . The usual considerable s u b j e c t i v i t y i n the burst count approach ( e s p e c i a l l y i n d e f i n i n g an appropriate event threshold, c f . s e c t i o n 1.1) a f f e c t s the usefulness of the method as a bursting d i a g n o s t i c i n the f i e l d . A s s u m i n g t h a t the b u r s t - l i k e e v e n t s i d e n t i f i e d at 1 m on the Fraser R. are r e l a t e d to turbulent b u r s t i n g , and t h a t W i l l m a r t h and Lu's (1974) c r i t e r i o n i s indeedapplicable, the evidence presented above points to somewhat lo n g e r b u r s t r e t u r n p e r i o d s than conventionally expected. For sediment transport modeling, i t may be more p r a c t i c a l to recognise a continuous d i s t r i b u t i o n of intense stress events, t h e i r recurence perio d increasing with t h e i r r e l a t i v e magnitude ( c f . F i g . 20). The lack of s t r i c t conformity to the recurrence s c a l i n g of b u r s t events e s t a b l i s h e d i n the l a b o r a t o r y i s not t o t a l l y s u r p r i s i n g . The study flows are of much higher Reynolds number than laboratory models, and have a s l i g h t l y stable density s t r a t i f i c a t i o n due to sediment suspension. The presence of a c t i v e bedforms of various scales on the flow boundary may also i n v a l i d a t e the s c a l i n g c o n d i t i o n s e s t a b l i s h e d over f l a t walls i n the laboratory. The instantaneous l o c a t i o n of the sensor within the s p a t i a l l y modulated f i e l d of shear stresses and pressure gradients near r i v e r dunes i s l i k e l y , i n a d d i t i o n to the o v e r a l l outer flow parameters U and H, to a f f e c t the i n t e n s i t y and timing of recorded (u'v') events. A f i x e d flow sensor ov e r l y i n g an advancing dune f i e l d might for example see p e r i o d s of g r e a t e r and l e s s e r turbulent a c t i v i t y , depending on whether at any time i t l i e s close to, or well away from, the centre of the t r a j e c t o r y of the large structures convected from active b u r s t i n g zones. Such s p e c u l a t i o n would best be tested i n the laboratory where bedform motion can be more e a s i l y documented. CHAPTER 4 TURBULENT SEDIMENT SUSPENSION EVENTS The simultaneous time-series of t u r b i d i t y values provided by the O p t i c a l Backscatter Sensor (OBS) alongside the v e l o c i t y meter w i l l be analysed i n t h i s chapter to c l a r i f y the impact that flow f l u c t u a t i o n s of d i f f e r e n t frequencies have on sediment suspension 1 m from the bed of the Fraser River. The c e n t r a l issue i n t h i s chapter i s to what extent strong " e j e c t i o n - l i k e " motions passing through t h i s l e v e l c o r r e l a t e with peaks i n suspended sediment c o n c e n t r a t i o n , and what i s t h e i r r e s u l t a n t importance to t o t a l v e r t i c a l sediment f l u x . As i n p r e v i o u s c h a p t e r s , the main conclusions drawn on the basis of the data from June 13, 1988 w i l l be backed up by records from other deployments. The time ser i e s of OBS output p l o t t e d previously (Figs 8, 9, 11) i l l u s t r a t e d the existence of f l u c t u a t i o n s i n t u r b i d i t y l e v e l w i t h time s c a l e s e x t e n d i n g from seconds to tens of minutes. Furthermore these f l u c t u a t i o n s q u a l i t a t i v e l y displayed obvious c o r r e l a t i o n w i t h v e l o c i t y c y cles at corresponding frequencies. However, before analysing these r e l a t i o n s i n greater d e t a i l , the correspondence between OBS returns ( i n mV) and actual suspended sediment concentrations at sensor l e v e l must be c l a r i f i e d . 4.1 OBS output as a measure of suspended sediment concentration. As explained i n s e c t i o n 2.2.2, the OBS output must be c a l i b r a t e d to actual samples of suspended sediments c o l l e c t e d at sensor l e v e l . Although theory p r e d i c t s that OBS output increases l i n e a r l y w i t h c o n c e n t r a t i o n of any g i v e n s i z e f r a c t i o n i n suspension, the s e n s i t i v i t i e s are not the same f o r every f r a c t i o n w h i l e the p r o p o r t i o n s of c l a y s , s i l t s and sands i n near-bed 86 suspensions are expected to vary i n a complex way through turbulent events. Thus, the resultant f i e l d c a l i b r a t i o n regression between t o t a l suspended concentration and OBS returns over f u l l scale need not even be l i n e a r , u n l e s s the p r o p o r t i o n s of the d i f f e r e n t f r a c t i o n s are e s s e n t i a l l y f i x e d i n the study environment. In p r a c t i c e i t i s not p h y s i c a l l y f e a s i b l e to sample the suspension at the time r e s o l u t i o n which the o p t i c a l sensor can i t s e l f achieve. During the June 13, 1988 deployment near Mission, reasonably short duration (7 s) samples of the f l u i d were c o l l e c t e d j u s t behind the OBS sensor through a pipe intake of 1 cm i n t e r n a l diameter, w i t h an i n t a k e v e l o c i t y adjusted to match the mean h o r i z o n t a l flow v e l o c i t y at sensor l e v e l ( cf. F i g . 1, bottom). This procedure produced 27, h a l f - l i t r e samples which were f i l t e r e d i n the laboratory and analysed for the concentrations of suspensates of d i f f e r e n t s i z e f r a c t i o n s . By c a r e f u l l y recording the sampling period on deck and accounting for the sample t r a v e l time from pipe intake to the surface, the actual sampling period at the intake was derived with an accuracy of one second. This procedure i n turn allowed the mean OBS r e t u r n d u r i n g the i n t a k e p e r i o d , as w e l l as the corresponding mean h o r i z o n t a l and v e r t i c a l v e l o c i t y components, to be extracted from the records. F i g . 23 presents the p a r t i c l e s i z e a nalysis f or 27 samples gathered on June 13, between 14:00 and 20:19 hrs, along with the mean OBS return corresponding to each sample. Although samples are numbered i n time sequence the cycles evident i n the s e r i e s are s p u r i o u s , and r e f l e c t a l i a s i n g o f the intense high frequency c o n c e n t r a t i o n f l u c t u a t i o n s i n p h y s i c a l samples spaced tens of m i n u t e s a p a r t . D e s p i t e b e i n g u s u a l l y thought of as q u i t e h o m o g e n e o u s l y m i x e d and s t e a d y i n the water column, the concentration of s i l t s and clays (D<0.063 mm), conventionally taken as the washload, does vary somewhat i n harmony with coarser bed 87 S a m p l e n u m b e r Fig. .23: Grain size analysis and concurrent OBS response f o r 27, 7 second duration suspended sediment samples drawn behind the OBS unit. June 13, 1988 deployment. 88 TABLE 3 STATISTICAL DATA ON OBS CALIBRATION SUSPENDED SEDIMENT SAMPLES. N=30 June 13, 1988, near M i s s i o n F r a c t i o n r e t a i n e d on s ieve of g iven s i ze (wi th in stack) , (/xm) Mean CONCENTRATION DATA (mg/1) Standard dev. Coef. of Var . 355 250 180 90 63 pass ing 63 nm 4 86 112 108 27 103 2.6 44 38 25 5 7 0.65 0.51 0.34 0.23 0.19 0.07 PEARSON CORRELATION MATRIX Cd i s the concentrat ion re ta ined on s ieve s i ze d (pm) C355 C250 C180 C90 C63 C355 1.00 0.38 0.15 0.21 0.36 C250 1.00 0.41 0.25 0.28 C180 C90 C63 1.00 0.75 0.21 1.00 0.40 1.00 89 material f l u c t u a t i o n s (consider samples 5, 7 and 21 i n p a r t i c u l a r ) . Nonetheless the r e l a t i v e s t a b i l i t y i n s i l t and cla y concentration i s notable when compared to that of the coarser sand concentrations. Summary s t a t i s t i c s on the d i s t r i b u t i o n s of the d i f f e r e n t f r a c t i o n s i n Table 3 c l e a r l y show increasing c o e f f i c i e n t s of v a r i a t i o n (and i n most cases standard deviations) of concentration from the s i l t - c l a y to the medium sand f r a c t i o n s . Three samples included i n Table 3 were excluded from F i g . 23 because of corrupted OBS data. Furthermore the d i f f e r e n t sand f r a c t i o n s vary together c o h e r e n t l y : the c o r r e l a t i o n c o e f f i c i e n t s among the major sand f r a c t i o n s present (0.09<D<0.355 mm) range from 0.25 to 0.7. These r e l a t i o n s i l l u s t r a t e the e f f e c t that f a l l v e l o c i t i e s , as they increase with sediment s i z e , have on ease of suspension. On the one hand, hydraulic conditions that can suspend heavier p a r t i c l e s w i l l a l s o increase the concentrations of f i n e r materials, w i t h i n the l i m i t s of the l a t t e r ' s a v a i l a b i l i t y on the bed. Thus the p o s i t i v e c o r r e l a t i o n s between p r a c t i c a l l y a l l the f r a c t i o n a l weights. The coarser the f r a c t i o n however, the less stable and more dependent i s i t s s u s p e n s i o n on short l i v e d and randomly occurring hydraulic forces, and so the more v a r i a b l e i t s presence i n samples at sensor height, as seen i n table 3. The tendency f o r the d i f f e r e n t f r a c t i o n s i n suspension to va r y t o g e t h e r w i t h some degree of harmony leads to re s u l t a n t backscatter i n t e n s i t i e s which track t o t a l concentration reasonably well, as i s apparent i n the correspondence between the OBS return and t o t a l concentration s e r i e s i n F i g . 23. Indeed the c o r r e l a t i o n c o e f f i c i e n t between OBS return and t o t a l sample concentration i s 0.90 for the 27 samples. The sc a t t e r p l o t of t h i s r e l a t i o n i n F i g . 24 indicates that a l i n e a r regression model does produce a good f i t within the range of the data, with a standard error of estimate of the t o t a l concentration of 42 mg/1. A l b e i t imperfect, c a l i b r a t i o n s of sensor output f o r r a p i d concentration f l u c t u a t i o n s as i n F i g . 24 r e p r e s e n t the present state of the a r t , given the response of o p t i c a l or dynamic sediment concentration meters i n environments 90 " ~ 1 6 0 0 1 7 0 0 1 8 0 0 1 9 0 0 2 0 0 0 2 1 0 0 ' O B S r e t u r n ( m v ) -Fig. 24: Scatter plot and least square regression l i n e e s t a b l i s h i n g a c a l i b r a t i o n of OBS output i n terms of t o t a l sample suspended sediment concentration. June 13, 1988 deployment. 91 with v a r i a b l e mixtures of p a r t i c l e sizes (cf s e c t i o n 2.2.2). As i n other studies of suspension time s e r i e s (Soulsby et a l , 1984, 1985; West and Oduyemi, 1989), the a n a l y s i s of c o n c e n t r a t i o n spectra and sediment fluxes w i l l assume nominally accurate c a l i b r a t i o n s . Where appropriate, the p o s s i b l e e f f e c t s of c a l i b r a t i o n e r r o r s on study conclusions w i l l be discussed. The regression model of F i g . 24 implies that OBS output needs to vary by more than approximately 140 mV, based on 7 seconds samples, for a s s o c i a t e d concentrations to be s i g n i f i c a n t l y d i f f e r e n t (at 95% l e v e l ) . Thus, t y p i c a l peak to peak turbulent f l u c t u a t i o n s i n the OBS s e r i e s , w i t h amplitudes of the order of 150-400 mV (Fig. 11), represent r e a l f l u c t u a t i o n s i n concentration. A key a s s u m p t i o n i n t h i s s t u d y i s t h a t observed f l u c t u a t i o n s i n OBS output e s s e n t i a l l y r e f l e c t v a r i a t i o n s i n suspension of the sandy "bed materials" near the frame, rather than random "wash load" f l u c t u a t i o n s unrelated to l o c a l entrainment. This i s a concern since the OBS sensor i s d i s p r o p o r t i o n a l l y s e n s i t i v e to f l u c t u a t i o n s i n s i l t / c l a y concentrations. The p r e c i s e c a l i b r e of sediment defined as wash/bed material c u t o f f i s however somewhat a r b i t r a r y , as there i s i n r e a l i t y a f a i r l y broad t r a n s i t i o n i n b e h a v i o u r w i t h varying sediment s i z e . Furthermore the range of sediment s i z e s t r a n s i t i o n a l i n behaviour between wash and bed material depends on the sedimentary and hydraulic environment. McLean and Church (1986) argue that 0.125 mm, rather than the conventional 0.063 mm, constitutes a proper c u t o f f between bed material and wash loads on the Fraser River near Mission. They note that very f i n e sands, of c a l i b r e l e s s than 0.125 mm, represent only some 2% of bed materials i n t h i s reach and that t h e i r suspension shows c l e a r "exhaustion" e f f e c t s (hysteresis) during a t y p i c a l freshet. However, bed materials may have been marginally f i n e r i n the side channel of the Fraser River monitored and no precise wash load c u t o f f can be determined on the basis of the data of June 13. The sample data nonetheless indicate that even very f i n e sand contents (0.063 mm < D < 0.090 mm) appear to f l u c t u a t e coherently 92 with coarser f r a c t i o n s , suggesting that enough may be accumulated on or near the bed to make them responsive to l o c a l micro-scale hydraulic events. whatever c u t o f f i s used to define bed materials, the sample data e s t a b l i s h that observed OBS f l u c t u a t i o n s e s s e n t i a l l y r e f l e c t v a r i a t i o n s i n concentrations of f i n e and medium sands, presumably from entrainment at the bed l o c a l l y . While the c o r r e l a t i o n c o e f f i c i e n t between OBS output and the concentrations f i n e r than 0.063 mm i s o n l y 0.26, i t i s 0.85 with the concentration of suspended sands coarser than 0.090 mm. F i g . 25 presents the s c a t t e r p l o t and regression of t h i s l a t t e r r e l a t i o n : the standard er r o r of p r e d i c t i o n of concentration of "bed materials" coarser than 0.090 mm i s 49 mg/1. The marked ou t l y i n g point corresponds to sample 7 (Fig. 23) which was e x c e p t i o n a l l y poor i n s i l t s and clays and thus produced unusually low backscatter r e f l e c t i o n f o r i t s sand content. Note that the precise c u t o f f f i g u r e used here, 0.090 mm, should not be taken as the wash/bed material boundary. In part i t i s simply an a r t e f a c t of the choice of sieve sizes used i n the a n a l y s i s . The s a m p l i n g d a t a a l s o i n d i c a t e t h a t h i g h e r sand c o n c e n t r a t i o n s i n the samples tend to c o r r e l a t e with p o s i t i v e (upward) v e r t i c a l v e l o c i t i e s at the sensor ( c o r r e l a t i o n c o e f f i c i e n t of 0.33 between mean v e r t i c a l v e l o c i t y and concentration of sands coarser than 0.09 mm) as well as with h o r i z o n t a l v e l o c i t i e s that are below average ( c o r r e l a t i o n of -0.47). Since the l a t t e r s t a t i s t i c s are based on only 27 sample values w i t h i n one run (or flow) they are susceptible to s i g n i f i c a n t sampling error. I t i s i n t e r e s t i n g to note that over the ocean Phelps and Pond (1971) s i m i l a r l y found that turbulent f l u c t u a t i o n s i n a i r humidity content had c o r r e l a t i o n s of the order 0.3 with v' and -0.5 with u'. Although the above r e s u l t s are c l e a r l y compatible with the h y p o t h e s i s that upwelling events are responsible f o r suspending sands from the bed, such i s o l a t e d mean v e l o c i t y values do not allow the necessary d i s t i n c t i o n s to be made between the suspension e f f e c t s of turbulent motions at d i f f e r e n t frequencies, and i n p a r t i c u l a r Fig. 25: same as Fig. 24, for a calibration of OBS output in terms of the concentration of the sand fractions coarser than 0.09 mm. 94 those of burst-scale events. The l a t t e r analysis i s best conducted on the basis of the more complete time seri e s of v e l o c i t i e s and OBS output and w i l l be the subject of the next section. While the c a l i b r a t i o n errors i n the regression models are c l e a r l y r e l a t e d to f l u c t u a t i n g proportions of coarser sands i n the suspended samples, the l a t t e r v a r i a b l e i s not s i g n i f i c a n t l y c o r r e l a t e d with mean u or mean v conditions at the time of sampling. The c a l i b r a t i o n r e s u l t w i l l l a t e r be used to compute v e r t i c a l sediment fluxes (C'*v') based on the combined OBS and v records. 4.2 V e r t i c a l v e l o c i t y and sediment concentration f l u c t u a t i o n s at the 1 m l e v e l . S i n c e t h e s t r o n g e s t g r a d i e n t s o f mean s e d i m e n t c o n c e n t r a t i o n near the bed are v e r t i c a l , the v e r t i c a l v e l o c i t y f l u c t u a t i o n s r e s p o n s i b l e f o r mixing across t h i s gradient, and m a i n t a i n i n g sediment t r a n s p o r t i n the f a c e of sediment f a l l v e l o c i t i e s , have long been of main i n t e r e s t to the students of sediment transport mechanics. For such t h e o r e t i c a l reasons, the study w i l l focus on the r e l a t i o n s between the OBS and v' (rather than u') s i g n a l s . Although the simple mechanism of concentrated sands being thrown up by energetic bursting events i s the focus of t h i s enquiry, such events nonetheless have to be extracted from a complex background, i n v o l v i n g among other things strong multi-minute f l u c t u a t i o n s i n both OBS and v signals (cf. Figs. 8, 9). There i s no c l e a r evidence, based on the s p e c t r a l analysis reported i n sec t i o n 3.1, that any other process than boundary layer turbulence need be involved i n these multi-minute flow o s c i l l a t i o n s . Nonetheless, the existence of s i g n i f i c a n t multi-minute cycles i n suspension a c t i v i t y has not been extensively documented previously i n large r i v e r s . I t may q u a l i f y i n important ways the widespread view (e.g. Matthes, 1947; Jackson, 1976) that burst-scale events (here of duration 5-15 s, see sec t i o n 3.2) dominate sediment suspension. For these reasons, 95 the s t a t i s t i c a l association between the OBS and v signals w i l l be analysed f i r s t with respect to their different frequency bands. In a later section (4.4.2), the relative importance of the multi-minute motions to the aggregate v e r t i c a l suspension flu x w i l l be quantified. As i n the previous chapter, this frequency domain analysis of the signals w i l l be complemented by an analysis of suspension in terms of the timing and importance of discrete burst-like events, the main focus of this study. 4.2.1 S t a t i s t i c a l analysis of the relation between the v and OBS signals. In chapter 3 (Fig. 12) , a power spectrum of OBS response (dashed line) was superimposed on those of u and v fluctuations based on 2.2 hours of data from June 13, 1988 near Mission. The bulk of the turbidity oscillations occured at frequencies below 0.1 Hz (T>10 s) . In the atmosphere, spectra of scalar contaminants (e.g. temperature, humidity) are typically similar to that of the u component (e.g. Anderson and Verma, 1985); in the Mission data, the OBS spectrum appeared to be somewhat intermediate in shape between the u and v spectra, with a peak around n = 0.06-0.08. Clearly, numerous replicate OBS spectra must be acquired in further studies i f one wanted to verify any general similarity between the OBS spectrum and that of either u or v flow components for river flows. To the extent that v e r t i c a l flow motions drive sediment concentrations at sensor level, a degree of correlation between the OBS and v cycles is to be expected. However, are the multi-minute flow cycles as important as the burst-scale motions in "controling" suspension? This section w i l l start addressing this question, by investigating the s t a t i s t i c a l strength of the relation between the OBS and v fluctuations within broad frequency bands. To more accurately assess the relations between turbidity and multi-minute ver t i c a l motions, the analysis is based on the longest uncorrupted record available, from June 13, 1988. i 96 F i g . 26 presents time seri e s of 1 minute means of OBS output along with u and v v e l o c i t i e s , s t a r t i n g at 17:42 hrs on June 13, 1988. E s t i m a t e s of suspended sand concentrations (the f r a c t i o n coarser than 0.090 mm.) based on the regression model presented i n F i g . 25 are also included on the OBS scale. Cycles i n t u r b i d i t y of 3 to 5 minute period are apparent, as well as a strong p o s i t i v e r e l a t i o n w i t h multi-minute v e r t i c a l v e l o c i t i e s , and negative r e l a t i o n with h o r i z o n t a l v e l o c i t y cycles. Could the f l u c t u a t i o n s seen i n F i g . 26 be spurious; more p r e c i s e l y , could the multi-minute OBS response f l u c t u a t i o n s have not been caused by r e a l f l u c t u a t i o n s i n sand concentrations at the sensor but rather represent f l u c t u a t i o n s i n OBS c a l i b r a t i o n error ? The answer appears to be no. In sec t i o n 4.1, the change i n OBS output necessary to i n f e r a r e a l change of sand concentration (at 95%) was estimated at some 140 mV, based on 7 s samples. Although low-frequency OBS f l u c t u a t i o n s i n F i g . 28 are of the order of only 100 mV, they nonetheless probably denote true cycles i n sediment concentrations. The r e s i d u a l error l e v e l s i n the c a l i b r a t i o n models ( F i g s . 24, 25) r e f l e c t momentary f l u c t u a t i o n s i n s i l t / c l a y / s a n d p r o p o r t i o n s w i t h i n the 7 second-long suspension samples. Such f l u c t u a t i o n s i n sample composition, and the r e s u l t a n t c a l i b r a t i o n e r r o r l e v e l s , are l i k e l y to exaggerate uncertainty i n comparing longer based averages. I t has also been noted that the c a l i b r a t i o n errors about the regression l i n e ( F ig. 25) do not appear to be c o r r e l a t e d with the u or v v e l o c i t y conditions at the time of sampling, while the OBS f l u c t u a t i o n s i n F i g . 26 c l e a r l y are. Moreover, i f any s l i g h t c o r r e l a t i o n of c a l i b r a t i o n error with v e l o c i t y conditions existed (but was too weak to be revealed i n our sample), such c a l i b r a t i o n T ime ( m i n , f r o m 1 7 : 4 2 hr PST) VO Fig. 26: Concurrent time series of 1 rain means of U, V ^ and OBS output, based on 80 minutes of data from June 13, 1988 deployment. 98 errors would be expected to lead to underestimates of concentrations i n conditions of low u, high v, and vice-versa; the proportion of coarser sands i n the suspensions, and thus the c a l i b r a t i o n errors, should be increasing i n such conditions of upward flow (leading to underestimates of true concentrations). Thus the r e a l c o r r e l a t i o n s may be somewhat underestimated i n F i g . 26. A multi-minute p o s i t i v e c o r r e l a t i o n between sand concentrations and v v e l o c i t i e s appears to be r e a l . Although a f a i r degree of "coincidence" of the OBS output and v cycles i n F i g . 26 i s quite apparent, the absence of a strong p r o p o r t i o n a l i t y between t h e i r amplitudes produces a f a i r l y low c o r r e l a t i o n c o e f f i c i e n t ; the c o e f f i c i e n t i s 0.28 between the OBS and v s e r i e s (0.31 when both are de trended), and -0.50 between the OBS and u s e r i e s . The c o r r e l a t i o n s t a t i s t i c i s optimised f o r l i n e a r r e l a t i o n s between s e r i e s ; here cycles appear to have a strong c o i n c i d e n c e i n phase but a weak l i n e a r i t y ( p r o p o r t i o n a l i t y ) i n amplitude. Fi g . 27 compares i n more d e t a i l 18 minutes of OBS and v f l u c t u a t i o n s , a l s o s t a r t i n g a t 17:42 h r s on June 13, 1988. Conspicuous multi-minute cycles i n both records are again apparent even i n e s s e n t i a l l y " u n f i l t e r e d " s e r i e s (e.g. i n the f i r s t 10 minutes o f the OBS r e c o r d ) . Superimposed on 2 s. mean values (dashed) of OBS and v are serie s that have been low-passed ( s o l i d l i n e ) , with the same d i g i t a l f i l t e r (with half-power at 30 s, cf se c t i o n 3.4) used i n the preceding chapter to extract intense burst-s c a l e motions from background lower frequency f l u c t u a t i o n s . The r e s i d u a l s e r i e s around the s o l i d curves are thus high-passed (hp) "burst-scale" signals with f l u c t u a t i o n s of duration t y p i c a l l y 5-15 s (cf. F i g . 16). In a d d i t i o n to the p o s i t i v e c o r r e l a t i o n of 2-4 minute-scale ( s o l i d ) cycles of OBS output and v already seen i n F i g . 26, shorter period OBS and v cycles i n both the low and high-passed seri e s d i s p l a y a degree of p o s i t i v e c o r r e l a t i o n . Based on 2.2 hours of data the c o r r e l a t i o n c o e f f i c i e n t of high passed OBS i s 0.31 with the hp v Time (min. f rom 17:42 hr PST) F i g . 27: 18 min time s e r i e s of OBS output and v e r t i c a l v e l o c i t i e s , r e v e a l i n g high-frequency f l u c t u a t i o n s (dashed l i n e s ) superimposed on lower frequency o s c i l l a t i o n s ( s o l i d l i n e s ) i n both sig n a l s . June 13, 1988 deployment. Events l a b e l l e d A and B are discussed i n the text. *° 100 s e r i e s and -0.32 with the hp u s e r i e s . Detailed aspects of the higher-frequency l i n k s between the OBS and V signals w i l l be further d i s c u s s e d below. For now, i t can be concluded that a p o s i t i v e dependency between the OBS and v signals occured over a wide range of frequencies. W i t h i n a systemic "black box" type of approach to the s u s p e n s i o n process, the t u r b i d i t y s i g n a l at 1 m can be simply envisaged as a response to v e r t i c a l v e l o c i t y d r i v i n g forces through t h i s l e v e l . An i n t e r e s t i n g question wit h i n such a framework i s whether the t u r b i d i t y f l u c t u a t i o n s are more strongly r e l a t e d to the multi-minute flow o s c i l l a t i o n s or to the higher frequency motions. A qu a n t i t a t i v e answer w i l l depend on the form of r e l a t i o n envisaged. F a i r l y simple s p e c t r a l methods can give information on the degree of l i n e a r r e l a t i o n between two signals (here t u r b i d i t y and v e r t i c a l v e l o c i t y ) over t h e i r d i f f e r e n t frequencies. The coherence 2 function (Bendat and P i e r s o l , 1986) between the OBS and v s e r i e s f o r the main data run (Fig. 28) measures the degree to which the two signals are r e l a t e d as would be the input and output of a constant parameter l i n e a r system. (Two signals i n the same frequency band are coherent i f they have a constant amplitude and phase r e l a t i o n s h i p . To produce a c o r r e l a t i o n c o e f f i c i e n t of +1 the phase di f f e r e n c e also has to be n i l . In the absence of extraneous noise l i n e a r l y r e l a t e d signals would have a coherence squared of u n i t y at a l l frequencies, while two "unrelated" signals have coherence 0.) The black box approach depicted above overlooks of course that flow events both upstream and well below the sensor l e v e l , and hence not n e c e s s a r i l y included i n the v s i g n a l at the sensor, also influence the sediment content reaching the OBS u n i t . In t h i s sense, the monitored v s i g n a l i s one of many inputs d r i v i n g the suspension "system" and should not be expected to completely determine OBS output. A l t e r n a t i v e l y , both the OBS and v signals at 1 m may be seen as outputs of a complex system encompassing the whole flow, and driven by i n f i n i t e s i m a l i n s t a b i l i t i e s near the bed. 101 F i g . 28: Coherence'1 function analyzing the degree of l inear r e l a t i o n between OBS output and V f luctuat ions over d i f f erent frequencies. Based on 2.2 hrs of records from June 13, 1988. 102 The c o h e r e n c e ^ s t a t i s t i c d i s p l a y e d i n F i g . 28 can nonetheless be used to assess the average degree of coherence, and by i m p l i c a t i o n possible i n t e r r e l a t i o n , of the two signals over t h e i r d i f f e r e n t frequency components. Although based on 2.2 hrs of data (June 13, 1988) t h i s s t a t i s t i c between OBS return and v has a very high degree of random error (Bendat and P i e r s o l , 1986): the standard error f or the smooth f i t p l o t t e d i s of the order of 25% of the expected value. Thus i t i s unclear whether the dip i n coherence l e v e l f o r components of approximately 20 s period i s s i g n i f i c a n t . Two conclusions can be drawn from t h i s p l o t . F i r s t , as expected a r e l a t i o n between sand content as output and v e r t i c a l v e l o c i t i e s as d r i v i n g force can be envisaged although, as coherence i s much below 1, i t could be only crudely approximated as l i n e a r (or, equivalently, other upflow events, uncorrelated with measured v, a l s o d r i v e OBS output). Secondly, the l e v e l of a s s o c i a t i o n between the two signals appears to be at l e a s t as great f o r the multi-minute flow cycles (f<0.02 Hz) as f o r the f a s t e r turbulent o s c i l l a t i o n s . These r e s u l t s generally confirm the conclusions drawn above from a comparison of c o r r e l a t i o n c o e f f i c i e n t s between multi-minute and burst-scale (multi-second) components of the OBS output and v s e r i e s . To summarize, c o n t r a r y to what might be expected the t u r b i d i t y f l u c t u a t i o n s at the sensors are not completely dominated by higher frequency suspension events: rather these are imbedded i n strong concentration cycles t i e d to multi-minute flow o s c i l l a t i o n s . These f i n d i n g s w i l l be interpreted next i n terms of p l a u s i b l e mechanisms of suspension, and t h e i r sediment transport implications assessed. 103 4.2.2 High frequency turbidity fluctuations: a physical interpretation. Fig. 27 documented a s t a t i s t i c a l association between positive (upward) high frequency vertical motions and equally rapid increases in suspended sand contents (and vice-versa). This result f i t s common expectations. The lack of an exceptionally strong relation between such events is also interesting from a physical (process) sedimentology point of view. The correlation coefficient between high passed (hp) OBS and v series was 0.31. More tel l i n g l y , Fig. 27 displayed a number of strong upward motions (e.g. points marked A) that produce only moderate increases in turbidity, and conversely many strong peaks in turbidity (e.g. points marked B) not coincident with p a r t i c u l a r l y energetic upward flow, or even accompanying downward vertical fluctuations. Such discrepancies appear to be too large to simply reflect errors in predicting sand concentrations (of the order of 50 mg/1, section 4.1). Such a weak degree of association is quite typical in turbulence. A c o r r e l a t i o n of 0.3 is common between turbulent fluctuations i n v and scalar contaminants (e.g. temperature, humidity) in the atmospheric boundary layer (e.g. Phelps and Pond; 1971). The correlation coefficient between high-passed u and v series on the Fraser is i t s e l f only of the order of -0.4, and so many turbulent upwelling motions (v>0) are not only relatively poor in sediment but also f a i l to bring with them the expected d e f i c i t in horizon t a l momentum (u'<0). That such behaviour also affects turbulent suspension is thus not, a p r i o r i , surprising. W i t h i n any one flow r e c o r d , the r e l a t i o n between instantaneous vertical motion and sediment concentration at sensor height i s , understandably, extremely complex and predictable only in a s t a t i s t i c a l sense (as average associations over many eddy motions). The interpretation of sand suspension events based purely on Eulerian (one-point) data that w i l l be attempted here is at least 104 as uncertain as (and indeed t i e d to) the v i s u a l i z a t i o n of bursting motions from one-point observations. Dispersion of the suspended phase i s best understood from a Lagrangian point of view, where f l u i d parcels are tracked and allowances made for contaminant loads at t h e i r o r i g i n , and exchanges along the t r a j e c t o r y to any point. For example, although on average the sand content of a par c e l of f l u i d t r a v e l i n g upwards may be e n r i c h e d r e l a t i v e to i t s surroundings, i t s actual content w i l l depend on the recent h i s t o r y of suspension events upstream, as they a f f e c t the instantaneous (as opposed to average) concentration where i t s motion was i n i t i a t e d . Not a l l upward f l u c t u a t i o n s at the sensors correspond to flow parcels d i r e c t l y o r i g i n a t i n g from near the bed, or ejected at a time when near-bed concentrations need have been p a r t i c u l a r l y high. "Sweep" or " i n r u s h " motions (u'>0, v'<0) near the bed may temporarily decrease l o c a l sand concentrations so that ejections or outward i n t e r a c t i o n s immediately a f t e r the sweep might b r i n g up less sediment than average. A further complication i n i n t e r p r e t i n g the si g n a l s r e s u l t s from the submerged weight of suspended sands: contrary to a passive chemical or p h y s i c a l contaminant, f o r example, sand p a r t i c l e s f a l l out of suspension and do not i n general stay long associated with the flow parcels that carry them (cf. the "crossing t r a j e c t o r i e s e f f e c t " ; Lumley, 1976; Yudine, 1959). Thus the sand content of a flow p a r c e l crossing the sensor depends not only on the i n i t i a l concentrations at the o r i g i n of i t s motion but also on the distance t r a v e l e d and v e l o c i t y h i s t o r y of the p a r c e l along i t s t r a j e c t o r y . In p a r t i c u l a r , ejected sands do not disappear when the forces that l e d to t h e i r suspension are spent, and as they r a i n down they may even produce t u r b i d i t y peaks i n downward flow parcels. The high-passed records seen as r e s i d u a l s around the s o l i d l i n e s i n F i g . 27 mainly reveal 1-10 m scale eddy motions, those responsible f o r seconds-scale u, v f l u c t u a t i o n s i n flows where mean v e l o c i t i e s are of order 1 m/s. I t can be argued, h e u r i s t i c a l l y , that eddy motions of t h i s scale that happen to involve at the same time 105 strong upward flow with strong h o r i z o n t a l d e c e l e r a t i o n are the ones most l i k e l y to ori g i n a t e from the low momentum zones c l o s e r to the r i v e r bed, and thus l i k e l y to carry greater concentrations of suspended sands. The hypothesis appears to be v e r i f i e d based on the. 2.3 hours of hp-u, hp-v, hp-OBS data (from June 13, 1988) analysed. For example the mean increment i n hp-OBS (high-passed s e r i e s ) during p e r i o d s when hp-v e x c e e d s +3 cm/s and hp-u i s n e g a t i v e (corresponding to an e j e c t i o n motion) i s +40 mV (s.d.=48 mv, N=415), while i t i s only +10 mV (s.d.=46, N=161) under the same v conditions when hp-u i s p o s i t i v e (outward i n t e r a c t i o n ) . These means are s i g n i f i c a n t l y d i f f e r e n t at the 1% l e v e l . F i g . 29 presents a smoothed response surface drawn through the h i g h l y s c a t t e r e d c l o u d o f hp-OBS, hp-u and hp-v values, associated with every 2 s period i n 2.2 hrs of record. As can be c l e a r l y seen, a greater d e f i c i t i n h o r i z o n t a l momentum (hp-u < 0) al o n g w i t h sudden upward flow (hp-v>0) leads to the greatest momentary increase i n t u r b i d i t y (hp-OBS>0). I n t e r e s t i n g l y , there i s an i n d i c a t i o n that midscale changes i n u or v produce the greatest marginal changes i n t u r b i d i t y and that, beyond these, there may be a tapering o f f of the suspension e f f e c t at the 1 m l e v e l . A planar least-squares f i t through these observations takes the form: (hp-0BS)= -0.9+ 4.7 (hp-v) - 3.3 (hp-u) and, by adding the (hp-u) v a r i a b l e , the multiple c o r r e l a t i o n c o e f f i c i e n t between (hp-OBS) and flow v a r i a b l e s increases from 0.31 to 0.48. As argued above, upward parcels that have a stronger d e f i c i t i n u v e l o c i t y (and so are thought more l i k e l y to have j u s t o r i g i n a t e d from near bed) are the ones that s t a t i s t i c a l l y tend to br i n g up higher concentrations to sensor l e v e l . 106 F i g . 29: Smoothed surface of (hp-OBS) responses ( in mV) d u r i n g 2 s p e r i o d s w i th v a r i o u s i n t e n s i t y of rapid (turbulent) U and V f luctuations (hp-U' and h p - V ) ( in cm/s). The l a t t e r values are rounded to s impl i fy d i sp lay . Based on 2.2 hrs of records from June 13, 1988. 107 In contrast to t h i s simple p i c t u r e of b u r s t - s c a l e turbulent suspension events, the r e l a t i o n between multi-minute t u r b i d i t y and f l o w o s c i l l a t i o n s ( F i g . 26) may r e q u i r e more c a r e f u l l i n t e r p r e t a t i o n . The view o c c a s i o n a l l y taken t h a t these slow disturbances simply r e f l e c t turbulence was argued previously to have troublesome implications. The extension of the simple eddy concept, advected at roughly mean flow v e l o c i t y , to t h i s scale of motion may not be j u s t i f i e d . Alternate i n t e r p r e t a t i o n s would depend on slow f l u c t u a t i o n s of mean streamlines at the sensor due to l o c a l bed changes ( c f s e c t i o n 2.6). 4.3 Recurrence analysis of high suspended sediment concentrations Before i n v e s t i g a t i n g the suspension e f f i c i e n c y of burst-l i k e motions, the recurrence of high sediment concentration "events" a t t h e s e n s o r w i l l be a n a l y s e d . I f i n t e r m i t t e n t i n t e n s e c o n c e n t r a t i o n events are i n o p e r a t i o n , i n f o r m a t i o n on t h e i r recurrence i s important. An approach complementary to t h i s analysis of simple high concentration events w i l l be explored i n a coming section: there, the recurrence of events characterised by intense sediment f l u x , v e r t i c a l l y through the sensor l e v e l , w i l l be studied along l i n e s s i m i l a r to that of intense momentum exchange events discussed i n chapter 3. A number of problems i n analysing the s e r i e s of OBS returns f o r high concentration events must be addressed. The f i r s t i s the i n a c c u r a c y and p o s s i b l e b i a s i n the c a l i b r a t i o n o f sediment concentrations, obtained i n s e c t i o n 4.1, f o r extreme values of OBS output. Predicted extreme concentrations are nominal, as such high OBS returns as w i l l be considered i n much of t h i s a n alysis were not accounted f o r i n the c a l i b r a t i o n samples, and often r e f e r to events l a s t i n g much less than the 7 s c a l i b r a t i o n sampling. Thus actual values of extreme sediment concentration proposed below amount to i i 108 strong extrapolations of the a v a i l a b l e regression model. Based on the patterns discussed i n section 4.1, h i g h l y t u r b i d parcels may be p r o p o r t i o n a l l y enriched i n sands r e l a t i v e to s i l t s and clays, and use of the regression models would thus lead to underestimates i n the case of extreme sediment concentrations and fluxes. I t must also be noted that, i n p r i n c i p l e , return periods f o r extreme OBS values may depend considerably on a choice of sensor c u t o f f i n the frequency domain. While the c o n t r i b u t i o n s of frequencies above 1 Hz (the nominal a l i a s i n g f i l t e r c u t o f f i n t h i s study) to v e l o c i t y spectra and e s p e c i a l l y momentum exchange are inherently minor, a complete o p t i c a l t u r b i d i t y spectrum might behave d i f f e r e n t l y . In t h i s study, low-pass f i l t e r i n g of the OBS output i n the f i e l d assured that l i t t l e power occured above 2 Hz ( F i g . 12). However, an u n f i l t e r e d OBS unit's inherently high frequency and wavenumber responses could react to the f i n e r - s c a l e texture of l o c a l c o n c e n t r a t i o n s , p o t e n t i a l l y p r o d u c i n g g r e a t e r i n s t a n t a n e o u s v a r i a b i l i t y (as i n d i v i d u a l passages of sand p a r t i c l e s a f f e c t the cm scale sampling volume of the OBS). Two second means of OBS output were retained i n the following recurrence analysis to allow only OBS cycles longer than 4 s to appear; any f l u c t u a t i o n s f a s t e r than t h i s c u t o f f were thought u n l i k e l y to correspond to large scale b u r s t i n g motions. F i g . 30 presents a 100 minute s e r i e s of smoothed u, v components from June 13, 1988, along with those peaks i n 2 s mean OBS return that exceed 2100 mv. This i s a moderately high t u r b i d i t y threshold ( c f . F i g . 27), s u i t a b l e to i l l u s t r a t e the t y p i c a l pattern of recurrence of high concentrations. This value of OBS output nominally corresponds to sand (D>0.09 mm) concentrations of 590 mg/1; i t i s exceeded only 3.4% of the time i n 2.2 hrs of the 2 s mean OBS s e r i e s . The high concentration events displayed i n F i g . 30 are generally associated with minute-scale periods of high v and low u i n the low-passed v e l o c i t y s e r i e s . This a s s o c i a t i o n i n large part r e f l e c t s the f a c t that under such conditions low-passed OBS returns are themselves highest (cf. section 4.2.2 and F i g . 26), and so the OBS output (mv) 2000 I I I I I I I L . 2200 ' i ' ' i i i i—i_ 2400 i I i 2600 -i i i i i i i I SB H - (D 3 r t O O- 3" O i-l o o 3 CD , If 3- & c H » I 3 o a H -CO 05 CO • 3* CD (_o O. o > 3 CD CO M O H , ° o • a c 3 i-h CD t—' c 1*1 r t (11 vo o OO 3 oo M Q, '—v CD t—' -a o M £ O • >o S to CD Co 3 CO rt CD • & CO ' H> CD ?r » CD CO o „ o Co co «; s i* a r t co V O w <; H * CD 3 i-l C ro O O * 3 | " O O bS. CD O O NO < c CD - w r o ~ ° ,CD ° C D S 3 2-CD 5 w < o CO C/) 60T o-1 °-10 -5 0 5 10 ,1 I I i I I I V (cm/s) 75 85 95 105 115 [ I i I I I i I 1 1 I I i I t I i i 1 I 1 1 I ( c m / s ) 110 b r i e f increases i n t u r b i d i t y caused by ejections occur on already high base t u r b i d i t y l e v e l s . In s e c t i o n 4.2.2, e j e c t i o n s (hp-u'<0, hp-v'>0) t h a t contribute strongly to momentum exchange at the sensor were seen to produce large t u r b i d i t y increases. Nonetheless, F i g . 30 suggests that the timing of strong turbulent ejections does not, of i t s e l f , completely determine that of exceptional concentration events. The presence of strong low-frequency t u r b i d i t y cycles, underlying these higher frequency f l u c t u a t i o n s , also c l e a r l y a f f e c t s the recurrence of absolute peaks i n sand concentrations at the 1 m l e v e l . 4.4 Horizontal and v e r t i c a l suspended sediment fluxes at sensor l e v e l . The simultaneous concentration and v e l o c i t y data w i l l now be combined to produce time s e r i e s of h o r i z o n t a l or v e r t i c a l suspended sediment fluxes at the sensors. This analysis w i l l allow estimates to be made of the mean fluxes, and more importantly the s p e c t r a l c o n t r i b u t i o n to these fluxes from motions i n the d i f f e r e n t frequency bands. Following the p r a c t i c e of e a r l i e r chapters, time s e r i e s of instantaneous fluxes w i l l also be analysed for large i n t e r m i t t e n t contributions. In p a r t i c u l a r , i t w i l l be p o s s i b l e to quantify the e f f i c i e n c y , i n terms of v e r t i c a l sediment transport, of turbulent ejections of various l e v e l s of i n t e n s i t y , an important objective of t h i s study. 4.4.1 An analysis of the v e r t i c a l sediment f l u x . The primary p r o c e s s of i n t e r e s t i n t h i s study i s the v e r t i c a l mixing of sediments across the sensor height. I t i s u l t i m a t e l y responsible f o r maintaining, despite the tendency of the sediment to f a l l out of suspension, a mean sediment concentration away from the bed, and thus a s u b s t a n t i a l downstream transport of I l l sediment along with the flow. The s t a t i s t i c a l a s s o c i a t i o n seen p r e v i o u sly of higher sediment concentrations with upward moving flow parcels, and lower concentrations with downward moving ones, implies prima-facie a net upward f l u x of sediment through the sensor l e v e l . Simultaneous OBS and v data can y i e l d an estimate of t h i s f l u x . In r e a l i t y , however, t h i s t h e o r e t i c a l "mixing" f l u x (due to sediment mixing by turbulent or other v e r t i c a l motions) i s reduced or may even be reversed by the tendency of the upward v e l o c i t i e s of the sands to be systematically s m a l l e r than t h a t o f the upwelling flow parcels (and downward v e l o c i t i e s h i g h e r ) , the more so the coarser the sediment (the greater i t s f a l l v e l o c i t y ) . Since only the v e r t i c a l flow v e l o c i t i e s and not the actual p a r t i c l e v e l o c i t i e s were monitored, the net e f f e c t of the f a l l v e l o c i t i e s must be f i r s t assessed, at l e a s t approximately, i f information on v e r t i c a l suspension fluxes i s to be gained. I t i s u s e f u l conceptually to separate the net v e r t i c a l sediment f l u x i n t o a nominal mixing component, here estimated through the covariance of the OBS and v s i g n a l s , and a f a l l v e l o c i t y component. A s i m i l a r , although le s s d e t a i l e d analysis can be found i n Soulsby et a l . (1985). In uniform two-dimensional flow (and sediment transport) conditions, the net v e r t i c a l sediment f l u x would be n i l , the r e s u l t a n t of a mean upward mixing f l u x and an equal downward sedimentation f l u x . The l a t t e r depends only on the mean sediment concentration and f a l l v e l o c i t y at sensor height. To f o r m a l i s e : i f i s the concentration of sands of c a l i b r e d ( f a l l v e l o c i t y : w^) i n a flow p a r c e l t r a v e l l i n g with a v e r t i c a l v e l o c i t y v, then assuming that the v e r t i c a l a c c e l e r a t i o n of the pa r c e l i s much smaller than g, the sand grain's actual v e r t i c a l v e l o c i t y i s approximately (v-w^) (Nielsen, 1984). Thus: (1) Cd( v" wd) 112 represents the v e r t i c a l f l u x of that sand f r a c t i o n at that l o c a t i o n and instant. Assuming steady-uniform flow conditions, i t s long-term mean v e r t i c a l f l u x through the sensor l e v e l i s : Cd (v-wd) ' 0 (here X i s a long term mean of a se r i e s X at the sensor). I t follows that under such conditions the long term mean concentration of that f r a c t i o n above sensor h e i g h t i s constant. Breaking the sand concentration into i t s mean and f l u c t u a t i n g parts: Cd = ^d + C d one finds that the net v e r t i c a l f l u x can be expanded to: (Cd + C d) (v - wd) = C d v - C d wd + C d v - C d wd = C d v - Cd" wd since v = C^ = 0 Thus f or each f r a c t i o n the net v e r t i c a l f l u x i s the sum of a mixing f l u x due to v e r t i c a l flow motions ( C d v ) , and a passive sedimentation f l u x (Cd wd) that on average depends on mean concentrations at sensor l e v e l and f a l l v e l o c i t y . Adding up these net fluxes f o r a l l the suspended f r a c t i o n s indexed by c a l i b e r d one obtains a t o t a l f l u x : S (Cd~^) - S (Cd" w d) - v (S C d) - (2 C^) w* where summations are over siz e f r a c t i o n s d and w i s a weighted mean f a l l v e l o c i t y : w* = (2 Cd w d) / (ECd") 113 Thus, the o v e r a l l net v e r t i c a l f l u x can be expressed as: v C' - C w* where C represents t o t a l concentration. The t o t a l f l u x over a l l f r a c t i o n s can thus be again expressed as the dif f e r e n c e between a flow driven mixing f l u x and a passive sedimentation f l u x . Since the mean sedimentation f l u x depends only on mean p r o p e r t i e s of sediment c o n c e n t r a t i o n s and f a l l v e l o c i t y , the contributions of the d i f f e r e n t frequencies of flow motions to the net f l u x occur through the mixing f l u x covariance term (v G » ) . F u r t h e r , assuming t h a t the l i n e a r r e g r e s s i o n model f or sand concentration as a function of OBS return (denoted "OBS") i s exact over the e n t i r e observed range of returns (more p r e c i s e l y that i t s error i s uncorrelated with v, as appeared to be the case i n the study samples, c f . s. 4.1): C = a OBS + b one can estimate t h i s t o t a l "mixing f l u x " by the covariance: (2) v C" = a (v OBS") and the net v e r t i c a l sediment f l u x becomes: (3) a (v OBS") - C w* How well do such i d e a l i z a t i o n s f i t the study conditions near Mission? The above analysis assumes s t a t i s t i c a l l y steady and uniform flow conditions and sensor data averaged over a large number of the longest wavelength bedforms present. Such assumptions do not s t r i c t l y h o l d i n t h i s study ( c f. sec t i o n 2.4). In such i d e a l c o n d i t i o n s , s i n c e the upward mixing f l u x exactly balances the downward sedimentation f l u x , the res u l t a n t v e r t i c a l f l u x i s n i l and constant mean concentrations occur above sensor height. However the 7 hour time ser i e s of OBS output presented i n chapter 2 (Fig. 8) reveals multi-hour f l u c t u a t i o n s and a possible long term d e c l i n i n g trend i n concentrations (of the order of 5 mg/1 per hr) at sensor 114 height during the survey. Equation (3) applied to the June 13, 1988 data f o r the sand f r a c t i o n (D > 0.09 mm) pr e d i c t s a 1 hour mean upward mixing f l u x of the order of 3 g/nr- s, counterbalanced by a s u b s t a n t i a l l y bigger downward sedimentation f l u x of the order of 9 g/mz s. The weighted mean f a l l v e l o c i t y w appearing i n (3) was computed based on the mean proportions of the d i f f e r e n t sediment f r a c t i o n s i n the sampled suspension at sensor l e v e l ( s e c t i o n 4.1), u s i n g s t a n d a r d curves, adjusted f o r water temperature, of f a l l v e l o c i t i e s against sediment s i z e f o r r i v e r sediments. The error i n t h i s estimate of w cannot be large enough (300%) to account f o r the imbalance between the two terms of (3). T h i s imbalance might r e f l e c t i n c i p i e n t l o c a l sediment d e p o s i t i o n , r e l a t e d to the approach of a large bedform. I t i s i n t e r e s t i n g to note t h a t Soulsby et a l . (1985) also obtained downward net v e r t i c a l fluxes, using a s i m i l a r method from sensor data at 17 and 33 cm above the c r e s t of a dune i n a t i d a l flow. These authors in t e r p r e t e d t h i s f i n d i n g to r e f l e c t a streamwise non-uniformity i n transport, r e l a t e d to c r e s t advance. Int e r p r e t i n g such a non-zero net f l u x should be done with caution, however. Lack of e q u i l i b r i u m between the two v e r t i c a l fluxes i n (3) could also occur i n stable, neither er o s i o n a l nor de p o s i t i o n a l environments, and be due to v i o l a t i o n s of other assumptions basic to the ana l y s i s . Poorly understood deviations from the assumed f a l l v e l o c i t i e s i n (1) for sediments wi t h i n turbulent parcels, or i n the OBS c a l i b r a t i o n i m p l i c i t i n (2) may severely bias t h i s computational method. I t i s p o s s i b l e , f o r example, that f o r many v i o l e n t v e r t i c a l motions, c o n t r i b u t i n g s i g n i f i c a n t l y to the mixing f l u x covariance, actual c o n c e n t r a t i o n s have been s y s t e m a t i c a l l y underestimated. F i e l d c a l i b r a t i o n models f o r a c o n c e n t r a t i o n sensor are n e c e s s a r i l y adjusted to moderate, longer duration events. More work appears to be required before the approach embodied i n (3) can y i e l d accurate r e a l - t i m e a s s e s s m e n t s of l o c a l a g g r a d a t i o n or d e g r a d a t i o n conditions. 115 Even where s teady/uniform transport conditions are not r e a l i s e d , however, the i n t e n s i t y of the upward mixing f l u x of sands (2) due to v e r t i c a l flow motions i s a key determinant of the concentration p r o f i l e : higher fluxes tend to be balanced by the s e t t l i n g of greater sand concentrations above sensor height. The r e s u l t i s higher concentrations away from the bed where h o r i z o n t a l v e l o c i t i e s are greater, and so larger suspended sediment transport rates. In t h i s way the processes behind the mixing f l u x strongly c o n t r o l the amount of suspended sediment transport. The question next addressed w i l l thus be: what are the r e l a t i v e contributions of f a s t e r b u r s t - l i k e motions and multi-minute flow o s c i l l a t i o n s to the net mixing f l u x 1 m from the bed? To answer t h i s question, the OBS and v time seri e s w i l l be analysed s p e c t r a l l y f o r the frequency contributions to the mixing covariance term (2) . Because of u n c e r t a i n t i e s j u s t mentioned i n the v a l i d i t y o f assumptions l e a d i n g to (2) , the r e s u l t s can be taken only as i n d i c a t i o n s of the r e l a t i v e importance of these processes. 4.4.2 The frequency contributions to the net v e r t i c a l mixing f l u x . F i g . 31 p r e s e n t s a cospectrum o f OBS output and the v e r t i c a l v e l o c i t y component. I t shows the contributions to the mixing f l u x (2) of the two signals from d i f f e r e n t frequency bands. The area-preserving p l o t i s based on 2.3 hours of data on June 13, 1988, and estimates were smoothed to a frequency r e s o l u t i o n of 0.0049 Hz. The whole spectrum accounts f o r the mean covariance of 23, 13.6 min long ( 2 ^ 2 points) time segments (each detrended and tapered). Because of the weak coherence between the two signals (coherence squared i s of the order of 0.1, F i g . 30) these smoothed cospect r a l estimates are a f f e c t e d by r e l a t i v e l y high random error; the standard error of estimate here i s of the order of 25% of the estimate. 116 E o > E in m o C O c O CD CD-CO o O * O On cn o . in CN 0 + m CM-I I o m-l T = 1 min cr CD m J u . i Frequency |resolution: 0.00488 hz Standard error for densities: 25» (approx.) i i i i i 11 h 1 — i i i i i 11 1 1 i i i i 1 1 1 0.01 0.1 F r e q u e n c y (hz ) 1 F i . 31: OBS, v cospectrum based on 2.2 hrs of records from June 13, 1988. 117 The c o n t r i b u t i o n o f f l o w f l u c t u a t i o n s l o n g e r than a p p r o x i m a t e l y 1 minute to the t o t a l v e r t i c a l sediment f l u x integrates to approximately 30% of the t o t a l , based on the area under the cospectrum. This r e s u l t i s of the same order as the co n t r i b u t i o n to momentum exchange of flow cycles longer than 1 min ( s e c t i o n 3.1). The c o s p e c t r a l a n a l y s i s thus q u a n t i f i e s the observation made previously that sediment suspension at the 1 m l e v e l , r a t h e r than b e i n g c o m p l e t e l y dominated by burst-scale turbulent e f f e c t s , i s i n important measure also driven by multi-minute flow perturbations. The r i v e r sedimentologist surprised by th i s r e s u l t should again bear i n mind that large low frequency contributions to v e r t i c a l contaminant fluxes such as temperature or humidity are not unusual i n the turbulent boundary layer over the ocean (e.g. Pond et a l , 1971; i n our data, T= 1 min corresponds to n «= 0.017). The cospectral peak near f=0.1 Hz nonetheless indicates that 10 s scale turbulent events dominate the o v e r a l l mean sediment f l u x , as they d i d the momentum f l u x analysed i n the previous chapter (F i g . 15). 4.4.3 Intermittent high sediment f l u x events. As was done i n the previous chapter with momentum exchange, i t i s possible to i s o l a t e f o r analysis b u r s t - s c a l e v e r t i c a l sediment f l u x events embedded within the multi-minute flow o s c i l l a t i o n s . T h ese e v e n t s a r e d i s t i n c t f r o m t h e simple h i g h sediment c o n c e n t r a t i o n events previously analysed i n s e c t i o n 4.3; t h e i r i d e n t i f i c a t i o n involves both OBS and v data. F i g . 32 presents a time s e r i e s of high-passed (hp; c u t o f f at T= 30 s) contributions to the v e r t i c a l "mixing f l u x " <0BS'*v'> from June 13, 1988. Also displayed f o r comparison are the low-frequency (low-passed: lp) v e r t i c a l Time (min, f rom 17:42 hr. PST) F i g . 32: A 22 min s e r i e s of h i g h - f r e q u e n c y c o n t r i b u t i o n s to v e r t i c a l s e diment m i x i n g (hp-OBS*hp-V ' ) and momentum exchange (hp-U'*hp-V') , along with low frequency f l u c t u a t i o n s i n V. June 13, 1988 deployment. E and I are " e j e c t i o n s " and " i n r u s h e s " . + and - events, r e s p e c t i v e l y , b r i n g up sediment - r i c h and b r i n g down sediment - poor flow p a r c e l s across the sensor l e v e l . 119 v e l o c i t y f l u c t u a t i o n s and the simultaneous turbulent (hp) momentum exchange s e r i e s . While major momentum events are l a b e l l e d as e i t h e r ejections (E: u'<0, v>0) or inrushes ( I : u'>0, v<0), two kinds of burst- s c a l e events strongly contribute to enrichment i n sediment of the flow above sensor l e v e l . These w i l l be named p o s i t i v e type (when high concentrations go upward) or negative type events (when low concentration flow parcels are brought down out of the upper flow). Although the correspondence between ejections and p o s i t i v e events, or i n r u s h e s and negative, i s f a i r l y good the r e l a t i v e c o n t r i b u t i o n of a given event to e i t h e r f l u x does not s t r i c t l y match. Possible reasons f o r t h i s were given i n a previous section: a moderate e j e c t i o n i n terms of momentum exchange (e.g. at 4.1 min) could f o r example o r i g i n a t e from, or pass through, an area that happens to be quite enriched i n sediment due to upstream events, and so contribute i n a major way to sediment mixing. T h i s e f f e c t can a l s o be observed i n F i g . 33, which c o n t r a s t s the sediment and momentum mixing c o n t r i b u t i o n s of i n d i v i d u a l 2 s periods during e j e c t i o n s . For these events, the c o r r e l a t i o n c o e f f i c i e n t between the two f l u x contributions i s 0.45, based on 2.2 hrs of data, and very strong sediment mixing can be associated with f a i r l y weak events i n terms of s t r e s s . The true l e v e l of c o r r e l a t i o n i s again degraded somewhat by the existence of random errors i n r e l a t i n g instantaneous OBS values to suspended concentrations. Despite t h i s lack of correspondence between the two k i n d s o f f l u x e s , which may also be r e l a t e d to the t r a j e c t o r y c r o s s i n g e f f e c t d i s c u s s e d i n s e c t i o n 4.2.2, major periods of a c t i v i t y i n F i g . 36 nonetheless coincide i n each s e r i e s . An i n d i c a t i o n of how e f f e c t i v e occasional strong ejections are i n maintaining suspension l e v e l s i s given by a compilation of t h e i r aggregate c o n t r i b u t i o n to the high-frequency part of the "mixing" f l u x (hp-0BS*hp-v) (which here i s 40% of the t o t a l mixing f l u x when a l l frequencies are included). F i g . 34 presents a ranking i i c u •5 I !/) w C CD ^ CL > cn CO o O -o _ O O o -Stress vs suspension efficiency of individual 2 s intervals during ejections u > - 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 - 1 5 0 - 1 2 5 - 1 0 0 - 7 5 - 5 0 - 2 5 0 (hp-U' • hp-V) (crnVs2) S t r e s s Fig. 33: Scatter plot comparing the high-frequency stress bearing and sediment mixing e f f i c i e n c i e s of in d i v i d u a l 2 s periods chosen during turbulent ejections. Based on 2.2 hrs of records from June 13, 1988. 121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 -140 -120 -100 -80 -60 -40 -20 0 (hp -U ' * h p - V ) ( c m 2 / s 2 ) Fig. 34: Aggregate duration as well as percentages of the high-frequency contributions to both momentum and v e r t i c a l sediment fluxes associated with ejection periods exceeding various thresholds of (hp-U'*hp-V). 2.2 hrs of records, June 13, 1988 deployment. 122 of e j e c t i o n s , by threshold high-passed kinematic st r e s s exceeded, and t h e i r aggregate c o n t r i b u t i o n to (hp) momentum and sediment exchange f o r the 2.2 hr main study run. Intermittency i n sediment 9 9 suspension i s i n evidence. Those ejections exceeding -45 cm^/s , for example, occupy only 1% of the t o t a l time, yet contribute 16% of the (hp) momentum exchange and 6% of the (hp) sediment mixing. These comparisons of course only bear on the high frequency f l u x components. Are burst-scale "events" negligeable however when a s s e s s e d a g a i n s t the o v e r a l l momentum and sediment fluxes, a l l frequencies combined? The answer, i n t e r e s t i n g l y , i s no. I t w i l l be seen that the intermittency i s e s s e n t i a l l y contained wi t h i n these high-passed s i g n a l s . F i g . 35 presents the same analysis as done on the high-passed f l u x records, but t h i s time based on 2.2 hrs of the u n f i l t e r e d u'v' and OBS'v' f l u x records. E j e c t i o n events exceeding v a r i o u s extreme (u'v') t h r e s h o l d s were s e l e c t e d and t h e i r c o n t r i b u t i o n to the o v e r a l l fluxes assessed. The r e s u l t s can be seen to be very s i m i l a r to those computed from the high-passed records (Fi g . 34). The top 1% of e j e c t i o n events now produce 10% of the stress and 7% of the sediment mixing. The e x t r a c t i o n of turbulent components with periods shorter than some 30 s (the f i l t e r half-power p o i n t ) , seen i n Figs. 32, only a l l o w s the b r i e f i n t e r m i t t e n t f l u x "events" to stand out more c l e a r l y than i f they were imbedded wit h i n the lower frequency c o n t r i b u t i o n s . While the f i l t e r cuts down on the str e s s l e v e l associated with any event, Figs. 34 and 35 show that i t does not s u b s t a n t i a l l y d i s t o r t t h e i r r e l a t i v e c o n t r i b u t i o n to the mean f l u x . This property of the 30 s f i l t e r was general i n our an a l y s i s . The " i n t e r m i t t e n c y p r e s e r v i n g " e f f e c t of the f i l t e r could also be gr a p h i c a l l y assessed i n chapter 3 when stress events were p l o t t e d before (Fig. 16) and a f t e r ( F ig. 22) high-pass f i l t e r i n g . In Figs. 34 and 35, e j e c t i o n events selected f o r t h e i r large c o n t r i b u t i o n to momentum f l u x are seen to be important to sediment mixing, though not generally quite as e f f i c i e n t i n t h i s l a t t e r respect. The true degree of intermittency of high-passed -1 I I I I I I I I I 11 I , I I I 1 I I I I 1 1 1 I I I I I I I I I I I I I I I I 1 I I I I I I I I I I I I 1 1 1 I I I I I -350 -300 -250 -200 -150 -100 - 5 0 ( U' * V ) (cm2/s2) Fig. 35: Aggregate duration as well as percentages of the total ( a l l frequencies) contributions to both momentum and ver t i ca l sediment fluxes associated with ejection periods exceeding various thresholds of ( U ' * V ) . 2.2 hrs of records, June 13, 1988 deployment. 124 v e r t i c a l sediment mixing i s much greater than i l l u s t r a t e d i n that f i g u r e , when a l l sudden v e r t i c a l motions throwing up sediment are t a l l i e d , i r r e s p e c t i v e of t h e i r c o n t r i b u t i o n to s t r e s s . F i g . 36 d i s p l a y s an ana lys i s of a l l "pos i t ive mixing events" ( i n the sense of F i g . 32) ranked by s i ze of c o n t r i b u t i o n to (hp) sediment mixing, i n terms of aggregate durat ion and suspension work. In t h i s ranking events exceeding some 540 mV cm/s of f lux occupy, as above, 1% of the r e c o r d , yet contr ibute 20% ins tead of 6% of the high-passed component of v e r t i c a l suspension f l u x . (The top 1% of events i n the u n f i l t e r e d s er i e s s i m i l a r l y produce 18% of the t o t a l sediment f l u x ) . The l a r g e s t 5% of (hp) events (by d u r a t i o n ) , exceeding 250 mV cm/s, contr ibute 40% of the (hp) suspension f l u x (the c o n t r i b u t i o n i s 45% i n the u n f i l t e r e d s e r i e s ) . Such intermit tence of sediment f luxes was not present only i n the June 13, 1988 c o n d i t i o n s . F i g . 37 superimposes the percentage c o n t r i b u t i o n to sediment f l u x against t o t a l d u r a t i o n of large p o s i t i v e events for both the June 13 and June 8, 1988 data runs near M i s s i o n (c f . s e c t i o n 2 .4 ) . In both deployment c o n d i t i o n s , events exceeded only some 1% of the time cause around 20% of the t o t a l suspension. F i g . 38 p r e s e n t s average recurrence per iods for h igh-frequency p o s i t i v e mixing events of var ious i n t e n s i t i e s , f or the June 13, 1988 d a t a . The l a r g e s t 5% o f events j u s t mentioned (exceeding 250 mV cm/s i n the hp s er i e s and producing 40% of the f lux) recur approximately every minute on average; on the other hand, events exceeding ten times the mean h igh passed mixing f lux (550 mV cm/s) and c o n t r i b u t i n g some 20% of aggregate f l u x , would r e c u r on average e v e r y 3 m i n u t e s . F i g . 39 super imposes the recurrence per iods for large p o s i t i v e events for June 13 and 8 study c o n d i t i o n s . To permit comparison, large p o s i t i v e mixing events have been normal ised by the average value of mixing a c t i v i t y a p p l i c a b l e i n each environment. 125 Fig. 36: Aggregate duration as well as percentage of (hp) v e r t i c a l sediment flux associated with periods when (hp-OBS*hp-V) exceeded various threshold values. Sand fluxes are nominal. 2.2 hrs of records from June 13, 1988. 126 • o F i g . 37: Superimposed curves of percent of sediment f lux accomplished in percent time for 2 d i f f erent deployment condit ions . Detai ls of flow conditions i n each deployment are given in section 2.4. 127 Mean t ime between s u s p . events exceed ing ( h p - O B S * h p - V ) . t h resho lds ( h p - O B S *' h p - V ) ( m v c m / s ) F i g . 38: Mean recurrence periods between "positive" turbulent mixing events (defined in the text) exceeding various thresholds of (hp-OBS*hp-V). Based on 2.2 hrs of records from June 13, 1988 deployment. Sand fluxes are nominal. 128 TD O O Mean time between susp. events exceeding normalised flux thresholds fission, 06.13.88, 134 min D = 10 m ; V , = 1.4 m / s / Mission, 06.08.88, 35 min / D = 8 m ; V, = 1.1 m/s | I I I I I I 1*1 I | I I i I I I I I I | I I I I M I I I | I I I I I I I I I | I I I II i I i i | 0 5 10 15 20 25 ( h p - 0 B S * h p - v ' ) / ( h P - 0 c 3 S * h p - v ' ) F i g . 39: Superimposed curves of recurrence periods between "positive" t u r b u l e n t mix ing events for two different deployments. Details of flow conditions in each deployment are given in section 2.4. The threshold flux levels on the abscissa are normalised by mean flux during each deployment. 129 The conclus ions of the recurrence ana lys i s ( F i g s . 38, 39) are two- fo ld: as i n the ana lys i s of s t ress "events" ( F i g . 20), there i s a f a i r c o i n c i d e n c e between the curves from d i f f e r e n t , flow c o n d i t i o n s . There may thus be, as can be expected, some general s t a t i s t i c a l law at work r e l a t i n g the number (hence recurrence per iod) of extreme turbulent f l u x events to t h e i r r e l a t i v e s i z e . C l e a r l y , many more deployments over a far wider range of flow condi t ions than were encountered on the Fraser River need to be c a r r i e d out to e s t a b l i s h any such r e l a t i o n and def ine the parameters a f f e c t i n g i t . What i s c l e a r however from F i g s . 20 and 39 i s that i n n e i t h e r case i s there an obvious s ing l e time s c a l e , d e s c r i b i n g the r e c u r r e n c e o f a s i n g l e c la s s of dominant s tress or suspension "events". In t h i s sense, the view that a p r e d i c t a b l e mean burs t p e r i o d (given for example by the convent ional outer flow sca l ing ) i s o f immediate p r a c t i c a l use i n u n d e r s t a n d i n g and q u a n t i f y i n g suspension i s put in to doubt. 4 .4 .4 Resul tant downstream suspended sediment t r a n s p o r t . The r e s u l t a n t mean downstream suspended sand f l u x q (D>0.09 mm) at sensor l e v e l on June 13, 1988 i s g iven by the mean product of instantaneous concentrat ion and h o r i z o n t a l v e l o c i t y , est imated below: q = (a OBS + b) u - a (OBS u) + b (u) - 345 g/m z s I t i s noteworthy that the (UBS u) product i s dominated by the mean values of the two v a r i a b l e s : OBS u = OBS u + OBS' U ' = (180400 - 600) mV cm/s OBS u The smal l negative covariance term ( O B s ' u") r e f l e c t s the repeatedly noted tendency of the f a s t e r h o r i z o n t a l flow to be as soc ia ted with somewhat smal ler sediment concentrat ions . The c o r r e c t i o n term i s I 130 seen to be neg l igeable (0.3% of the t o t a l ) , however. This negative c o r r e c t i o n term was a lso reported to be neg l igeable i n Soulsby et a l ' s (1985) study. T h u s , the mean downstream f l u x can be e s s e n t i a l l y expressed as: q - a (OBS u) + b u = (a OBS + b) u C u so t h a t over the 2.2 hrs s tud ied , the suspended load i s qui te a c c u r a t e l y determined by the product of the mean concentra t ion maintained by the v e r t i c a l mixing and the mean downstream flow at sensor l e v e l . The ex is tence , documented a l l through t h i s study, of s trong m u l t i - m i n u t e o s c i l l a t i o n s i n b o t h c o n c e n t r a t i o n l e v e l s and h o r i z o n t a l v e l o c i t i e s at 1 m from the bed i m p l i e s , however, that repeated sampling over long periods i s necessary to assess e i t h e r of these mean values accura te ly . T y p i c a l hydrometric procedures to assess sediment transport near the bed of a sand r i v e r are often b a s e d on o n l y a few r e p e a t 30 to 120 s samples o f p o i n t concentrat ions and h o r i z o n t a l v e l o c i t y . The M i s s i o n data suggest that r e l a t i v e l y inaccurate assessments of the important h o r i z o n t a l f l u x at such a l e v e l may be expected from these procedures . For example , i f one 30 s long simultaneous observat ion of average concentra t ion and average v e l o c i t y was used to estimate long term h o r i z o n t a l f l u x , there i s approximately a 1 i n 5 chance that the r e s u l t would be i n e r r o r by more than 20% (based on the s t a t i s t i c s of the ( lp-0BS*lp-u) s er i e s at M i s s i o n ) . The sampling e r r o r i n t h i s case r e s u l t s not from the c o r r e l a t i o n of concentra t ion and u, but simply from the s u b s t a n t i a l e r r o r i n es t imat ing e i t h e r mean from only 30 s samples. 131 CHAPTER 5 CONCLUSIONS 5.1 Summary of research quest ion . As d iscussed i n the i n t r o d u c t i o n , previous work on b u r s t -l i k e motions i n l a r g e - s c a l e flows has mostly been conducted i n benth ic and t i d a l boundary l a y e r s . The under ly ing mot iva t ion for the Fraser R i v e r study was to beg in to i n v e s t i g a t e the re levance of convent ional burs t concepts (as put f o r t h i n Jackson, 1976 or A l l e n , 1985) i n an e x p l i c i t l y f l u v i a l context , i n p a r t i c u l a r wi th regard to sediment suspension. The main p r a c t i c a l d i f f i c u l t i e s i n such a study are m a i n t a i n i n g a s t a b l e s e n s o r deployment d u r i n g h igh flow c o n d i t i o n s , as w e l l as p e r s i s t e n t s i g n a l c o r r u p t i o n problems due to f o u l i n g of the sensors by large suspended organic m a t e r i a l s . As only minimal p r i o r work e x i s t e d to guide the i n v e s t i g a t i o n , a number of i ssues were explored . A t t e n t i o n was thus g iven a l l along to the frequency content of s tress and suspension processes 1 m o f f the r i v e r bed i n the Fraser R i v e r ; i n p a r t i c u l a r the r e l a t i v e importance of mult i -minute flow o s c i l l a t i o n s i n these matters was po in ted out. The key aims of the study however were to i n v e s t i g a t e the very existence of i d e n t i f i a b l e " b u r s t - l i k e " (u 'v ' ) events (def ined i n s e c t i o n 1.1) and a l so to tes t the relevance of the outer flow s c a l i n g for b u r s t recurrence , o r i g i n a l l y e s t a b l i s h e d over f l a t wal l s i n the l a b o r a t o r y , i n a much higher Reynolds number f l u v i a l boundary l a y e r , and w i t h the complex w a l l geometry of a c t i v e bedforms. A v a i l a b l e data al low only specu la t ion on the r e l a t i o n of "burst-l i k e " (u 'v ' ) events i n the study environment to "c las s i c" turbulent b u r s t i n g , however. These issues were discussed i n chapter 3, and the main f ind ings w i l l be summarised below under the heading of Momentum Exchange. 132 I t has a l so been noted i n chapter 1 that measurement of turbulent suspension time ser i e s has only very r e c e n t l y begun to be c a r r i e d out, and no ana lys i s has been accomplished to date of the a c t u a l c o n t r i b u t i o n of s trong s t r e s s - b e a r i n g " b u r s t - l i k e " episodes to t o t a l v e r t i c a l suspension f luxes . C a r r y i n g out such an a n a l y s i s was a c e n t r a l objec t ive of t h i s study, whatever t h e i r r e l a t i o n to c l a s s i c b u r s t i n g , intense b u r s t - l i k e motions have been assumed by many to p l a y a major r o l e i n a l l u v i a l sediment t r a n s p o r t . These and s u b s i d i a r y i s sues , d iscussed i n chapter 4, are summarised below under the heading of Sediment Suspension. 5 .1 .1 Momentum exchange: main f ind ings OBJECTIVE 1 was to inves t iga te the relevance of "c las s i c" b u r s t i n g event d e f i n i t i o n s and t h e i r r e t u r n p e r i o d s c a l i n g i n the f i e l d environment. Quadrant a n a l y s i s o f the ( u ' v ' ) s e r i e s c l e a r l y reveals i n t e r m i t t e n t but intense e j e c t i o n (u'<0, v'>0) and inrush (u'>0, v'<0) event s ( s e c t i o n 3 .2 .1 , F i g . 16), convent iona l ly taken as i n d i c a t o r s of boundary l ayer b u r s t i n g episodes. Energet i c events occupying only 12% of the record accounted for as much as 80% of the t o t a l momentum exchange ( F i g . 17). D i f f i c u l t i e s were encountered i n o b j e c t i v e l y d e f i n i n g and counting b u r s t "events" i n the f l u v i a l environment. Perusa l of the l i t e r a t u r e suggests that t h i s i s a common problem i n s tudies of b u r s t recurrence based on one-point (u 'v ' ) records . As u s u a l , event recurrence periods appear h i g h l y s e n s i t i v e to thresho ld s e t t i n g s , wh i l e ob jec t ive and uniform c r i t e r i a to set such event -de f in ing thresholds have not become widespread ( sec t ion 3 .2 .2 , F i g s . 19, 20). Based on the W i l l m a r t h and Lu (1974) thresho ld c r i t e r i o n , the recurrence p e r i o d for b u r s t - l i k e events i n the study data i s of the 133 o r d e r o f 8 minutes , and so much greater than the 20 to 50 s p r e d i c t e d by convent ional outer flow s c a l i n g (Rao et a l . , 1971) for t h i s environment (s. 3 . 2 . 2 ) . In any case, f or p r a c t i c a l purposes i t may be more u s e f u l to acknowledge the continuous d i s t r i b u t i o n of recurrence per iods for extreme f l u x events of v a r y i n g magnitude. The i n f e r r e d dimensions (5-10 s event durat ions * 1 m/s = 5-10 m) of these b u r s t - l i k e events make them s i g n i f i c a n t l y l a r g e r than would be pure eddy shedding s truc tures generated at the lee of the l a r g e s t dunes present (heights - 1 m). Unless one assumes that turbulent b u r s t i n g i s somehow completely repressed i n large r i v e r f lows, i t may be assumed that i t under l i e s at l e a s t some of these intense (u 'v ' ) events on the Fraser River (s. 3 .3 ) . A t e n t a t i v e i d e n t i f i c a t i o n of b u r s t i n g events i n the study data i s thus based on the i n t e r m i t t e n c y of (u 'v ' ) con tr ibut ions to momentum exchange, r a t h e r t h a n on c o n f o r m i t y to b u r s t r e c u r r e n c e s c a l i n g from labora tory f lows. I t i s speculated that the s p a t i a l v a r i a b i l i t y of shear and downstream pressure gradient condi t ions near the dune covered Fraser R i v e r bed might i n v a l i d a t e the convent ional b u r s t recurrence s c a l i n g e s t a b l i s h e d i n more uniform labora tory f lows. In p a r t i c u l a r , i t i s argued that b u r s t i n g a c t i v i t y at a f i x e d sensor should be modulated i n time, i n response to the advance o f ac t ive bedforms ( s ec t ion 3 .3 ) . D i f f i c u l t i e s i n t r a c k i n g l o c a t i o n and movement of the smal ler s c a l e bedwaves u n d e r n e a t h the sensor i n the study environment prec luded however a t e s t i n g these ideas . A more d e t a i l e d understanding of the l i n k between b u r s t - l i k e (u 'v ' ) events, monitored at an apprec iable d is tance from a dune covered r i v e r bed, and convent ional l abora tory b u r s t i n g s t ruc tures may r e q u i r e the development of sensor arrangements a l lowing f u l l e r f low v i s u a l i z a t i o n , and bedform monitor ing , i n f l u v i a l boundary l a y e r s . 134 5.1.2 Sediment suspension: main f i n d i n g s . OBJECTIVE 2 concerned c l a r i f y i n g the importance of the b u r s t - l i k e s t re s s events, d iscussed under Object ive 1, i n terms of sediment suspension. C o n d i t i o n a l ana lys i s of the concentra t ion and v e l o c i t y time s er i e s produces o r i g i n a l i n s i g h t s in to the suspension e f f i c i e n c y of b u r s t - l i k e motions i n the study context . The data i n d i c a t e that intense b u r s t - l i k e e j e c t i o n / i n r u s h motions are indeed important i n v e r t i c a l l y mixing sediments across the 1 m l e v e l i n the flow. For example, very intense e j e c t i o n motions with (u 'v ' ) values exceeded only 1% of the time, and c o n t r i b u t i n g some 10% to mean turbulent momentum f l u x , appear to produce 6% of t o t a l v e r t i c a l sediment f l u x (s. 4 .4 .3 ; F i g s . 32, 34, 35). Intense b u r s t - l i k e "eject ion" events do not completely dominate the suspension process , however, i n the study environment. Two e f f ec t s appear to l i m i t somewhat the r e l a t i v e i m p o r t a n c e o f the i n t e n s e ( e j e c t i o n / i n r u s h ) s t re s s events to sediment suspension at 1 m from the bed. F i r s t , a l t h o u g h b u r s t - l i k e mot ions t h a t c o n t r i b u t e s i g n i f i c a n t l y to momentum exchange are qui te e f f e c t i v e i n sediment m i x i n g , the s t a t i s t i c a l a s s o c i a t i o n between the momentum and sediment m i x i n g e f f i c i e n c i e s of any given motion appears only m o d e r a t e l y s t r o n g . V e r y i n t e n s e s u s p e n s i o n f l u x e s are o f t e n a t t r i b u t a b l e to r a t h e r "weak" e j e c t i o n s ( i n terms o f s t res s ) ( s ec t ion 4 . 4 . 3 , F igs 32, 33). These d i f f erences may i n p a r t r e f l e c t the "cross ing t r a j e c t o r i e s e f fec t" , which expresses the divergence of the t r a j e c t o r i e s of flow parce l s and sediment grains over any length o f time. The complex r e l a t i o n between sediment and water t r a j e c t o r i e s due to p a r t i c l e s e t t l i n g may weaken the coupl ing between the v e r t i c a l mixing of momentum and sediment. A weak degree of c o r r e l a t i o n between flow v e l o c i t i e s and even pass ive contaminant c o n t e n t s , u n a f f e c t e d by f a l l v e l o c i t i e s , i s qu i te t y p i c a l i n 135 turbulent mixing, however. S e c o n d l y , s t r o n g m u l t i - m i n u t e f l o w o s c i l l a t i o n s s i g n i f i c a n t l y a s s i s t the b u r s t - s c a l e turbulent motions i n v e r t i c a l sediment mixing (cf . F i g . 26). The l o n g - p e r i o d (T>1.5 min) flow o s c i l l a t i o n s may be assoc ia ted with some o n e - t h i r d of the t o t a l upward v e r t i c a l sediment f l u x , based on the v-OBS output cospectrum from June 13, 1988 ( s ec t ion 4.4 .2 and F i g . 31). In any case, turbulent sediment suspension, l i k e momentum exchange, i s h i g h l y i n t e r m i t t e n t . A f t e r s e l e c t i n g events only for suspension e f f i c i e n c y , the l a r g e s t ones, occupying only 5% of the time, contr ibute 40% of the turbulent sediment f l u x ( s ec t ion 4 .4 .3 , F i g s . 36, 37). As with momentum exchange, there i s no i n d i c a t i o n that the convent ional s c a l i n g of b u r s t recurrence corresponds to the r e t u r n of any d i s t i n c t i v e event l e v e l f or suspension ( F i g s . 38, 39). A continuous d i s t r i b u t i o n of recurrence per iods for extreme f l u x events of v a r y i n g magnitude i s again observed. 5.2 Further i m p l i c a t i o n s of the f ind ings and avenues f o r research . I t was seen t h a t the F r a s e r R i v e r o b s e r v a t i o n s are compatible with (but do not c l e a r l y e s t a b l i s h ) the operat ion of turbulent b u r s t i n g , a l b e i t with mean recurrence per iods which appear to d i f f e r from labora tory r e s u l t s . An important but d i f f i c u l t set of observat ions s t i l l to be conducted involves m u l t i - p o i n t t r a c k i n g of b u r s t - l i k e motions and e jec ted suspended sediment plumes through the flow column. Such observations would fur ther c l a r i f y , f or l a r g e -sca le geophys ica l f lows, the "burst ing conjecture" l i n k i n g surface b o i l a c t i v i t y , large motions i n the outer flow and near-bed flow i n s t a b i l i t i e s ( e .g . Jackson, 1976). There i s a l so a p r e s s i n g need to develop b e t t e r sensors and s t a t i s t i c a l c a l i b r a t i o n models to m o n i t o r i n s t a n t a n e o u s suspended c o n c e n t r a t i o n s i n the f i e l d environment. A more accurate assessment of the turbulent suspension 136 process appears to depend on such developments. The sca le of mult i -minute flow o s c i l l a t i o n s at the sensor l e v e l and t h e i r importance to sediment mixing i n r i v e r flows were unforeseen, and suggest that the nature of these o s c i l l a t i o n s be f u r t h e r c l a r i f i e d . The t en ta t ive hypothes i s , formulated i n s e c t i o n 2.6, that the passage of smal l bedforms under the sensors may p a r t l y be r e s p o n s i b l e (through assoc ia ted streamline per turbat ions ) for some of the mult i -minute flow o s c i l l a t i o n s i n the records would need to be pursued. At l e a s t i n deep and fa s t f lows, i n v e s t i g a t i n g t h i s h y p o t h e s i s would appear to requ ire the development of portab le forward- looking sonar apparatus. I t may be p o s s i b l e to i n v e s t i g a t e a s i m i l a r e f f e c t i n much shallower streams, where the progress ion of smal l bedforms can be more e a s i l y monitored. I n s e c t i o n 3 . 3 , the t h e o r e t i c a l p o s s i b i l i t y o f a m o d u l a t i o n o f b u r s t a c t i v i t y over d i f f e r e n t par t s of f l u v i a l bedforms was d i s c u s s e d . By m o n i t o r i n g the flow at d i f f e r e n t e l eva t ions over s i n u s o i d a l wavefie lds i n the l a b o r a t o r y flume i t s h o u l d be p o s s i b l e to inves t iga te the existence of any s p a t i a l modulation of b u r s t and suspension a c t i v i t y , i t s phase r e l a t i o n to the bedform p r o f i l e , as w e l l as i t s dependence on bedform steepness, flow separat ion , e tc . I f modulation i s i n e f f e c t , i t s consequences for t r a d i t i o n a l b u r s t recurrence s c a l i n g at one po in t over n a t u r a l a c t i v e dunes cou ld a l so be i n v e s t i g a t e d i n d i f f e r e n t condi t ions of flow and bedform t r a n s l a t i o n . Based on the f ind ings l i s t e d above, i t does appear that turbulent mixing of both momentum and sediment over a t y p i c a l sandy r i v e r bed i s dominated by i n t e r m i t t e n t , intense events. However, the e a s y e x t r a p o l a t i o n o f i n t e r m i t t e n t " b u r s t i n g " c o n c e p t s and s t r u c t u r a l constants from s m a l l - s c a l e l abora tory flows to the l a r g e r f l u v i a l environment may be mis l ead ing . Furthermore, the momentum-bear ing cores of large b u r s t - l i k e events do not appear to be the o n l y s i g n i f i c a n t c o n t r i b u t o r s to sediment s u s p e n s i o n ; weaker p e r i p h e r a l motions may a l so be able to e f f i c i e n t l y p r o j e c t sandy flow p a r c e l s fur ther out in to the flow. 137 The i n s i g h t s gained i n t h i s study c l e a r l y do not po in t to any easy breakthroughs i n p r e d i c t i n g suspended sediment t ransport based on the b u r s t concept. A s u b s t a n t i a l f r a c t i o n of turbulent s u s p e n s i o n away from the sediment surface , i n the zone where downstream transport i s most important, appears to invo lve motions, of both long and short t imescales , not t i e d d i r e c t l y to the s trong b u r s t - l i k e events. The steps l i k e l y r e q u i r e d to e s t a b l i s h t ransport models based on b u r s t i n g events are i n any case t r u l y formidable: these would inc lude b e t t e r parameter is ing mean b u r s t recurrence as a f u n c t i o n of flow condi t ions over bedforms, as w e l l as i n v e s t i g a t i n g the d i s t r i b u t i o n o f b u r s t i n t e n s i t i e s and the c o n t r o l s on the suspension e f fec t iveness of b u r s t s . Indeed, i f there i s a feedback between bedform development and b u r s t l o c a t i o n , t i m i n g and i n t e n s i t y , then b u r s t i n g must, i n any case, be seen l e s s as an i n v a r i a n t b u i l d i n g b lock of the turbulence , u s e f u l i n p r e d i c t i n g two-phase flow, than as a l i n k i n the coupl ing of turbu lent flow to the deformable boundary. REFERENCES A l l e n , J . R . L . , 1985. P r i n c i p l e s of p h y s i c a l sedimentology. A l l e n and Unwin. 272pp. Anderson, D . E . , Verma, S . B . , 1985. Turbulence spec tra o f CO2, water vapor, temperature and wind v e l o c i t y over a crop sur face . Boundary Layer M e t . , 33: 1-14. Anton ia , R . A . , Atk inson , J . D . , 1973. High-order moments of Reynolds shear s t res s i n a turbulent boundary l a y e r . J . F l u i d Mech. , 58: 581-593. Anwar, H . O . , 1981. A study of the turbulent s t r u c t u r e i n a t i d a l f low. Es tuar . Coas ta l and She l f S c . , 13: 373-387. Anwar, H . O . , A t k i n s , R. , 1980. Turbulence measurements i n s imulated t i d a l flow. Proc. ASCE, 106: 1273-1289 Bendat , J . S . , P i e r s o l , A . G . , 1986. Random data: A n a l y s i s and measurement procedures. 2nd e d . , J . Wiley , 566 pp. Bogard, D . G . , Tiederman, W . G . , 1986. Burst de tec t ion wi th s i n g l e -po in t v e l o c i t y measurements. J . F l u i d Mech. , 162: 389-413. Buckles , J . , Hanratty , T . J . and A d r i a n , R . J . , 1984. Turbulent flow over large-ampl i tude wavy surfaces . J . F l u i d Mech. , 140: 27-44. B r o w n , G . L . , Thomas, A . S . W . , 1977. Large s t r u c t u r e i n a turbulent boundary l a y e r . The Physics of f l u i d s , 20: s243-252. Cantwel l , B . J . , 1981. Organized motion i n turbulent f low. Ann. Rev. F l u i d Mech. , 13: 457-515. C o l e m a n , J . M . , 1969. Brahmaputra r i v e r - c h a n n e l p r o c e s s and sedimentat ion. Sed. Geo l . 3: 129-239. Downing, D . J . P . , S t e r n b e r g , R . W . , L i s t e r , C . R . B . , 1981. New instrumentat ion for the i n v e s t i g a t i o n o f sediment suspension i n the shallow marine environment. Marine G e o l . , 42: 19-34. 139 F a l c o , R . E . , 1977. Coherent motions i n the outer reg ion of turbulent boundary l a y e r s . The Physics of F l u i d s , 20: S124-S132. Gordon, C M . , 1974. Intermit tent momentum transport i n a geophysical boundary l a y e r . Nature, 248: 392-39 G o r d o n , C . M . , 1975. Sediment en tra inment and suspension i n a turbulent t i d a l flow. Marine Geo l . 18: M57-M64. Gordon, C M . , W i t t i n g , J . , 1977. Turbulent s t r u c t u r e i n a benthic boundary l a y e r , i n Bottom Turbulence, Proc . 8th Int . Liege C o l l o q u i u m on Ocean H y d r o d y n a m i c s , J . C . N i h o u l ( e d . ) , E l s e v i e r Oceanography S e r i e s , no 19. : 59-81. Grass , A . J . , 1970. I n i t i a l i n s t a b i l i t y of f i n e sand bed. J . Hydrau l . D i v . , ASCE, HY3: 619-632. Grass , A . J . , 1971. S t r u c t u r a l features of turbulent flow over smooth and rough boundaries . J . F l u i d Mech. , 50: 233-255. Grass , A . J . , 1974. Transport of f ine sand on a f l a t bed: turbulence and suspension mechanics. Euromech 48. Univ . Denmark, p 33 Heathershaw, A . D . , 1974. "Bursting" phenomena i n the sea. Nature, 248: 394-395. Heathershaw, A . D . , 1979. The turbulent s t r u c t u r e of the bottom boundary l a y e r i n a t i d a l c u r r e n t . Geophys. J . R. a s t r . S o c , 58: 395-430. Heathershaw, A . D . , Thome, P .D. , 1985. Sea-bed noises r e v e a l r o l e of turbulent b u r s t i n g phenomenon i n sediment t ransport by t i d a l c u r r e n t s . Nature, 316: 339-342. Hsu, S . , Kennedy, J . F . , 1971. Turbulent flow i n wavy p i p e s . J . F l u i d Mech. , 47: 481-502. Ikeda, S . , Asaeda, T . , 1983. Sediment suspension with r i p p l e d bed. J . Hydrau l . E n g . , ASCE. 109: 409-423. I s h i h a r a , Y . , Yokos i , S . , 1967. The spectra o f turbulence i n a r i v e r f l o w . P r o c e e d . 12th C o n g r . , I n t . A s s . H y d r a u l . R e s . , Colorado: 290-297. Iseya, F . , 1984. An experimental study of dune development and i t s e f f e c t on sediment suspension. Environmental Res. Centr . Papers, No 5 . , Univ . of Tsukuba, Japan. I t a k u r a , T . , K i s h i , T . , 1980. Open channel flow wi th suspended sed iments on sand waves. T h i r d In t . Symp. on S tochas t i c H y d r a u l i c s , Tokyo, Japan: 589-598. 140 Jackson, R . G . , 1976. Sedimentological and f lu id-dynamic i m p l i c a t i o n s of the turbulent b u r s t i n g phenomenon i n geophys ica l f lows. J . F l u i d Mech. , 77: 531-560. Kaimal , J . C , Haugen, D .A. , 1969. Some e r r o r s i n the measurement of Reynolds s t r e s s . J . A p p l . M e t . , 8: 460-462 K e n d a l l , J . M . , 1970. The turbulent boundary l ayer over a w a l l with progress ive surface waves. J . F l u i d Mech. , 41: 259-281. Kennedy, D . A . , C o r r s i n , S . , 1961. S p e c t r a l f l a tnes s f a c t o r and ' i n t e r m i t t e n c y ' i n turbulence and i n n o n - l i n e a r no i se . J . F l u i d Mech. , 10: 366-370. K l i n e , S . J . , Reynolds, W . C , Schraub, F . A . and Runstadler , P.W. , 1967. The s t r u c t u r e of turbulent boundary l a y e r s . J . F l u i d Mech. , 30: 741-773. Large , W . G . , Pond, S . , 1981. Open Ocean momentum f l u x measurements i n moderate to s trong winds. J . Phys. Oceanography, 11: 324-336 L u , S . S . , W i l l m a r t h , W.W., 1973. Measurements of the Reynolds s tress i n a turbulent boundary l a y e r . J . F l u i d Mech. , 60: 481-511. L u m l e y , J . L . , 1976. Two-phase and non-Newton ian f l o w s . i n Turbulence, Bradshaw, P. ( e d . ) . Topics i n A p p l . Phys . , 12: 289-324. Matthes, G . H . , 1947. Macroturbulence i n n a t u r a l stream flow. Trans . Amer. Geophys. U n . , 28: 255-265. McLean , D . G . , Church, M . A . , 1986. A re-examinat ion o f sediment t ransport observations i n the lower Fraser R. Inland Waters D i r e c t o r a t e , Environment Canada. Report IWD-HQ-WRB-SS-86-6. 57 pp + tables and f i g s . McLean , S . , S m i t h , J . D . , 1979. Turbulence measurements i n the boundary l a y e r over a sand wave f i e l d . J . Geophys. R e s . , 84: 7791-7808. Nakagawa, H. , Nezu, I , 1981. S tructure of space-time c o r r e l a t i o n s of b u r s t i n g phenomena i n an open-channel f low. J . F l u i d Mech. , 104: 1-43 N i e l s e n , P. 1984. On the motion of suspended sand p a r t i c l e s . J . Geophys. R e s . , 89: 616-626. Panofsky, H . A . , Dutton, J . A . , 1984. Atmospheric Turbulence: Models and methods for engineering a p p l i c a t i o n s . J . Wi ley . 390pp. 141 Phelps , G . T , Pond, S . , 1971. Spectra of the temperature and humidity f l u c t u a t i o n s and the f luxes of moisture and sens ib le heat i n the marine boundary l a y e r . J . Atmosph. Sc iences , 28: 918-928. Pond, S . , 1968. Some e f fec t s of buoy motion on measurements of wind speed and s t r e s s . J . Geophys. Res . , 73: 507-512. Pond, S . , Phelps , G . T . , Paquin, J . E . , McBean, G. , Stewart, R.W. , 1971. Measurements o f the turbulent f luxes of momentum, m o i s t u r e and s e n s i b l e h e a t over the ocean. J . Atmosph. Sc iences , 28: 901-917. Rao, K . N . , Naras imha , R. and Bad r i Nayayanan, M.A. , 1971. The "bursting" phenomenon i n a turbulent boundary l a y e r . J . F l u i d Mech. , 48: 339-352. R a u d k i v i , A . J . , 1964. Study of sediment r i p p l e format ion. J . Hydr. D i v . ASCE. 89: 15-33. Rood, K . M . , H i c k i n , E . J . , 1989. Suspended sediment concentra t ion i n r e l a t i o n to surface- f low s t r u c t u r e i n Squamish R i v e r estuary, southwestern B r i t i s h Columbia. Can. J . Ear th S c i . , 26: 2172-2176 Smith, S . D . , Chandler, P . C P . , 1987. Spectra and gust f a c t o r s for gale force marine winds. Boundary Layer M e t . , 40: 393-406 Soulsby, R . L . , 1977. S i m i l a r i t y s c a l i n g of turbulence spec tra i n marine and atmospheric boundary l a y e r s . J . Phys. Oceanogr. , 7: 934-937 Soulsby, R . L . , 1980. S e l e c t i n g record length and d i g i t i z a t i o n rate for near-bed turbulence measurements. J . Phys. Ocean. , 10: 208-219. Soulsby , R . L . , S a l k f i e l d , A . P . , Haine, R . A . and Wainwright, B. , 1985. Observations of the turbulent f luxes of suspended sand near the sea-bed. Proc . Euromech 192, Transport of suspended s o l i d s i n open channels , Munich, 193-186. Sumer, B . M . , Deigaard, R . , 1981. P a r t i c l e motions near the bottom i n turbulent flow i n an open channel , Part 2. J . F l u i d Mech. 109: 311-337 Sumer, B . M . , Oguz, B. , 1978. P a r t i c l e motions near the bottom i n turbulent flow i n an open channel . J . F l u i d Mech. , 86: 109-127. Suther land, A . J . , 1967. Proposed mechanism for sediment entrainment by turbulent flow. J . Geophys. R e s . , 72: 6183-142 Tennekes, H . , Lumley, J . L . , 1972. A f i r s t course i n turbulence . MIT Press . 300pp. T i f f a n y , J . B . , 1963. Review of research on channel s t a b i l i z a t i o n of the M i s s i s s i p p i R iver 1931-1962. Channel S t a b i l i z a t i o n Comm. U . S . Army Corps Engrs . V icksburg , M i s s . , Tech. Rep. no .2 . Water Survey of Canada, 1970. Hydrometric and sedimentary surveys, Lower F r a s e r R i v e r , 1965-1968. Environment Canada, Water Resources Branch, Sediment Survey. 133 pp. West , J . R . , Oduyemi, K . O . K . , 1989. Turbulence measurements of suspended s o l i d s concentrat ion i n e s t u a r i e s . J . Hydr. E n g . , ASCE. 115: 457-474. W i l l i a m s , P . B . , Kemp, P . H . , 1971. I n i t i a t i o n of r i p p l e s on f l a t sediment beds. Proc . ASCE, J . Hydrau l . D i v . , 97: 505-522. W i l l m a r t h , W.W. and L u , S . S . , 1974. S tructure of the Reynolds s tress and the occurrence of burs t s i n the turbulent boundary l a y e r , i n Turbulent d i f f u s i o n i n environmental p o l l u t i o n . F r e n k i e l , F . N . , Munn, R . E . ( eds . ) . Academic Press: 287-314. Wyngaard, J . C . , R o c k w e l l , L . , F r i e h e , C . A . , 1985. E r r o r s i n measurement of turbulence upstream of an axisymmetric body. J . Atmos. Ocean. Techn . , 2: 605-614 Y a l i n , M . S . , 1972. Mechanics of sediment t r a n s p o r t . Pergamon. 290pp. Y u d i n e , M . I . , 1959. P h y s i c a l c o n s i d e r a t i o n s on h e a v y - p a r t i c l e d i f f u s i o n , i n A t m o s p h e r i c D i f f u s i o n and A i r P o l l u t i o n . F r e n k i e l , F . N . , S h e p p a r d , P . A . ( e d s . ) . Advances i n Geophysics , 6: 185-191. Z i l k e r , D . P . , Hanratty , T . J . , 1979. Influence of the amplitude of a s o l i d wavy w a l l on a turbulent flow. Part 2: Separated f lows. J . F l u i d Mech. , 90: 257-271. 

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