SALINITY INTRUSION IN THE FRASER RIVER, BRITISH by DONALD B.A.Sc. M.A.Sc. A thesis the ORHOND University University submitted in requirements Doctor in of the C i v i l of of Waterloo, Waterloo, partial for the 1969 1970 fulfilment degree of of Philosophy Department of Engineering We a c c e p t t h i s t h e s i s reguired standard: THE HODGINS UNIVERSITY AUGUST OF as conforming BRITISH 1974 to COLUMBIA the COLUMBIA In presenting an advanced this thesis d e g r e e at t h e L i b r a r y s h a l l make I further for scholarly by h i s of agree this written it of 23 British available for that permission for extensive p u r p o s e s may be g r a n t e d for It financial Civil gain August 1974 Columbia the requirements Columbia, reference copying of I agree and this for that: study. thesis by t h e Head o f my Department: o r is understood shall Engineering The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada Date freely permission. Department fulfilment of the U n i v e r s i t y of representatives. thesis in p a r t i a l that not copying or publication be a l l o w e d w i t h o u t my i ABSTRACT estuary the The dynamics was studied use series of of by numerical conductivity kilometers above winter tides the observed f a i r l y in velocity data by 80 60 to A minutes agreement of comparable to velocity stress as and was stresses in the were the minutes interface KiyoD|U|Fi Fi i s an included found flows. to the at where as be sufficient not 2 ebb and 3 in a gradients were mixing took conductivity lagged to was and two-way predicted total 15 high cm/sec. and water 0 Froude Kb^'u'lu'l where s i g n i f i c a n t ^ in i s salt and water a phase Velocities The the Ki=0.0075, the depth intrusion. included i n t e r f a c i a l low mouth. maximum but 15 inequality. between s a l i n i t y intrusion cycles despite flood Both Time estimated column ebb to that the within t i d a l an water and motion. Mixing typically model of of river 3 Fraser measurements diurnal the appeared river cent measurements across formulated energy ±40 of periods. two-layer per large m /sec. maximum the f i e l d tidal several Longitudinal that near 10 of out 1100 ebb the equations indicating and revealed within tides wedge in exceeding currents salt layer, flood the of spanning water layer. numerical thickness mixing the each of throughout surface and during for salt water well-defined detectable programme averaging although meters/second, place washed salt intrusion penetrations Steveston discharges disperse a measurements significant ebb both water solutions indicated Large salt model were neglected Reynold's the relative number. The Kb=0.0055, the stress layer bottom and dissipation both of i i TABLE OF CONTENTS PAGE ABSTRACT TABLE i OF CONTENTS LIST OF TABLES LIST OF FIGURES i i iv . , NOTATION i x ACKNOWLEDGEMENTS CHAPTER 1 The 2 1 Fraser 3 Estuary Work 6 INSTRUMENTATION Location of 10 Instruments 11 Conductivity Profilers Operating Principles I n s t a l l a t i o n and S e r v i c i n g Calibration 12 15 16 20 Data 23 Processing Current CHAPTER x i i INTRODUCTION Previous CHAPTER V 3 and Accuracy Metering 29 OBSERVATIONS Conductivity Salinity Temperature Profiles Conductivity Current and 34 Charts Structure Parameterization 34 36 41 47 49 i i i CHAPTER 4 THEORETICAL CONSIDERATIONS The Equations The Characteristic A Steady The CHAPTER 5 of Flow Boundary SOLVING Motion - THE The Barotropic I n i t i a l Control and Two-layer Conditions 66 MODEL ' Equations and Boundary Conditions . . . . . . Wash-Out with Observations 106 107 Comparisons 112 118 Alternate Interfacial Stress Essential Features the of Forms 121 Model 123 AND C O N C L U S I O N S 130 Remarks for 133 Future Research 135 BIBLIOGRAPHY APPENDIX A 100 105 analysis Recommendations 87 88 Results Qualitative Concluding 62 95 Predictions SUMMARY Conditions Model I n i t i a l i z a t i o n 6 Boundary 78 TWO-LAYER Difference Computational CHAPTER and Stresses Finite Sensitivity 59 Structure Model The Comparing 56 138 e E E Rf If N eG c t sA S PoEf C TMS i x O i nF g T H an E N TGhI N E d S TSUt Dr Ya t i f i c a t i o n .... 114471 > iv LIST OF TABLES TABLE 1 PAGE Comparison for 2 3 4 of station Summary of instruments project. derived on 2 March s a l i n i t i e s 1973. 28 with River 33 Comparison of River Salt wedge estuaries of 29, measured accuracies associated used for the Fraser from Fraser and Richardson data and numbers Taylor obtained (1931). intrusion characteristics various depths. 82 for 143 V LIST OF FIGURES FIGURE PAGE 1 Map o f Fraser 2 Fraser R i v e r h y d r o g r a p h f o r 1973 a t Agassiz, British Columbia. T h e Hope d i s c h a r g e reading i s adjusted f o r i n f l o w s above Agassiz. 3 Lower the 4 south-western B r i t i s h Columbia River and S t r a i t o f Georgia. Fraser various estuary showing measuring the showing locations 2 4 of instruments. 13 Cross-sectional profiles and probe line locations at the three measuring s t a t i o n s i n the Lower Fraser e s t u a r y . 14 5 Diagram general of the timber pile platforms showing arrangement of instrumentation. 18 6 (a) I n d u c t i v e c o n d u c t i v i t y probe and sensing line. Guide wire and c o u p l i n g shackle appear to the l e f t . (b) F r o m l e f t to right: lead acid storage batteries, Rustrak recorder, and instrument electronics. (c) Timber pile p l a t f o r m a t s t a t i o n 2. 19 Timber pile platform damage. Skirt logs p i l e clamp on f u r t h e s t The current speed meters/second. at station 1 after are m i s s i n g and upper pile i s ineffective. i s approximately 1.5 21 Comparison of measured different instruments predicted temperatures March 29, 1973. c o n d u c t i v i t i e s by two (a,b) and measured and (c,d) f o r two t i m e s on 7 8 9 10 (a) O p e r a t i n g t h e portable salinometer off the s k i f f . (b) H y d r o P r o d u c t s c u r r e n t meter and t r o l l e y r u n n i n g a l o n g a guide w i r e . (c) O p e r a t i n g the c u r r e n t meter a t s t a t i o n 2. 31 Typical s a l i n i t y data from the on a strongly ebbing tide. d i s c h a r g e i s 960 m /sec. 35 Fraser The estuary Agassiz 3 11 24 C o n d u c t i v i t y and temperature data obtained with ' a n RS5 s a l i n o m e t e r on f o u r o c c a s i o n s i n the Fraser estuary. 37 vi 12 13 Salinity-depth February 1 0 , 1973 stations 1, 2 a n d greatest sounding profiles obtained and March 18, 1973 3. Channel bottom is a t s t a t i o n 1. Contour maps of conductivit s t a t i o n s i n the Fraser estuary. marked relative to the p r o f i l e r surface l i n e s are indicated usi data at stations 1 and 3. d i s c h a r g e i s 1130 m / s e c . Times P a c i f i c Standard Time. 3 14 on at the at three Bottom is and the free ng measured The Agassiz are noted in 38 y 43 Contour maps of conductivity at three stations in the Fraser estuary. Bottom is marked r e l a t i v e t o the p r o f i l e r and the free surface lines are indicated using measured data at stations 1 and 3. The Agassiz d i s c h a r g e i s 1060 m / s e c . Times are noted in P a c i f i c Standard Time. 44 Current stations March 30, 48 3 15 16 17 18 speed in 1973. measurements the Fraser made at estuary Comparison of h c a l c u l a t e d from and the measured conductivity M a r c h 1 8 , 1973 a t s t a t i o n 1. 1 equation structure two on (4) on 51 Two-layer parameterization of the conductivity data obtained in February 1973. Bottom l i n e s r e p r e s e n t the r i v e r bed at the platform sites. Free surface lines are p l o t t e d from measured data at s t a t i o n s 1 and 3. 53 Two-layer conductivity Bottom lines platform site plotted from 3. 54 parameterization of the data obtained in March 1973. r e p r e s e n t t h e r i v e r bed a t the s. Free surface lines are measured data at s t a t i o n s 1 and 19 V i s u a l i z a t i o n of Fraser estuary. s a l i n i t y 20 Notation mathematical 21 Possible flow states for the two-layer s t r a t i f i e d computation. The r e q u i r e d number of boundary c o n d i t i o n s i s i n d i c a t e d . used in intrusion into the modelling. 58 58 65 v i i 22 Notation used in steady flow solution. 23 Stage-discharge estuary. 24 Measured and p r e d i c t e d s u r f a c e three stations on the Main estuary. relationship an Fraser elevations at Arm o f Fraser arrested wedge. 74 26 Typical i n t e r f a c i a l stress curves for arrested salt wedges asuming a uniform surface slope. 77 Profiles of °~t and March 2 9 , 1973 at s t a t i o n 2. of the Brunt-Vaisala frequency R i c h a r d s o n number are shown. 83 velocity on Distributions and gradient 28 Finite 29 I l l u s t r a t i o n of relationship between continuum and f i n i t e difference domains of dependence for a stable e x p l i c i t difference scheme.. 30 31 Schematization of the hydraulic 34 35 of of at of on at molecules. Fraser River used and surface stations 5 93 in 96 surface 3 75 90 model. stations predicted observations Comparison observations and 2. Lower predicted observations Comparison with 33 barotropic Comparison with 32 computation salt 69 Typical difference for for 25 27 solutions 69 and elevations 4. 98 elevations 6. 99 predicted velocities with March 3 0 , 1973 at s t a t i o n s 1 Relationship between the e s t u a r y and parameters. Conductivity p r o f i l e r s stations 1, 2 and 3 a r e shown i n t h e i r configuration. model at March Comparison of t y p i c a l i n t e r f a c i a l positions predicted by the s t r a t i f i e d f l o w model with two-layer parameterization of observations at s t a t i o n s 1, 2 a n d 3 . 101 103 108 v i i i 36 37 38 39 40 41 42 Comparison of predicted and measured layer velocities at stations 1 and March 29 a n d 3 0 , 1 9 7 3 . upper 2 for 111 Interfacial solutions from the s t r a t i f i e d flow model a r e shown s u p e r i m p o s e d on c o u t o u r c h a r t s of c o n s t a n t d e n s i t y ( °~t) for three days in February 1973. The periods of s u p e r c r i t i c a l o u t f l o w a r e i n d i c a t e d by c f <0 on t h e s t a t i o n 1 c o n t o u r c h a r t . 113 Interfacial solutions from the s t r a t i f i e d f l o w model s u p e r i m p o s e d on c o u t o u r c h a r t s of constant density ( °~t) for three days in March 1973. The periods of s u p e r c r i t i c a l o u t f l o w a r e i n d i c a t e d b y c 7 <0 o n t h e station 1 contour chart. Supercritical inflow by cf >0. 114 Interfacial solutions for the t i d a l cycle on February 10, 1973. Isohalines interpolated f r o m t h e d a t a i n F i g u r e 12 a r e s h o w n i n each section. 116 Tidal variations in the i n t e r f a c i a l and b o t t o m s t r e s s e s and t h e mean layer velocity shear at station 2 for March 17, 1973 (upper). Six l o n g i t u d i n a l sections are shown f o r f l o o d and ebb phases (lower). 126 Comparison of the measured boundary c o n d i t i o n f o r h' at station 1 with the theoretical condition of Vreugdenhil (1970) (upper). Comparison of u' calculated from the s t r a t i f i e d flow model and the theoretical r e l a t i o n of vreugdenhil (lower). 128 Advection paths of into the M a i n Arm s m a l l numbers along time in hours follow 145 four particles released of the Fraser R i v e r . The each path indicate the ing release. ix Notation The following notation has been used in O c c a s i o n a l l y symbols have been used more than subsequently l i s t e d with each meaning. a = salt a-, water depth = coefficients = square b = storage b; B width = multiple = column c = x plane, area coefficient = dx/dt = least squares dimension analysis, 2n x 2n, river, coefficients, dependent inverse variable slopes cf of = celerity comparable o f i n t e r n a l waves on i n t e r f a c e between but d i f f e r e n t d e n s i t y ; e.g. water over C,Cs on a free curves of of waves characteristic dimension = celerity = constant gravity of derivatives, c* C long a river, matrix, regression of from of across vector = conductivity in vector of force terms, dimension n, f = column vector of force terms, dimension n, F (V) = column dimension n, F; U /J = M/J £ gh vector = g e 77 h * / h = acceleration h •= t o t a l water = thickness i - time j = space line line of densimetric g h« x-t surface, two salt fluids water, millimhos/centimeter, = column = in n, integration, C FA thesis. and are x=0, obtained A = cross-sectional A at this once to column in in Froude = i n t e r f a c i a l due of functions salt the the gravity depth water x-t x-t in plane. dependent number, Froude number, = 9.800 m/sec , river, layer, plane, of 2 variables, X K = dimensionless Ki = Kb = bottom Kc = inductive L,L i n t e r f a c i a l m = number n stress of = integer N (z) = mean P = solution length, characteristics di)/ point = solution g = discharge per Q = discharge in Q = solution point € gh = N(z)/( Req = gch/u / V 3 2 flow at a given boundary, layers, Brunt-Vaisala frequency, the = equivalent x-t width or salt = plane, x-t plane, (m /sec), 2 m /sec, 2 plane, water x-t thickness, plane, densimetric = gradient 2 = overall Reynolds number, Richardson Richardson S = s a l i n i t y in in x-t parts per = characteristic t = number, T = temperature u = instantaneous plane, thousand s a l i n i t y of Strait ), of time, = time mean number, resistance, point h x-t in du/ dz) = solution u in in point S Sg = in point = solution 0 p 3 R R i discrete m /sec = non-dimensional Ri of unit R = J entering pressure, P R^ constant, number p coefficient, coefficient, c e l l (-g dp / = coefficient, stress = intrusion 0 stress in degrees velocity barotropic Celcius, in x direction, velocity, Georgia water (%«, ) , xi u = observed layer 0 velocity, u = t i m e mean v e l o c i t y u* = fluctuating U = u-u 1 i n x direction, o r t u r b u l e n t v e l o c i t y component i n x d i r e c t i o n , = mean l a y e r velocity shear, V = column v e c t o r o f dependent v a r i a b l e s , w = instantaneous velocity w = t i m e mean v e l o c i t y dimension n i n z direction, i n z direction, w* = t u r b u l e n t v e l o c i t y c o m p o n e n t i n z d i r e c t i o n , x,y,z = r i g h t hand C a r t e s i a n c o - o r d i n a t e y = Rustrak recorder = p~\ = s p e c i f i c d 8x = spatial St = time ordinate, volume, increment, increment, = p' - p /p € 1 =Ap/p* 77 = h-h* = f r e s h - density water l a y e r X =p / p* = d e n s i t y contrast, thichness, ratio, V = kinematic v i s c o s i t y of water, P = fresh p % i T w a t e r d e n s i t y i n gm/cm - s a l t w a t e r d e n s i t y i n gm/cm (p-1 . 0 0 0 0 ) x10 = interfacial = bottom <z = v axes, 3 3 o r Kg/m , 3 o r Kg/m , 3 3 = sigma-t, stress, stress, (du/dz)/-<u*w*> = k i n e m a t i c e d d y viscosity x i i ACKNOWLEDGEMENTS The Fraser has proven area and undeniably, persons have particular I i n t u i t i o n provided research. would Leblond, and equation and the also studies l i k e to by in a s a l i n i t y very also me a interesting the acknowledge f i e l d M. work and Oceanography, advised steady am most wish to express at grateful much for me and to help in valuable the gave in me converting Professor during both and supervised use. flow the times. points (Oceanography) p r o f i l e r s I who in challenging one guidance Quick, conductivity the and d i f f i c u l t the Osborn the intrusion frustrating by Professor integrated (31). the be T. during preparing to helped Professor encouragement and into River research Many investigation the P. theoretical equations to yield for their assistance the Westwater guidance. I also Research Centre monitoring making available boats Limited and success of help. The helpful and the the valuable were f i e l d of in the to Institute the instruments. and I the of Canada I gratefully would l i k e things f i e l d to done" Canada both Engineering the f i e l d for organizations Rice contributed M i l l s to acknowledge Department thank around programme of Oceanography Both used. of C i v i l to expenses the Survey "getting contribution the extensively work particular experience to of Water staff in and most which appreciation underwriting programme, provided whose for my on Mr. the more the their were most Geoff Sharp, river made than one a x i i i occassion. Mr. platforms for appears the as The were excellent the figures on of the services C i v i l National in fine job R. Brun, Mr. this thesis is IBM computer and 370 Columbia f a c i l i t i e s support of a along Research Engineering did modelling British Financial the also river. numerical done University Sharp the in whose also with during the Council of University the excellent work thanked. the data available Computing are fabricating reduction through Centre and the their acknowledged. study Canada of period and British was the provided by Department of Columbia. 1 Chapter 1. INTRODUCTION The Columbia, water 1). Fraser discharges passage The water River, into connected confluence above respects c i r c u l a t i o n established while river layer. salt in a study 73, can flows into are these reported The nature of and problems had description different programme the 1973 salt of to to for The of seawater plain period the the P a c i f i c large Ocean Georgia results bottom extending in salt (Figure a salt several shown that salt wedge estuaries landward along of a relatively the in a where very each large layer. carried many is the bottom fresh surface well defined tides produce The out in results during of 1972 and examine the thesis. of Strait tackled stress the and of structure. be Georgia, estuaries circulations intrusion the of British have in maintained, this density flows seaward objective between currents of in of typical water t i d a l to river pattern t i d a l main the relation of S t r a i t Strait coastal be south-western Observations flows other in ends the salt water wedges the mouth. which Unlike intensified the the both along kilometers a at with intrusion located along arrive Georgia This along an project was at tides to a quantitative and the observed related meant that several way, such as the interface arriving between two at a fluids density. study proceeded f i e l d measurements collect wedge suitable movements on along data a was to two main directions. undertaken provide sub-tidal a scale. during detailed To F i r s t , the a winter picture complement, of • 3 and help explain s t r a t i f i e d The t i d a l Fraser Hope flows lower to l i t t l e t i d a l over as Since the the of of number Strait 2, percent resulting extensive derived The in during watershed from annual define (Figure of discharge and the low s t r a t i f i e d estuary conditions as extending 1), undergoes flows low and snowmelt, typical lower estuary lesser the of only main of The probably accentuated high of the It i s to arm is the a are significant curve which that discharges. there winter is are a large for flows 1973, result the in subject and the of the 9 connected carries deepest dredged meters, a to the has been approximately channel throughout and with an the seaward 30 to provide a feature which has intrusion. t i d a l water are channels investigation which continuously importance. sedimentation which meters depth principal This river also two of tide. s a l i n i t y of into some 15 channel understanding fundamental concerns: arm main shipping An at 10 minimum divides branches, the,flow. depth kilometers. of Georgia is Georgia to average is may kilometers an i s we elevation 110 flow which of in variation. of of confined 80 models study. The a as has the Figure density this mathematical developed. Strait much flow in observations, River, change river proportion shown were Fraser the relatively seasonal f i e l d Estuary The from the hydraulics There quality. are, in the perhaps, Preserving estuary two the main 4 F i g u r e 2. Fraser River hydrograph for 1973 at Agassiz, British Columbia. The Hope discharge reading i s adjusted for inflows above Agassiz. 5 shipping large channel public wedges; of that Vancouver result, and a the a be lower the of f i r s t the 2., discussion In wedge of together the effort study i s a or to in for the s t r a t i f i e d one side by on the a part of river city of other. As concern is a for domestic either on salt principally produced monitoring relies the and quality, of studies. river, recently f i e l d a forming gather the the comparison ^concluded and techniques of and about by using complicated knowledge by of the features project, was flow in description and 6 tidal problems along presented model observed Chapter a models developed of the data is this on and the mathematical steady are data river examples basic for v i c i n i t y storage water and s i g n i f i c a n t procedures with has commonly the the and is in communities of continuous patterns. of the 4 use on consuming by It sedimentation flanked smaller models typical solution numerical The Some the movement motion some Chapter analytic is of capacity in investigation intensive instruments, Chapter value intrusion f i e l d salt accentuated Assessing c i r c u l a t i o n The i s disposal, water principal load. predictive dispersion salt s i l t timber quality. the water-borne concentrated the numerical necessary estuary waste operation, made of i n d u s t r i a l dredging and number transportation, water's round deposition would The year the therefore, hydraulics a expenditures, sedimentation observed is are is with of i s with in a Chapter 3. and an The Chapter predicted a in brief presented. in the given derived, applied and variations discussion 5 results. of some 6 important aspects of s a l i n i t y intrusion Considerable research effort Previous sedimentation twenty years. model constructed Professor Notable E. schemes made and (1952,1953). the flow confined made the penetration. Although indicated relate water of conditions to were s a l i n i t y Markert and were Branch valuable of in made in density and structure made. temperature 1971 (1967). profiles by A. Environment Canada i l l u s t r a t i n g s t r a t i f i e d H. at Ages (unpublished) D. and and no to long physical various t i d a l series of reported by series of was Several conditions this have estuary, and low during piling the can Baines sedimentation various of which conditions for by stage flow research One measurements Meickle by timber the scale of discharge and last controlling series river the Columbia tide-low However, in rarely during high hydraulics presence salinity/temperature/depth Waldichuk, for 1952. borers the of toward physical channel discussed made over B r i t i s h extensive are the the of unstratified marine salt measurements in to was calculations were directed Fraser various Two data, conditions were salt regard which cubature attempts delta estuary. been lower University on series has the this the these The was at in developed. from tide-high in Pretious were measurements period the Work controlling be in locations Marine these for in the Sciences data high were tides 7 during the winter months, and aided in the design of the instrumentation. The Water continuously River at at of semi-annual P i t t estuary River. " t i d e l e s s " Keulegan t i d a l l y numerical have and In made between are only physical the arrested in salt Fraser motions are modelling, offered published by far varying a the good Vreugdenhil the Fraser theoretically Mississippi from lengths data. a From was chance of and River achieved. flow i t a i s and the standpoint of are required success. behaviour (1970) applied However, the in by between steady equations unsteady Georgia the flume important. time describing i s of penetration comparisons experimental estuary for salt The detailed Keulegan to good Georgia. Strait data Fraser elevation (1953). penetration obtained and Morgan the very the studied wedges predicting model models and of publishes been Farmer solution Marvaud surveys have and the been also controlling induced numerical Works in Canada surface Strait mechanisms Morgan mathematical the hydraulic for that of river basis. "steady-state" clear the discharge continuous (1966) and and Environment a success Farmer on estuaries results where These available 1), upstream Public of freshwater (Figure sounding The his B.C. Branch the locations Department and monitors Hope, eight Survey of salt Boulot, and Two wedges Braconnot (1967). both conservation of analyses mass and a two layer momentum model equations was for assumed each layer and were 8 numerically integrated et did not include their model and i t They presented a l . distance of resulted from using can salt be results less water showing one small The model of but unfortunately and physical predictions was Vreugdenhil*s salt and water discussed in Rotterdam same Waterway equations reproducing i s the - The distances on to the model give salt a in a l . , water slope ranges in between the and salt and the i n t e r f a c i a l states good the 9 that from he was 2 stress able to correspondence with calculation the their model of model are from the essentially the the method features. succeeds Of times from in 3x10~ shown) the has a calibrate the t i d a l to suggesting a Penetration 1.6 coefficient term in interest (ebb) 4 velocity. for empirical downstream measurements Using data Km in mixing from several water meters neglects Vreugdenhil's for a discussed. prototype shown over distance 0.14 between results intrusion in analysis. Grand-Rhone also and layers short averaged were Boulot o s c i l l a t i n g This correlations model (estimated variation front the the no-mixing Netherlands. shape concludes analysis The i n t e r f a c i a l vary Vreugdenhil no to layers, et a which observed Boulot (flood) 4 salt schemes. between kilometer. layer the to wedge as measurements in main mean considerable the as the salt cycle. 8x10 relation the applied two between exchange tides amplitude. Aries, difference c l a s s i f i e d than the f i n i t e meter tide. which enters dominant effect the observations predictions using this coefficient. By using a for horizontal tide, that is 9 the barotropic or u n s t r a t i f i e d v e l o c i t y f i e l d as a f u n c t i o n time and p o s i t i o n i n t h e e s t u a r y , V r e u g d e n h i l reduced the of total number o f e q u a t i o n s r e q u i r e d f o r t h e s i m u l a t i o n from f o u r t o two. As a r e s u l t he found t h a t the o v e r a l l b e h a v i o u r of the s a l t wedge was l a r g e l y dependent on t h e h o r i z o n t a l tide prediction. 10 Chapter 2. INSTRUMENTATION Previous indicate winter the presence months. penetration Strait of f i e l d measurements of salt However, and tides are data. Tidal amplitudes percent of depth for several Under i s and kilometers these River river bottom during salt water the extent between the s a l i n i t y to determine the river of to reverse the of seawater the region value of structure entrance s u f f i c i e n t above conditions, was clear that adequately describe measurements in conductivity 1972/73. were the Three installed to over point and from can the these exceed river 40 flow penetration. measurements in time of would f i e l d and the and as i n s t a l l a t i o n by of column to programme of the and which every 15 February of the winter of Osborn 1973 "conductivity were: reguired records during Farmer March water a continuous undertaken described be (1973) provided minutes,"and p r o f i l e r s " . 01 to 13 The and March 30. are parameters Canada was described of data emphasizing February most series density r i v e r , during periods The River the instruments subsequently actual time structure, conductivity 16 are Fraser in d i f f i c u l t at the the limited. It are along variations correlations Georgia the water from two most important the tide and are continuously (Environment calibrated the gauging forcing freshwater monitored Canada). staff at Hope, The functions discharge. by the discharge B.C. for on an the Both Water i s Fraser of Survey computed average these daily from of a basis. - 11 This figure upstream used is then point of the f i n a l carried out provided comparable during were the made sensing and using The B.C., the Agassiz large wire abandoned for d i f f i c u l t y in during well to In many furthest figure while not current w i l l was of depth the of a readings be 20 the °) with ebb exceeding boat. 30 °. measurements explain why of water slack in the most periods the - pound real The weight used currents produced equipment i l l u s t r a t e s the available over when were salt were the Fraser data was limitation measurements in occasions times measurements winch light and This This other 25 The Ebb this phase a the speed. was salinometer. above but At (STD) RS5 line small current (exceeding angles winch metering measurements. data. physical main River, obtained water was river. Instruments any factors protecting s a l i n i t y Instruments a stern portion established of March, conductivity and to accurate making high Location the depths considerable helps attached angles of with Industrial off very days salinity/temperature/depth an was operated of two velocity winter, accurate and Agassiz, influence. simultaneously head capable a t i d a l for throughout. During to adjusted the scheme to influence in the time instrument conductivity interfering considerations collect with Fraser p r o f i l e r s series from disposition. in navigation River. data .It the large f a c i l i t i e s , was also estuaries Securing ebb were and currents, the important main to 12 monitor as p r o f i l e r s Figure part much adjacent 3 shows of the 1 2 Timber the system protection tides, The a 3 for thickness 4 two were river t r a f f i c of meters located separate of the in the for on covering indicating the of column. extent of coverage stations 1, 2 and gauges, river This and of provided a was low monitored. Rice made each of At to M i l l s obtain cross-sectional for a degree Canada were and beside currents. water pier The tide 2. the Conductivity the and installations water and from temperature the properties periods found. was s a l i n i t y characteristic to erected 6.1 chart, shape p r o f i l e r , are 3. P r o f i l e r s months 25 were lines Figure from two. sensing and established these the the river t i d a l to mooring of winter between adjacent the gauges. instruments. 1 and coverage The located enlarged locate tide penetration, permanent platforms p r o f i l e r Conductivity the water and maintained profilers improved in possible, for where shown with salt debris, minimum as channel Limited, the were pile from third River of placed navigation rigid Fraser column government various and was water the region of p r o f i l e r s the to the the locations p r o f i l e r of when along 29 The the parts fresh of Fraser the two salt water river bottom, per had collected River water from thousand, water data the and Strait some During of those Georgia typically temperatures temperatures the i l l u s t r a t e masses. s a l i n i t i e s during ranging of 6 from was ranged to 2 8° to C Figure 3. Lower Fraser measuring instruments. estuary showing the locations of the various 14 G.D. LOW WATER LEVEL J STATION 12 LOW WATER G.D. LEVEL STATION 2 G. D. |0 \ 2 4 6 8 10 M E T E R S STATION 3 100 F i g u r e 4. C r o s s - s e c t i o n a l p r o f i l e s and probe l o c a t i o n s at the three measuring stations in Lower F r a s e r estuary. 200 line the METERS 15 5° C throughout For these the temperature profiles are Thus a measure infer the primarily both however, these temperature Operating inductive and the conductivity of be the STD and can be used to structure. should by density structure. density temperature the s a l i n i t y . s a l i n i t y distribution improved from detectable the hence and can be recorded; incorporating the measurements. sensing located probe by by cycle to e l e c t r i c a l conductivity successively l i n e inside i s current c o i l current water Each secured the act as of two in interrogating the water instrument housing, a any check on of column. is d r i f t also in the c o i l s applied in in i t s the acts of to core. sea in a mu-metal insulated one This water c o i l , current path proportional to the copper which in linking complementary annular the e l e c t r i c a l wire. induces turn fashion cores induces two to the A an an c o i l s . f i r s t , conductivity of path. probe a consists torroidal current second on a depths the response. e l e c t r i c a l a on every voltage e l e c t r i c a l measure fourteen in surrounded recorded no conductivity available probe, Each sea the profile probes e l e c t r i c a l the both function estimates at interrogated carrying a instruments fifteenth The ranges and Principles water constant period conductivity data The A of s a l i n i t y Ideally, sea measuring was Rustrak interrogated chart for recorder. one minute The and sensing the line output was 16 interrogated from occupying fifteenth the completed hour, a every bottom to position. fifteen frequency top, In minutes, considered with the this way, producing satisfactory calibration a four for probe sequence was cycles the to examining tidal phenomena. Timing small hobbyist's inside ±4 the minutes per a batteries, Ebb A could would be in the be also in by near was with an outdoor constant power accuracy of lead supply replacement once by a supply exceeding the operating volt 6 controlled independent independent four line Rustrak conditions. acid storage voltage each the seemed to of conjunction had to be a l l logging in for two week. real be free with of addition, types, the and the river floating Holding under 2 and constraint challenge. the types exceeding industry. place, best purposes. other In of securely a currents River. t r a f f i c provided and produce Fraser boat variety possible, operated platform cost, a for required from sensing platform serve an timing feature a on clocks, regularly primarily reasonable the interval Servicing tides a These provided considerable protecting operating powered charts and meters/second of were which Installation debris interrogation made desirable Rustrak carries clock, week, instruments weeks. the instrument. behaviour, The of Servicing of the solution from measuring conductivity strong because a small equipment profilers. o s c i l l a t i o n s which i t boat could Any would 17 affect the Rustrak operation and could lead to structural deterioration. A f i n a l equilateral three and feet the apart 5 station the 2. piles, a deck. The of and protection crossbraced sketch in of the i n s t a l l a t i o n at floating for an spaced arrangement actual logs, in frames were dimensions the tube frames working triangle arranged steel These shows some The by guide at the was by a probe brass The wire line stressed rigging. on Two piles. 6 (c) perimeter sensing 5). wire weight the piles the just outside probe line by secured to debris. platform, guide chosen. pertinent provided The (Figure the timber supported Figure The deflecting the triangle and three was ^joined gives instrument of triangle lower Figure design down weight was probe are shown line kept i n s t a l l e d , the i t a guide and in wire resting coupled snap-shackles, l e f t , probe heavy line inductive the lowered in often on five the bottom places to used in sensing line, coupled Figure 6 (a). the s a i l A boat to 30 the pound extended. s Once The platform the probe without This cover plywood large lines and box As shown Rustrak meant during enough that bad also for conveniently, d i f f i c u l t y . instrument box. was instruments were Rustrak weather, provided a some in one and were person to batteries Figure arranged charts frequent security in easy raise could 6 (b), a could to the service. and be exchanged batteries, weather-tight be plywood replaced occurrence against lower in winter. vandalism. under The 18 FLOOD GUIDE CURRENT WIREN PROBE LINE. EBB CURRENT P L A N VIEW HIGH WATER C C C C LOW WATER C O PROBES GUIDE -SLIDING (14) WIRE WEIGHT -PERMANENT ELEVATION Figure showing WEIGHT VIEW 5. Diagram of the timber pile platforms general arrangement of instrumentation. 19 Fijure 6. (a) Inductive c o n d u c t i v i t y p r o b e and sensing line. Guide wire and coupling shackle appear to the l e f t , (b) From l e f t t o r i g h t : lead acid storage batteries, Rustrak recorder and instrument electronics. (c) T i m b e r p i l e p l a t f o r m at s t a t i o n 2. 20 Two so the strong the that f i r s t problem d i f f i c u l t i e s two total significant week more period weights encountered. probe of added weight of this the last line The to to type the currents occurred To guide 185 a ebb deflections i n s t a l l a t i o n . were submerged i n s t a l l a t i o n s were during alleviate wires, pounds. minimum were figure this increasing For of 300 future pounds is recommended. During was damaged. causing the entire v e r t i c a l . broken A and the s k i r t logs were structure to on resulting to progressive next February weld susceptible the of The the upper loss in deterioration two weeks, o s c i l l a t i o n , the to 1 sustaining 1.5 one this design's platform smashed triangle (station free 5 pile made of remaining third of clamp the the remained damage. The in also more occurred securing Figure over clamps were amplitude of operative to the 7 shows current the was off Consequently, increased effectiveness. 1) piles, platform welds the the degrees o s c i l l a t i o n s . and meters/second 1 approximately r i g i d i t y the platform attesting approximately of u n t i l Despite the go flow-induced ineffective. after week is end, platform ebbing at photograph. Calibration Following (1973), stages. of the the procedure calibration First probe the a c e l l casing, of each constant was found. developed probe Kc, was by carried depending The value Farmer of only this and out on the Osborn in two geometry constant 21 Figure 7. Timber p i l e p l a t f o r m a t s t a t i o n 1 a f t e r d a i a a g e . Skirt logs are missing and upper pile clamp on f u r t h e s t p i l e i s i n e f f e c t i v e . The c u r r e n t s p e e d i s approximately 1.5 meters/second. 22 varies of s l i g h t l y the solution instrument the output voltage probes were sea was in a Reg, found sea water c e l l constant from which probe solution. i s find Kc the about 11 and selected ranging the were each water function known the calibrating conductivity. immersing after each The which the A conducting loop box was the "equivalent passed voltage solution of conductivity. dried. output the of by solution, and same of and to In from increasing value in mean the of through the resistance", obtained conductivity, be in the Cs, the sequence practice, to was process were used used for was to each typically value. measured 100 three averaging constants a conductivity these were calibrated through output. of c e l l conductivities recorder a response involved determined resistance average of the box as stage independent by: scatter electronics resistance the worst percent Once the always (1) solutions The for i s Cs separate probe. f i n a l Knowing Three and The i t e l e c t r i c a l solutions the defined = Reg. the casing, yielded but and were water variable each probe recorder recorded removed with Kc chart constants several series opening and c e l l in to recorder. electronics probe probe conductivity and The in from 1000 by of in known, the simply resistances the nine ohms. f i e l d chart adjusting compatible and resistance A least recorder noting values squares the with the were analysis 23 was used output chart to find and the record a functional resistances. has the a-, are recorder Data mmhos/cm and on one the to least a a and and relative range l i e within to the results from two = Kc 2 of the the quote an of mmho/cm +2 individual mmho/cm discussed ±1 conductivity conductivities of different (1973) accuracy of nearly station 2 on conductivity from in of 0 RS5 mmho/cm. another on and y is figure and subsequent p r o f i l e r s . The for the of the one best. the These values I this value Figures conductivity for found calibration applied plotted ±2 probes during In of the mmhos/cm. sections. are two 8 (a) obtained times at j March an 29, line In of are f i e l d The ±2 the comparison the'latter the with recorded and shaded mmhos/cm. shown were comparison worst 1973. represents accuracy profiles each 35 have instruments accuracy between measurements profiles salinometer i l l u s t r a t e of the (2) absolute to simultaneous profiler based the reducing 3 coefficients i values for a, + a y + a y : squares Osborn line to 8(b) equation recorder Accuracy, repeatability and f i n a l the output. Farmer apply (mmhos/cm) the Processing any The between form: conductivity where approximation case band range The of an error within 15 obtained, and accuracy obtained bar minutes in of each possible values results the on of ±1 of one Figure those ±2 in 8 (a) 8(b) mmhos/cm 24 CONDUCTIVITY ( MMHOS/CM ) STATION • CONDUCTIVITY 2 PROFILER MARCH T E M P E R A T U R E (°C ) 29,1973 K H RS5 SALINOMETER F i g u r e 8. Comparison of measured conductivities by two- d i f f e r e n t instruments (a,b) and measured and p r e d i c t e d t e m p e r a t u r e s (c,d) f o r two t i m e s on March 29, 1973. 25 seems two very deep side probes of the magnitude, a small results due reasonable, in Figure line in suggesting ebb from to measurements or of a i t does 8(a). 8 (a) a tide. those either as for The are almost that Therefore, the salinometer s h i f t in calibration the i s near identical quite between that surface results cn in of 2 and and either shape stable departure water factors the profiler structure the both and following the 5 profiler meters is column structure between are in error certain and a for j probes. be The second observed differences profiler their are error), instrument to outdoor effects become cases a on within the flooded, f a i l laboratory but In these practice of the probes, were found period and their and was and . A more serious probe heads. were appearance for heads, three data were values RS5 considered the problem Often as probes of apparent the was deep Rustrak charts retained in the the f i n a l was from and in under moisture probes removal distinguishable during the but done detected. after on humidity concerned easily values condensation determined the the (including effects and not the. applicable. calibration were of was on calibration effect can although the seepage influence moisture 8 (b) temperature electronics and Figure trend accuracy exact entirely similar mmho/cm influence The the "moist" ±2 moisture their conditions. beads to heads. minimize few figure humidity changes the in overlapped seemed probe l i k e l y probes Since accuracy electronics temperature order this most same always probe: the is smaller. factors each inside the results Two for for cause In to would other the normal. flooded i n s t a l l a t i o n analyses. The data 26 presented charts in subsequent using i n s t a l l a t i o n induced calibration and no changes. positively sections factors attempt Probe were was made eliminated and density data were used in the A estimate of s a l i n i t y reasonable temperature effects improved the computed for salinometer but if Rustrak prior for to moisture failure each of of and representative of Knowing from b, C for measured 8(c) following S = + b T S = s a l i n i t y C = conductivity T = temperature 2 on data where derived from could be made and without including temperature data Temperatures linear relations from accuracy of between RS5 periods. are ±0.5 were the i n s t a l l a t i o n shown °C would in be way. temperature, the s a l i n i t y was relation: + bjCT, (parts measured results. accumulated this the the temperatures an in of background based derived conductivity the be particular and (d) , data can estimates. temperature surveys Comparisons the conductivity and derived parameterization incorporating accuracy conductivity where account were and computed to the immediately heads conductivities Figures obtained from determined. Salinity the reduced per (3) thousand), (mmhos/cm), (°C), as derived from the conductivity data. The coefficients bj were obtained from a multiple regression 27 analysis performed from Lafond»s from Figures compared in s a l i n i t y ranges calculated root mean then, that are Table the 1. quantities in accuracy of Sigma-t is (P closer represents of of given results, is listed and tho each previously in differences column 6 from the conductivity values indicate. maximum l i m i t temperature In if data fact profiles computed error range inaccuracies combined a appears, the the a l l have It than error between and thousand. are computed quoted per actual profiles s a l i n i t i e s for The obtained f i e l d parts the would computed terms of ± 0.01 for related fresh sea to an of combined used The for in of properly taken often as written or 3 for and the maximum the specific is Kg/m ) 3 O" t range accuracy. way was can in gravity the in worst be by and of 1.0000 in sea and this data and (7) the been from evaluated their in one-half Table an 1 l i s t s , by the specific (that done the including of Since density has and p water, 3 of to temperature. gm/cm , terms Lafond calculated diroensionless. established Column given s a l i n i t y calculated temperature worst relation which the gm/cm accuracy °~t, values water i s the given and 3 water using sigma-t, conductivity equation. figure was units estimate were to the and -1.0000) x10 density i s 0.53 the measured appear derived ±3. 1 % o and temperature. of parameters way. (1951) gravity value s a l i n i t i e s Density = (3) and conductivity °~t accuracy and square three Using computed equation measured the (1951)). (d), An of conductivity the %o possible To and on averaging ±3.1 values (Lafond 8(b) considerably error of Tables based for on here. p r o f i l e r errors Lafond's of a this Table 1 Comparison o f d e r i v e d and measured s a l i n i t i e s f o r s t a t i o n 2 on M a r c h 29-, 1 9 7 3 ( 1 5 5 2 h o u r s ) . * i n d i c a t e s i n t e r p o l a t e d values. DEPTH (meters) ( D 0.3 0.8 1.3 1.8 2.8 3.3 3.8 4.3 7.3 . COND. (mmhos/cm) (2) 4.47±2.0 3.89 4.61 5.01 6.65 9.06 12.09 1 4 . 18 26.34 TEMP. (°C) (3) 5.89±0.5 5.86 5.89 5.91 6.00 6.12 6.27 6. 38 6.99 SALINITY CALCULATED MEASURED* (7oc) (%o) (5) C O 3.83±2.9 3.24±2.9 3.97±3.0 4.37±3.0 6.02+3.0 8.42+3.1 11.43±3.1 13.49±3.2 25.28±3.4 3.00±0.5 3.25 3.60 4.30 6.75 9.00 11.20 14.15 RMS - value DIFFERENCE (%o) ( 4 ) - (5) = (6) +0.83 -0.01 + 0.37 +0.07 -0.73 -0.58 +0.23 -0.66 - 0.53 SIGMA-T (7) 3.04±2.3 2.58±2.3 3.16±2.3 3.47±2.3 4.77±2.3 6.66±2.4 9.02±2.4 10.63±2.5 19.8U2.7 NJ CO 29 sequence of together with and as in °"t • s the the calculated errors. case of from An the average s a l i n i t y this profile value figure of in Figure ± 2.4 was represents 8(b) obtained the maximum range. C«££gnt Metering One aspect measurements tide. is Due the to measurements from v e l o c i t i e s motion i t s e l f exceed However, once current The speed years. A March our siumlataneous and two at located record at the of At these station The suspend the 2 platform current meter is a Canada impossible on station and time the boat particularly in the i t both from became The a catamaran River was object three to for with several undertaken station was as a conductivity however, vessel. angle. occupying density the feasible wire Fraser programme 2. the addition, In operated boat f i e l d the constant the by once suspended has Survey velocity to 1 on and obtain function profilers probes at a of were station 1 lost. station meter. current at stations; at reliable flow Water were making installed measuring this to were of at relation errors, equipment velocity tide. functioning the Survey 1973 with and in its meter/second. the measuring equipment depth meter joint 30, i f examined v i r t u a l l y large platforms Water current one is seldom and angles, boat induce direction, River structure wire small can the Fraser current a current a the large river hold of To 2 was used eliminate as the a fixed problem point of to changing 30 wire angles the platform constant meter using stable platform meter of equipped and in 300 10 this rope for each i n s t a l l a t i o n operating the RS5 sensor, a and magnetic and In ± 5 a s o l i d compass. degrees general, the when minimum clearance in vane An i n the a of 1 give the manner to and the was reading. Figure 9 (c) shows and in is was Figure guide 9 (a) hand To tied obtain off the the wire by depth. a current lowered required gave The on from This rope to current method of shown. a Hydro Products rotor ± 3 is quoted were became small. from minimize by the platform the to speed manufacturer. each guide nearest speed relative for The speed the for stable the series readings percent values meters 400 activates direction of direction 1/2 running raised provides speeds i n s t a l l e d . currents. was accuracy the a l l Savonius direction except located A in running hauling meter meter. was wire the salinometer current direction to guide trolley configuration, the and a system a anchor degrees and The current, pound with calibrated most the a angle 9(b)) a changes to wire was (Figure the with depth wire pile had and interference of a was the flow. The primarily current pound but the channel Water for meter estimating is weight. suspended The direction at Survey station of Canada discharges on a magnitude relative 1 is to f a i r l y in single of the the eguipment was unstratified line just current river is straight and the rivers. above vector not designed is a 150 obtained measured. principal The flow The 31 F i g u r e 9. (a) O p e r a t i n g t h e p o r t a b l e salinometer the skiff. (b) Hydro Products c u r r e n t meter and trolley running along a guide wire. (c) O p e r a t i n g t h e c u r r e n t m e t e r a t s t a t i o n 2. ofr 32 directions at station desired is are more 2. Although direction reasonable represent to flows 29, minutes, on A instrument presented in be be parallel actual current aligned with the 2 was Velocity March the Table also the from the speeds shoreline component station exceeding than in a 1 data, i t 20 cm/sec banks. occupied profiles during were daylight measured hours every on 45 30. of derived 2. to velocity computed that summary and the cannot 1973. as to assume Station March l i k e l y the data accuracies for the associated Fraser River with project each is 33 Table 2 Summary o f a c c u r a c i e s a s s o c i a t e d w i t h the Fraser River project. * indicates explained i n the t e x t . CONDUCTIVITY PROFILER (D instruments used for derived values as RS5 SALINOMETER (2) HYDRO PRODUCTS CURRENT METER (3) CONDUCTIVITY (mmhos/cm) ±2.0 ±0.5 - TEMPERATURE (°C) ±0.5* ±0.5 - ± 3 . 1* ±0.3 - SALINITY < %o> °t SPEED (cm/sec) DIRECTION (° of arc) ±2.a* - — - - - ± 3 ±5.0 PERCENT 34 Chapter OBSERVATIONS 3. On five occasions salinity/temperature/depth collected primarily p r o f i l e r s and temperature once the water short space in the of conductivity straddle deepest These 60 On data water buoy the are f a i r l y was done well be decreases in the downward Conductivity The to and Figure feature the the upstream dilute the of ebb s a l i n i t y of river the over were a sampled with locations located in the found. longitudinal section depths shape the - of at each the salt p r o f i l i n g s t r a t i f i c a t i o n stations in indicating water quick coincide currents between f a i r l y were like - the approximately water isohaline direction salt a wedge on upstream salt and angles average stations station, of 10 the especially the the strong wire in were conductivity examination and the is was stations traces period data the two fourth for an distance the limiting that a At in on profiles four 1973 2 no These locations and maintained, seen 8, study information allowed 1 Despite at check f i r s t channel, obvious f i e l d spanning by' i n t e r p o l a t i n g One also March profiled intrusion. 28 mixes of made. various The 3. were these and at p r o f i l e r s part plotted Making minutes, station station. can time. a the background station kilometers. 10.5 i s on structure space as provide was of surveys act structure. boat salt to to during 1 and at is 2. It the salt wedge that fresh water below. Temperature measured conductivities reflect the extent of mixing 35 SALINITY (%o) SALINITY (%o) (d) 2 0 2 BUOY 27 4 DISTANCE (KM) 6 BUOY 28 8 (e) F i g u r e 10. T y p i c a l s a l i n i t y data f r o i n the F r a s e r estuary on a s t r o n g l y e b b i n g t i d e . The A g a s s i z d i s c h a r g e i s 1 6 0 m /sec. 3 36 of salt between approximation, in a like the manner temperature data in 11 Figure and relation between of as overall Salinity in inequality of predecessor produces in the stations be last in summarized for and is the Figure from the two week 2. This considering profilers and group from Chapter estimate linear during particular of groups a each density section The three relation and s a l i n i t y are warmed temperature a rough distributed intervals, masses reasonable on day for a conductivity. conductivity conductivity range a the when to of very a 1, derived 2 Fraser the the effect of density. from 3 which below data. t i d a l Figure plotted which each tide high-high intrusion extreme conductivity in the amplitudes, produces In for the variation succeeding different been and estuary large, meter markedly have considerable each conductivity profiles were this is zero fraction the a 30 water the to to considered s a l i n i t y in gives of is results described assumed as Profiles There nearly and and measurements roughly pertinent calculate accuracy temperatures by the calculation STD data both p r o f i l e r i n s t a l l a t i o n type the be related Since to conductivity i f masses can during another period, used linearly temperature reasonable. was 11 one water temperatures collected from measuring two and separated very the looks a ranging much high-low water. This two series i l l u s t r a t e tide type. profiler data the as of from as water characteristics 12 diurnal i t s only variation revealed s a l i n i t y behaviour The using a at s a l i n i t i e s equation 37 8 STATION I A JAN. 30 0925 O JAN. 30 I 3 0 0 O MAR. 8 1 0 3 9 © + • 0 9 STATION 2 J A N . 29 0920 J A N . 29 1 2 5 0 MAR. 8 I I 0 I MAR. 29 0 8 5 3 MAR. 29 I 5 5 2 ~0" o BOTTOM WATER SURFACE WATER ± 10 15 CONDUCTIVITY ( 0 Figure 11 obtained occassions 20 MMHOS/CM) Conductivity and temperature with an RS5 salinometer on in the Fraser estuary. 25 da t a four 30 Salinity [%o 10 Station I >{k River discharge M 3 0 m V s e c . a> °"'» 0355 H l' 20 2 4 E • Station 1 • Station 2 * Station 3 20 22 0 2 4 6 B 10 February •0 20 10 10 - 12 14 * 16 18 20 22 0 Hour* 10, 1973 Salinity K 20 IQ •/ (%o) 2Q 6 VI ^ 0856 \ 0933 \ V \ \ \\ • Station 1 \ * StOtion 2 * StoNttn 3 •'Deepest Channel bottom at Station Station I I River discharge l 0 6 0 m V s e c . 22 0 6 2 8 10 12 14 16 20 March 18, 1973 22 0 rtoun Salinity *. u *\ * 0258Hou't • S'01'On 1 * * Siot.on 2 | • SiO'.on J I \ \ \f f 0456 } \ 0358 ff > j | * t tt ' " X •U .6 10 r : \ ZD HJ 0658 "'V \ (%„) 10 Y\ V\ 20 * ;•0 07 SB \ i ! \ \ V 10 56 20 iV \ \ • \ " i io 20 \ "V ' ^ 09S9 { 3B O 1 \ \ > \ 3 ' * 1 i \ » i \ Deepest Channel bottom ot Station I Figure 12. 18, 1973 a t station 1. 20 Salinity-depth p r o f i l e s o b t a i n e d on February 1 0 , 1973 and March s t a t i o n s 1, 2 and 3 . C h a n n e l b o t t o m i s t h e g r e a t e s t s o u n d i n g a t CO CO 39 (3) and the profile is plotted particular could the less nearer to meant that any for the not of the fresh This water layer u n t i l the station shallowest with respect i s the at Despite upstream these station and water The that we are has 2. to any centimeters error would profile can be position has monitored at as i s probe s l i g h t l y has the f a i l e d behaviour actual salt least five at station station be occur each is the Furthermore, of this 1 and watching reached datum estimate situation additional of the platform column l i t t l e at 50 below an intrusion above at Each measurements line series. seeing I The where means and 3. 11. surface and the probes the f i r s t kilometers worse of datum, since bottom lost Figure free 1 and channel series 1. stations of of approximately s o l i d the March of The percent for the station 70 the horizontal series water. relations to error each deepest only a for combination at motion respect maximum most station worse a high represents the with profiles for seen, temperature station, introduce between much linear so 1 wedge or six is this of the problem positions. limitations there i s much to be gained by series the s examining long high the water penetration, The at duration and at a l l station been recorded March at three this has manner. resulted exceeding associated tide the in probably p r o f i l e r halocline by data 3 has with maximum series, a February very long kilometers s a l i n i t i e s the the shorter pattern high water wedge station the interface exceeding This salt above measured salt-fresh penetration. where in clearly the stations 15 In distinct around 25 is 1. %•> high have contrasted duration has 40 produced to be a s i g n i f i c a n t l y measuring improved gain nearly 3 The by the after typically between halocline has the 2 depth March at suggest layer. a These local mixing surface 10 %o. In lost to an almost 1 and the back these previous ebb v i c i n i t y . of river and Strait These does with not produce a measurable the salt more tide, the wedges upstream - i s 18). show a maximum, any distinct of s a l i n i t y preserved instruments the result flooding flood strong of tide, far as (near the f i n a l salty or a duration formed as and water from tide in 1 salt convection waters, water by stations is mixing 1 and confluence 2 of ). show localized dispersed longitudinal surface certainly high data to d i s t i n c t series reach over the The Sandheads Georgia profiles have arrested of brackish or the series and both for could masses by 17 (17 seems fresh increase flowing mechanisms. during the convect 1 for halocline s a l i n i t i e s water tide uniform layer and 3 of less salt February through upstream to from 14 a s a l i n i t i e s the The surface surface s u f f i c i e n t the 2. profiles between of surface 15 mixed high waters combination water, high station to and well following of spite between column) mixing profiler In relocated water at and l i m i t . was two-way recorded stations series of and high been 3 profiles p r o f i l e s just with meters evident penetration intrusion (profiler more is suggested that the coverage halocline is near shorter t i d a l the s a l i n i t y mixing density s a l i n i t y that gradients is structure gradient Fraser in strong and the estuary associated enough there surface to is a and 41 bottom waters estuary can be discernable The near in particular these If salt-fresh coupled w i l l small. data the maximum two hours to seaward water at confirms to of the these occur velocity quantify penetration of approximately Conductivity The two week 1 and (and three two to be w i l l layer, mass 2. the and the in water tide at station gradients water being forces. flow where water three the lags but occurs 3, 10 are maximum high i t high and w i l l be the the flows relative the just show February one to after two that the increased during downstream that The the a due salt March series penetration seems tide. i t In is appears tide the the about and phase. across of In upstream. measurements relationships time. suggests following these small are to motions accelerated This to is the pressure momentum and density) is of separation exchange 9 t i d a l response layer phase Profiles a of which the comprised salt hours during salt layer of observations, phase of separation continues data the high pressure about most relative large surface depth throughout then i f behaviour layers of large of the two the penetration s a l i n i t y when the a following period in the have stations v e r t i c a l each Conversely w i l l at i s and motions hours in However, terms exchange interface highly in balances the tide. data motion force f r i c t i o n . be viewed in changes high absence d i f f i c u l t that at the the station to maximum 1 by hours. Charts conductivity periods, since by p r o f i l e r s were the 13 end of or operated 14 days basically in the for river 42 sufficient damage to removal warrant these time constant the values two where of vertical axes meters time. stations this 1 and datum surface from is based probe the bottom the platform As during the known. on t i d a l was 1 lines assumption was would to be the of a the these previously period. examining applied and map line The anchor also directly relative to indicates the depth the the are dimensions represent 14 horizontal used position 1. data and 13 lines were broken t i d a l the of between represent and datum level contours of datura of the to bottom and unlike river bed at of f a i l failure charts and reduced data. within the error were plotted, at time only general probes any could in which at the bounds were the water of the operative appropriate section. surface (G.D.) would data: indicate zeros time Rustrak stable To the probes The the to s t a t i c a l l y left Records . geodetic 2 from measurements. section depths, station contour maps one, line presenting Figures surface estimated i n s t a l l a t i o n One a free station explained by for in 2 locations. determined individual number probe 12, a of 1 and interpolating contour from Figure of plotted Sandheads the At by stations method form data in be column above since 3 the and at Conductivity are probe bottom heads obtained tide for heights the cycle. above The Tidal in conductivity types probe A convenient is different plotted. for data values in the repair. each the is of to for distance axis and series measured for occurred height are also at station plotted in 1 relative to Figures and 13 the '1 STN.I FEBRUARY Figure 13. Contour estuary. Bottom i l i n e s are indicated d i s c h a r g e i s 1130 m 3 1973 maps o f c o n d u c t i v i t y a t t h r e e s t a t i o n s , i n s marked r e l a t i v e to t h e p r o f i l e r and t h e u s i n g measured data a t S t a t i o n s 1 a n d 3. /sec. Times are noted i n P a c i f i c Standard the Fraser free surface The Agassiz Time. O J STN.I MARCH 1973 Figure 14. Contour maps of c o n d u c t i v i t y at. three s t a t i o n s i n the Fraser e s t u a r y . Bottom i s marked r e l a t i v e to the p r o f i l e r and the free surface lines are indicated u s i n g measured d a t a a t s t a t i o n s 1 and 3. The A g a s s i z d i s c h a r g e i s 1060 m V s e c . Times a r e n o t e d i n P a c i f i c S t a n d a r d Time. 45 14. Chart datum for representing the of Geodetic position. such a more contour recorded pronounced occurred lowest diurnal inequality height is 8 and produced to the and therefore Figure inequality. 16 is is a a sloping level a line function plane and as obtained from the datum. in February River considered reference March and t i d a l charts between from Fraser datum convenient The data the 11, In 20, 13 were 1973 for contrast 1973 the have conductivity data tides a having tides small contoured a which diurnal in Figure 14. Care data. wire 2 As must mentioned angle during of excessive and f i r s t during wire the angles did this into account a approximately 2.5 of on this error data) periods than data is i s of to the probe not for I estimate measurement 3.0 meters contours to indicate the case. This wire angles where an during scale attempt absence problem were at of been was water to and ebb The the of effect to adjust for longer corrected confined that reading made and stations large a a ebb. period, shown. salt daily both the to has 1 indicate recording that giving large one February stations phases Probe the at the correspond on (no on t i d a l entire the deflections occurred period occur. the interpreting line degrees remaining function points 20 when i n s t a l l a t i o n not lowest March previously, 2 did taking the exercised approximately the Observations 1 be for less than the 10 degrees. The conductivity profiler at station 3 produced data for 46 only one t i d a l operative for The the salt at If and water true entire period in Figure feature in both scale cycle. salt in predominant horizontal tidal the cycle of we is 2 station 1 due the (Figure 13) and However, the flood indicate a water were degree an The vertical of mixing the data; March p r o f i l e r was penetration. show end that of layer ebb has is the the water appreciable taken of and place. only mixing 15 most of both true station to i s is figures probe line the salt of however, 10 the certainly indicative the the of measured ebb the cycles and flood for stations 1 and 3 indicate that the of the following fresh both 14). kilometers. contours very at February (Figure study; upstream of acertain tides the removed when certainly in on February contours on from i s on during This to each separate periods flood this large time March 1 was during to measurements in 3 the is of in exceeding close steepness salt station wedge d i f f i c u l t On made the contour station were is deflections water. comparable located is direct This water long but probes). figures probes at distance results i t probes), (10 instrument. No spacing tide. The at present s t r a t i f i c a t i o n the salt length 14 are line of large. intrusion of probe records not (seven salt there although tide of the each loss detected portions 3, 13 millimho/cm the penetration indicates 15 at large return s t r a t i f i c a t i o n the and of masses, present stations deflections the water not to motion use fresh Figure rapidly water down l i m i t the and into ebb toward the 2 in tide the salt 47 The water did not result, move the profiler The conductivity contour both toward predominantly water turn the become Current the two-way, furthest (except on for times 15(a). not The for March surface is suffer to the the further cf each 3 and mixing processes since greatest a at 1 to rate reasonable as interface. station mixing salt and the and are the dilution salt and in mixing. In upstream and station 2 bend. 1973. Profiles made plotted in 15 are indicated are current are from general An to the the the 15(b)) the . mean of 90 for the ebbing tide from speeds apart 2. in Figure the f i e l d directions period two 1 and relative and at minutes 30 flow the out stations directly since was carried March Throughout were to the occupied its at direction value. directions examination the component current location to plotted current downstream due 2 plotted surface ±15° are (Figure station Figure relative speeds 1 At this only was 30, station 2 metering 6) current station sharp trend If that present from current no. measured. varied flood along completion show Structure stations data 14 each increases toe. would 3 on mixing wedge susceptible Simultaneous The in of this Figure s t r a t i f i c a t i o n degree upstream more in generally the in station variation spacing that increase past differences reflect suggests much records of the speeds at are station station river 2 - bed greater 1 than on the in both those inside topography near at of a STATION 1 k 6 CL" < I < Q 0 1 0 1 6 12 MARCH (a) -150 1 1 18 24 1 CURRENT -100 3 0 , 1973 SPEED -50 ( CM SEC.) 0 downstream -150 CURRENT -100 SPEED -50 upstream (CM/SEC.) 0 F i g u r e 1 5 . C u r r e n t s p e e d m e a s u r e m e n t s made a t t w s t a t i o n s i n t h e F r a s e r e s t u a r y on March 3 0 , 1973. 49 station the shows 2 bend located (Figure on that One the 4 salt and as on the have also 5). can increases than trend return near can to the the be ebb flows. After continues to increase at station the seen station bewteen in data 2 profiles the t i d a l 5 of the increasing p r o f i l e although and flows the induced the be behaviour of the transport trend velocity data in surface profiles velocity a shear is not shear also each of to (compare 1 the These 6. stream upstream Such 5. outside shore. 2 in ebb, effect flow observed in the the station increase has on main to between lag suggests rather readily in removal started This be apparent phase side sediment and 4) s i g n i f i c a n t p r o f i l e s currents of considerable so also indicate a layer. Parameterization The conductivity the behaviour and use in of the the the height of salt the water column the layer of fresh egual to that Thus the two water provide masses, mathematical,modelling parameterize decompose charts lower data in terms water. came from measured water and a lower characteristic layer depth, a a l l the water of h*, detailed but for procedures, of Since a length the Strait column layer the i s is scale associated Georgia, to with found we = VSg / o S(z) dz in can two layers: an an average s a l i n i t y having Strait of Georgia upper water. by: h h» of analysis convenient o r i g i n a l l y of into defined further i t salt description (4) 50 where Sg water, S (z) total depth salt in layer is is the of the characteristic the of measured water o r i g i n a l thickness There are gives and part a salt not of problem data when the reliable calculated and used depth to contours salt chart for a the water are loss probe below at and this way of Georgia h is a l l into of the of probes of the of the the salt The meters constant of the this way station the error the it to of not +50 included (Figure 4). The which in plagued this line, way and intrusion. superimposed tide in the s a l i n i t y Figure represents the conductivity, river not 30.5 % the s a l i n i t y ; 16 does wedge c Strait mouth. the onto salt of is The parameterization once is the probe 18 here at maximum March total expected probes been of to each column be have reference adjacent at percent the features since defined 1 introduced 2 kind extend location on the this parameterization near 1 and intrusion 80 deep low 1 h bottom to error station the water is in not maximum line i s do so the obtained analyses 10 of The level line. f i n a l lines In least loss portion of essential to z involved the error the are to probe 1. water h' reached Georgia station and estimated the from estimates the Strait redistributed 1 and portion to arises the depth lines At A greater for despite in section an the due at is relative having values contour reproduce has cross integration. second the line. probe station stations the the the at other most F i r s t , due at d i f f i c u l t i e s monitored centimeters worst main datum. accurate, March column to most the probe referred was the the water two layer depth in s a l i n i t y of h*. parameterization. deepest at s a l i n i t y was of The 0 h'from equotion ( 4 ) Sg =30.5 %o conductivity probes vertical scale: \.Q - 2.0 meters n 8 Figure 16. conductivity 10 12 March 18 14 C o m p a r i s o n o f h» c a l c u l a t e d f r o m e q u a t i o n s t r u c t u r e on March 1 8 , 1973 a t S t a t i o n 1. 18 16 (4) and the measured 20 Hours 52 however, the conductivity equivalent f o r the temperatures Figures data from figures both contoured time periods o f 28 station %> was over chosen. this several figure previously results exceeding 25 c e n t i m e t e r s . the periods. These as the c o n d u c t i v i t y data a comparison structure. This between t h e In order The value to on t h e deep difference of 30.5 % i n a d i f f e r e n c e i n the i n t e r f a c i a l of h e i g h t s not wedge i s f l u s h e d o u t o f t h e e s t u a r y on l a r g e whereas the •i n t e r f a c i a l 17 and 18 n e v e r completely data to zero revealed at station that c o l u m n was composed estuary. Station 1 i s t h e mixing the pockets t h e main in values of Figures 17 and 18 i s an a r t i f a c t does not r e p r e s e n t ranging shallowest after less ebb tide, from o f remnant s a l t remain z the of s a l i n i t i e s reflect upstream An e x a m i n a t i o n following probably several 1. Figures which of the section t r a c e s of s a l t there water Thus, 1 1/2 t o 2 m e t e r s t h e i n t e r f a c e the s a l t wedge of the i n t e g r a t i o n position. goes digital throughout and that tides 1 t o 5 Hi , wedge has r e t r e a t e d downstream. than ebb the e n t i r e water 2.5 mentioned Q the s a l t in an probes The c o n d u c t i v i t y c h a r t s i n d i c a t e line to presented corresponds recorded cycles. and nearly parameterization for f o r Sg and f o r d a t a o f t h e maximum s a l i n i t y 1 % o between salinity must be f o u n d are i n the estuary. 13 and 14 and a l l o w 1 average value at same h , a value a figure found values and March m e a s u r i n g h* and t h e d e t a i l e d evaluate here the i n Figures calculated salinity 17 and 18 show t h e t w o - l a y e r the February span and water which the are would for shown i n p r o d e d u r e and Bottom o STN.2 o g ' ____ If) o cd ' _a> o •x> (m OJ o o. CO o o Bottom p cvi O g STN.3 ' o .—. if) CO " o QJ £ —• o O . CJ o o Bottom oooo HRS. FEBRUARY 1973 10 _L_ F i g u r e 17. Two-layer p a r a m e t e r i z a t i o n of the c o n d u c t i v i t y d a t a o b t a i n e d in February 1973. Bottom l i n e s represent the r i v e r bed a t t h e p l a t f o r m sites. Free s u r f a c e l i n e s are p l o t t e d from measured data at S t a t i o n s 1 and 3. 12 _i on STN.I Bottom STN.2 Bottom STN.3 Figure 18. Two-layer p a r a m e t e r i z a t i o n of the c o n d u c t i v i t y d a t a o b t a i n e d in March 1973. Bottom l i n e s r e p r e s e n t the r i v e r bed at the platform sites. Free s u r f a c e l i n e s are p l o t t e d from measured d a t a at S t a t i o n s 1 and 3. 55 Although position, provides between dividing a good the lags the forms a just feature ebb tide penetration, example, the salt the contour spite This and wedge of implies required in i s charts the the range actual into two the phase figures of determined at 2 out. There to can salt wedge consider the data on Figures velocities water. 13) past within penetration on the that 2, hours, order the no the in 3 salt to station three to 1 60 to the maximum water come a often point maintain 10 (indicated at 80 the removed. (Figure four recorded of where consistent rapidly February way maximum The longer i s this relationship show seems which flushed layers station since water. water i n t e r f a c i a l p r o f i l e s . high salt completely salt Both s a l i n i t y stand considerable that the when we the following does of the particularly the easily after i f in in column layer. water, from plateau water description f a l l s not the uncertainty each high is One For in conclusion penetration in graphic difference with is the motion penetration time there 17), in hours in station 3. cm/sec are 56 Chapter 4. THEORETICAL An important large 15 of features the flood of small tides their and 14). u t i l i z e s such and these i s the is for a to be density into exceeding even for masses mixing phase (Figures t i d a l estuary flows relation river discharge. d i s t i n c t at the the Since the as the currents furthest does A provides in boundary upper interface. which described provides model stations and 13 between station layers, information remaining the motions and across by distinct position water, to period created wedge river tend t i d a l salt to forced water quantitative resulting 10 relatively also the the be that layer not allow similar data to predictions. The hence the fresh the the several appears can throughout model. at and water structure two It water tides, mathematical parameterization the salt fresh a tide the low of of heat into model functions or the and revealed lengths i l l u s t r a t e provide salt verify also the measured that two has behaviour. despite as two-layer of 1, salt can chapter, assumed mixing the decomposed previous The parameters forcing seaward data data, and properties data data intrusion extremely station The between important the on A mathematical If the above wedge produce discharges. currents. relationship prototype salt identifying estuary strong the Steveston, estuary freshwater the of often above the retain in examination kilometers out CONSIDERATIONS f i e l d salt the data layer density also as i t indicate flows contrast that fresh upstream between the water reducing two mixes down the s a l i n i t y water masses. 57 This effect produces lost. the would a well At any be mixed zone rate, detailed leading edge of theoretical work the a r b i t r a r i l y chosen These estuary When river water above usual which the traces downstream compatible at s t r a t i f i e d retain the solve have aim motions time has been in neglected. made. the the are ). The the salt The by be one the f i n a l recourse model to To further estuary geometry in estuary front is by of Figure or an in the 19. the computed by the documented in the and or baroclinic the calculations wedge for meter. shown be is subsequent defined s t r a t i f i e d modelling The to can two probably available the to well governing derivatives. variations been the the and of which located of in as hydaulics of not mathematical out position. boundary analytically procedures l a t e r a l t i d a l a t i d a l motion and visualized (1964,1970) this the to forced are equal and 1 s t r a t i f i c a t i o n considered water be the the of the Since lead equations (Dronkers calculation flows been front, barotropic literature to has i s "toe' distinct wedge salt may wedge observations toe of the the salt wedge depth uear where the assumptions flows salt greatest two-layer must be toe. to examine the d i f f e r e n t i a l equations equations d i f f i c u l t are numerical simplify and integration the density equations structure seaward limit sail front fresh water discharge Q barotropic computation Figure 19. Visualization into the Fraser estuary. of s a l i n i t y intrusion freshwater density p river mouth Figure 20. modelling. Notation used i n mathematical 59 The E q u a t i o n s In fluid o f Motion the case of t w o - l a y e r model w i t h o u t m i x i n g , t h e m o t i o n s i n e a c h l a y e r a r e g o v e r n e d by t h e l a w s momentum c o n s e r v a t i o n . right-hand at a cartesian the river mouth The e q u a t i o n s o f motion c o - o r d i n a t e system ( F i g u r e 20 ) . o f mass and are referred to a with the origin located Neglecting lateral variations t h e l o n g i t u d i n a l momentum e q u a t i o n f o r a n i n f i n i t e s i m a l v o l u m e i n e i t h e r l a y e r c a n be w r i t t e n a s (Cameron a n d P r i t c h a r d where -a du + u dn dx u w a r e t h e i n s t a n t a n e o u s v e l o c i t i e s i n the x and z dt and du = dz + w d i r e c t i o n s , p i s the pressure ( ). In equation neglected the of (5) 3p dx and 0! i s the specific volume (5) t h e m o l e c u l a r v i s c o u s s t r e s s e s h a v e been s i n c e they a r e s e v e r a l o r d e r s o f magnitude s m a l l e r turbulent stresses. c o n s i d e r e d t o be composed (a) (1963) ) : a time The instantaneous velocity than u i s o f two c o m p o n e n t s : u o b t a i n e d by a v e r a g i n g o v e r periods s u f f i c i e n t d u r a t i o n t o remove t u r b u l e n t f l u c t u a t i o n s . Thus, u represents mean v e l o c i t y , the slowly varying velocity field over time intervals longer than t h e averaging period. (b) a velocity fluctuations in deviation, having u* , arising from the turbulent time s c a l e s s h o r t e r than used f o r averaging ( a ) . S i m i l a r r e l a t i o n s a p p l y t o w. F u r t h e r , i f we compared with neglect velocity turbulent fluctuations, density the mass fluctuations conservation 60 equations for du dx + d_v dz d u dx + jTw. = dz both the to be water to are: give where the 7 mean du at ax dz < > indicates stresses (1956) -<u*w*>, that the du dt has over velocities and - by that the (8) - turbulent of the basis be The (8) kinematic momentum of significant can combine d <u* w*> process. the only (7) di terms on and the motion: ax the concluded, (6) of d <u*u*> each = d_P d - et -<u*Uj>. form his study of w i l l be stress further transfers the simplified " _d_<u*w*> dz x to derive the f i n a l the depth of each densities du/dz=0 in w i l l hydrostatic, du dt (8) equation order upper equation averaging from (5) , assuming to overbar): integrated be time + u _du + w d u dx dz In dp - a equation v e l o c i t i e s , Equations ax the estuary, and (dropping = arising in mean longitudinal + u du_ + ¥ River and incompressible. time Pritchard (a) ( ) 0 instantaneous represented James (6) du Reynolds are 0 layer. are Onder and the model, considered these f i n a l (9) equation layer, to where be the can the uniform. assumptions equations (9) be mean That i s , pressure are: layer + u where d u = - CL C d p dx rj J, d x _dp_ = dx p g d h dx dz - _1_ Tj <u*w*> z=h -<u*w*> \ z= h • (10) p 61 (b) lower layer J2U at h' 2 -a^rap'dz + u ' au« = ax ap' where dh ax Since in the this flow In t h i s and i = interfacial T b = bottom au + u au at ax dt + u i - b T T (13) yO'h' dx =(/o'-p)/p\ and (13) form together the governing with the c o n t i n u i t y system of non-linear = -g ah - T± dx PV = 0 dx + u' a u ' = - g X a h - g € dh' + ( T j dx dx (14) p* h dx + _a_(u«h») = 0 ax eguations are c l a s s i f i e d characteristics definite € layer, + _a_ ( U V ) ah' real (12) dx (12) au dt These be become: = - g X a_h_ - ge_a_h_2 + dx a u' at will equations: dt at surface stress other = -<£>'u*w*> a t z=0, =/o/yo'and f o r each au the free of T dx differential be r e q u i r e d i n t e r m s evaluated = - g ah - x ax prj Equations equations be e x p l i c i t l y s t r e s s = -</3u*w*> a t z=h' (11) au' + u* a u ' X will analysis stress (10) and where terms cannot letting T eguations ax a substitution variables. z=0 z=h • 1 ax turbulent stress form, neglected, h• + (yO - yO ) q ah ' h' J "air = pq (11) -<u* w*> -_L_J<U*W*> in requirements the for as h y p e r b o l i c i n t h a t x-t the plane, and presentation they possess therefore impose of boundary and 62 i n i t i a l data. No general eguations are (11) even negligible. developed by application solutions for flows f l u i d the non-linear Rattray there accelerations obtained If analytic i s are in (1964) no a negligible. this although method characteristics of differencing (Grubert Equations s t r a t i f i e d conditions are In the the four discussed Thg but in the the of It h« suspect basis ) for a must variables the ), can a and in have been as implicit be this difference such or the f i n i t e used. mathematical data solution be method convective f i n i t e boundary before the solutions (1966) for stresses however, procedures (1972) stresses model and and equations i n i t i a l can be obtained. formulated in terms of considerations are these Boundary are Conditions written in terms of V) and 1 u /2 2 + g ( 77 + h » ) - T u i) + a ax u , 2 /2 of sections. Structure -n u« the subsequent u a (Abbott turbulent used; to found excluded e x p l i c i t appropriate flow momentum h using required dependent be numerical form boundary are reason Abbott the also Characteristic If and (14) flows, addition other terms been the Approximate study techniques, where may priori have + g(h» + Xi7 u'h« i/y077 0 ) ( T i - P' Tb) h' (15) and 63 Or d_V + d F (V) v, Since f (16) ax at where = F (V) and V = V(x,t) dV the where the in O O O (16) and au/ dx fl 0 du/ at 0 0 0 gX 0 u' 1 g 0 dV/ dx f. 0 0 0 0 h' 0 u' 0 dV/ at 0 dx dt 0 0 0 0 0 0 au1/ dx du 0 0 dx d t 0 0 0 0 auv at AV 0 0 0 0 dx d t 0 0 ah'/ dx du' 0 0 0 0 0 dx dt ah«/ at dh' i s of by [B] the 0 n = [C] number discrete the of become: 3 (18) dependent layers. values determinant (17) n flow characteristic matrix [A] for variables Abbott this = 0. After and (1961,1966) system of elementary n i s has the shown equations are operations on [A], =x=dx/dt, x-t g equations 0 (u-c) g 0 g V (u-c) 0 0 0 0 the O form, 0 I A| = c matrix 0 2n (15). (17) 1 2nx2n equation are: u the given variation in 0 number that g defined V [A] or l of as dx together u vectors aV d x at Written are equations dt + _r3_v = f plane. the (u'-c) gX 0 inverse h« slopes g (19) (u«-c) of the characteristic curves in 64 Finally: [ (u-c) Equation (20) system) be the evaluated following c = two-layer of their uh* h , and ± / two-layer surfaces. to with each the speed of These roots can e the order by (1953)): gh (21) u'V + ± / • ' the ge 77 h ' positive positive and described by four conditions must be supplied Abbott 2 rj h h' surface internal a l l to c h a r a c t e r i s t i c Now, variables, time. the gravity waves. dependent for (22) 2 negative negative boundary the (u-uM and known with - h be and a represents Schbnfeld must Grubert (20) associated approximated conditions accordance = 0 (for pairs roots or X 77 h ' 2 quartic into boundary in g J the flows - respective (Schijf represents cf pair + h gh' ] divide numerically, = u 1 c* and on relations cf where roots each waves - 2 characteristic four Physically gravity waves g 77 ][ (u •-<;) is whose layer. long - 2 four Furthermore, domain of in the computation structure. To guote (1972): "The boundary data is of m-point type where m i s the number o f c h a r a c t e r i s t i c s e n t e r i n g the r e g i o n of c o m p u t a t i o n from the boundary in the d i r e c t i o n of computation." Three situations consideration two-layer of which solution and region the is are are of interest summarized computation equations being of have advanced been in in in for Figure the x-t solved. time to the the 21. In plane We two problem may each is points graph shown imagine P, under the in part that and the P 2 65 Subcritical flows at both boundaries .'. two boundary conditions required at e a c h x=0 end. = toe x Supercritical both outflow at boundaries I boundary condition at seaward end,and 3 boundary conditions at Solution determined x=0 upstream e n d . x = toe Supercritical inflow both at boundaries I boundary condition at upstream end , and 3 boundary conditions at Solution seaward determined x= 0 x end. = toe Figure 21. P o s s i b l e flow s t a t e s f o r the two-layer s t r a t i f i e d computation. The r e q u i r e d number o f boundary c o n d i t i o n s i s i n d i c a t e d . 66 using the (1966) been method ). For that and the Model values equivalent steady provide the here, "arrested salt allowing the estuary to values of of is (14) (1970) were and use of provide into a in in a surface these flow waves. Figure requires The 21 and numerical et a l . (1967) to the integrated alternate approach, solution required mechanisms stationary or numerically analytic the the Boulot An an i n i t i a l transformed then the In and conditions. to result show technique. motion make observations internal shown have s u p e r c r i t i c a l flows) variables. relations of a l l Abbott Conditions dependent insight existence for not or curves flow, f i e l d do equations i n i t i a l wedge" provides Since Vreugdenhil flow i s s u b c r i t i c a l solution of (1965) characteristic c~<0 I n i t i a l equations (Smith propagation the the used . by unsteady adopted - for and boundary of to the the solution procedures method to regardless Any to of Flow four inflow. in c+>0, refer specification starting the corresponding i s , conditions A Steady point conditions (that applies characteristics s u p e r c r i t i c a l t i d a l bore, the each sketched outflow of for values. This controlling, salt wedge in water intrusion the or suitable estuaries. studied Steady-state models in and behaviour his the past described, analysis Keulegan for the mechanisms principally deals salt mainly by with G. governing H. the Keulegan penetration have the been wedge (1966). length In of 67 arrested saline wedges experimental data the equation following L where = 6.0 0 L = h R (2F water = , U (L )// = 0 Equation (23) fresh was water the i n t e r f a c i a l forces the wedge. similar function of A by for second Farmer the and of stress varies wedge. To penetration geometry is in this of K p 0 (L) an to the the also of estuary: water, in river present of not a assuming and w i l l remain must be using to effect, an was form the wedges to be a or from then, described solution i n t e r f a c i a l constant coefficient derive and determined studies, the arresting given. closed by and required arrested wedge wedge In the parameters salt flume possible shape arrested K were provide is situations. data the of considerations relation solution as . assumptions which They 2 x=L no found range the.arrested prototype is wide at way stresses (1953). length, '•calibrated" It a analysis evaluate viscosity dimensional this although as an at number Keulegan Morgan shape kinematic from In over x/Lo, in arrives number velocity derived regarding be length He (23) Froude data. to intrusion flumes. from )* A v - experimental on the forces g e h 0 U (L ) laboratory Reynold's = densimetric A necessary depth, = densimetric A in the length, = J g e hyC F for h R! = total evaluates obtained intrusion D and the along the from the the wedge solution K. analytic solution for 68 the wedge shape wedge to be takes place, in the stationary the udu dx + gdh dx dJUT/ ) g X dh dx the + and the 2 w i l l h' that constant be where C = Solving h i = (14) distance at L reduce fresh water to: defined for i r the in Figure or i t l a t t e r 22. can be method Either a eliminated equations (24) + q d (h?) 2dx Letting flow exists u 17 an The + q 6 h '2 2 of V in (from h - the 2 exact h* upper equation + _g_e_d_(h • ) 2 dx f i n a l = Q +^e_d_(h»2) 2 dx = making use of that i s a layer, (25) ) we have: 0 d i f f e r e n t i a l result and with respect to x and i s : = C (27) integration. h»: - 3 constant either and (26) h h ' 2 + (h 2 - C ) h ' + (Ch e The salt salt 0 Following is constant for i P'h* as Q = term + gh£ 2 of the (24) T + g_d_(hZ) 2dx integrable. 77 - . discharge Q2 equations required d (uZ) dx 2 thus mixing assume = 0 dh' dx steady each we to: Q _d(!/7?) dx where no If (25) €={p'-p)/p' fact that way. 0 = + g e reduce h the i equations. (26) where T pi) notation substitution from and governing dx with following C x is is = 0 at unknown and h3 - e determined or - x = at L x from where = 0 the = 0 2Q2) (28) g ^ the h'= boundary 0. depth Now, of in salt conditions, general water is the 69 z =h Fresh water d e n s i t y /O x= 0 Figuce x= L, 22. Notation used o Barotropic in steady flow solution. solution K = 0.006 0.75 to O xrixO.5 0 0.2 5 0 Discharge Figure Fraser 23. Stags-discharge estuary. Q (m/sec.) relationship for 70 unkown. the However, equation required the of in steady the effect of that along the pass the = 0 interface. control and (uz where - = 0 gh) (-gh) The at - = h constant x = 0, C of where = only term wedge x h. - € a 2 shape of Only the the in hypothesis on showing which a point; just at long flow the waves control. waves section and in in the conditions narrower channel can surface gravity wave positive +x d i r e c t i o n . Thus equation of prevent control internal from control concept conditions "internal" the the The certain 0, provides produce flows. = occur can (20), with becomes: - g^XT; V 2 ( Q / g e )' 2 h' = 0 2 (29) /3 integration i f h'(x=0) + h2 = a be determined (Figure from conditions 22): (30) 2 (28) i f C can + 2Q /g(h-a) the variation This an communication those can stationary flows to °- / Equations salt past x investigation width flow become speeds reasonable channel from for , .-.gey h« in c| = Q/y u open propagation waters a (1952) propagating no postulated wave be channel two-layered means receiving in current upstream to Farmer's comes the wider u' and from the case prevents appears section against is This two-layer waves section characteristic increases progressive moving control the Stommel control In for sudden sections a a relation. basis that i f in derivation (29) surface and elevation equation is (30) (28) enable is enters substantially the us specify the known; indeed the through the same to as surface described 71 by Hodgins the choice w i l l be given and of Quick the R to - 3 h (L) R + 2 where level this (1 - previous + densimetric = u (L)/y that F parameter g e h of unsteady situation for in h an + 2 case € h' e l l i p t i c a l with the use C = solving which has a the real a dimension (31) does as seem be a result to be a of and flows. than du/dt (24) and flows. and for as h' (26) has the i t is convective usually therefore This the one might hypothesis without the we can udu/dx form: = C (32) As before C can be evaluated at x = 0 (29): (33) (3 2) - the useful + hz (C was number directly and solution equation 2 = +/ (28) (L) steady equations equation. of e a 2 equation h' udu/dx, solving which by computations = 0 2 neglected similar term, 2FA ) can less by new with computations magnitude tested simplified equation tidal of be 1 - s t r a t i f i e d or a some dividing Froude term, term, expect - appears A acceleration orders and been study by (Ci = fundamental two has (L)z acceleration most i t (L) convective In datura form Ci ) R = C/h interesting although : R = h/h C, is In as non-dimensional equivalent It bottom presented. in (1972) for h )/ root 2 h': (34) € only i f C > h . 2 Thus the value of x at 72 which this h = C 2 very Together I a must they given have a specify momentum and coupled model is r h and and with i s a continuity provides in the dh, at only a crude often and (9) the turn evaluate solved is integrated continuity h', in the over equation f r i c t i o n where the K a is a six equations were technigue similar width a per approximation improve to to the the unit width rivers having simulation whole the cross-sectional (37) width. term ^b variable equations for on = 0 , b = storage bottom unit in relationship form: + _a_(uA) ax where The Q and calculation applied conditions discharge (36) is then independent. = 0 equation and in (35) continuity u|u| not b To Kp wedge obtained: forms. The - eguation channel b salt ax (36) A, the are derived irregular area, of ph ax + _a_(uh) Q stage model the ax and unique _£a = - g _3JL - at at the h barotropic If + u dh that To hydraulic au Eguation noted depth barotropic basis be way. length" analysis. estuary. t o t a l "penetration represent used following the the simple It for is were days solved to calibrated using continuity replaced dimensionless during the was the an scheme equation to tide measuring central described by used here relation coefficient, and e x p l i c i t was the f r i c t i o n the March with discharge period. difference Cronkers for The (1970). ease and 73 speed in computing; procedure based sections. Once was run for a the surface and within minutes density two constant in Figure increase dh/dx. in excluding incorporating each the freshwater sign for a velocity parameter equation the solution can be with i n t e r f a c i a l internal waves density gradient, a shears. Ultimately the a stress associated process Thus with enhanced convective stress arises from the by and the € varied i s plotted with an solutions than term those resists having the discharge in when udu/dx i s the growth and region increasing acceleration and solutions The same worst dh/dx, layer, the 4, 24). also this in hence lengths since and cm) increased dh/dx. upper lower are are penetration stress. of in acceleration in (34) lengths i n t e r f a c i a l breaking the 70 typical Q and The (the dh/dx 25(b) the The four 3 (Figure are 2 5 (a) as retained. times to predicting water in shorter obtained in variation of changes stations low model shown approximately water decrease convective is successful parameters penetration have of at the estuary. way at following discharges lower tides in obtained this percent low Figure a were were Figure Solutions and du/dx In in The € u . shown while 25 (b). and important are € =0.025, ± 5 appear the measured computational varying in difference high e (28) for same most contrast equation the for in equations a (37) and obtained within to and tide the width corresponds ± 20 with unit with sophistocated (35) slope dh/dx elevations The of Q and more coefficients surface Compared calibrated f i t f r i c t i o n mean between a equations amplitude relation the of zero the 23. on the produce Fiyure details reduces of large velocity the 2 r Station I x = OKm G.D G.D Station 4 x = 24.4Km / / V + - \ T — 12 March 17 • o + Measured _L_ values 18 _ l _ from tide 0 0 Hours 1.8 March 18 Barotropic prediction gauges Figure 24. Measured and predicted t h e M a i n Arm o f F r a s e r estuary. 12 surface elevations at three stations G. D on 75 d h 20 30 x (Kilometers ) xio 40 50 40 50 (a) 20 x 30 ( Kilometers ) (b) Figure wedge. 2 5 . Typical solutions f o r an a r r e s t e d salt 6 76 velocity gradient hypothetical system Once calculated r i along the the the toe. The from depict the situation would be increasing provide the flow. The velocity near an of This the the for the upper right The to may Since an increasing layer stresses the these forces, (1953) assumed at of toward zero at stresses are accurately velocity shear in i is surface slope to form calculated be increase driving to to not thickness conditions maximum these and force a can x, T variation decreases mouth an the to that estuaries. pressure stress larger values experimental examples. to average approximately slope Morgan using the appropriate. Mississippi the and and model surface in shows rapidly a term. stress, zero with the upper and a serve in layer increasing control here least T the section to f i x v i c i n i t y toe. particular wedge was 2 then compared the 26 near out result mouth. Farmer K^ou(L) would magnitude wedge from toward decreasing of Figure pointed real necessary river order in stress established stress uniform produce acceleration an (26). be calculated expected. such increasing must a the is eguation end. reduces without wedge It hence interface from upstream the and 1.8 shown River 0;25, their River data dynes/cm , 2 in has derived Figure a I and find which 26. from discuss state this The the as evaluated f i t t i n g that a K their K of 0.001 corresponds to an favourably to the of the South West Froude data varied data, compares densimetric both stress prototype b r i e f l y Mississippi Using of They or the of Pass number Keulegan and of 77 x/L Figure 26. Typical a r r e s t e d s a l t wedges slope. i n t e r f a c i a l assuming a stress curves for uniform surface 78 Farmer and Morgan. unsteady analysis closely with experimental expected would (K the and a function equations absence f i n a l Morgan of 2 i t derived. the longitudinal mixing the uniform with stress variation due the The importance (28) which provides the required stresses T i Boundary The each layer and Tb now in to of gives the a this i n i t i a l remains terms terms, studies, to with values flow in the stress stresses but l i e s concept of near equation solving the flow of provides in for the slope, section formulate dependent but the control wedge only. surface maximum study the steady of the squared x=L stress the flows stress shear at be allows along variation of might The the in their water solve other formation salt squared his more for value velocity c o n f l i c t i n g mouth. It or slope river model. to form report constant in compares masses. variations the unsteady is i n t e r f a c i a l agreement to local i t 0.005 Vreugdenhil velocity about A in assume of which turbulent since the K larger water possible regarding dynes/cm?, increased is information be of freshwater eliminating conclusions cannot a and the where the a Morgan The identical function summary by case a of and 0.006). between not as Farmer In about are vary = used Waterway, Farmer unsteady mixing (1970) Rotterdam studies formulations whereas the value in to of the enhance stress Vreugdenhil the boundary variables. Stresses Reynold's appear in stresses equations resulting (14) as from the the bottom turbulence and in i n t e r f a c i a l 79 shear stresses a l l turbulent six unknown and flows. In an flow closure case variables associated four is the no e x p l i c i t substituted in of bottom. on the in way or - < pu*v*> of with equations interface dependence is are there at assumed problem there since -<pu*w*> Traditionally, the this quantities, representing dependent represent the other equations of motion. The drag bottom force which squared. Both replaced T by b dimensionless assumes are that changes the lower in the barotropic layer. and understood be involved examples. vertical turbulent the intensity interface. the the lower and The bottom may the the also the of are have boundary used the due K relation (1967) being a formulation diffusion neglects generated this to of the of s u f f i c i e n t l y enough in any turbulence for T both b, density stresses either layer large, scales of arise side of i f turbulence produce is mechanisms between from momentum system, to gradient generalizing horizontal on two a complexity d i f f i c u l t y turbulence large a l . This a equations. Reynold's the et and like velocity momentum variation 2 be layer Boulot turbulent u ' to K yO'u ' | u ' | , presence diffusion Considering layer by subject mean and form of s t r a t i f i e d in the assumed proportionality. rate with have mixing specific upon I often with the of the associated Turbulent may in i s (1970) of represented in which only relations scales well ^b, Vreugdenhil length a varies coefficient adequately not stress, and the the depend density velocities in generated at mixing at the 80 interface. order of When the reduces Biles a i s growth due to proposed Richardson number, N (z) is -q(dp/ dz)/p water , mean and has and parcel column. not i n s t a b i l i t y to Taylor for some (1931). profiles 3.0 cm /second 2 Compared with a persist Richardson to for compare Taylor and some the of the pointed when that as in by V= € shown boundaries the a gradient in the by o s c i l l a t i o n of out Ri in given in that f a l l s that c r i t i c a l Ri the he results stable a this does below 1/4 mixing can f numbers on the of viscosity turbulent momentum River of 1.0. It observations 0.25. I have and eddy molecular exceeding discussed velocity reported -<uV*>/(du/dz) numbers Fraser turbulent continuous Richardson kinematic seems of displacement results channel, for it 2 of or (1973)). everywhere frequency has the waves (Turner that the case frequency, i n i t i a l at disturbances > 1/4 2 appears analyzing cm /second, this internal is the examples. 1/4, defined small on considerably influence f l u i d the $4.1) always t i d a l a the to dz) small i t » In from coefficients, to Ri from dn/ approximates (1973, of not generated In breakdown s t a b i l i t y a be shear. Brunt-Vaisala given referred also i n s t a b i l i t i e s away = N(z)/( Turner that even the are dissipation may s t r a t i f i e d Alternatively, persist with the turbulence viscous velocity for continuously water the that condition Ri wall Turbulence i n v i s c i d , a the Kelvin-Helmholtz (1961) flow. of thickness, associated of sufficient scales effect. i t s e l f turbulence the layer this interface the density viscosity order ten of by of or 1.0 more. order 0.02 diffusion can is interesting with taken the those of velocity 81 profiles from shear, d u / d z , using required about minutes numbers March 10 are using A z plotted in of Richardson than with and March I 30, few from the salt As stresses, and as have Such investigations where the measuring and Turner usual the are based I on know the a strong two of their have been confined has been practice found terms the in rate the of at to computed Table was with in as of entrainment Although stations on viscosity probe lines of bends too as the the v a l i d i t y . Reynold's velocity estuary -p had at even the to and flows. experiments <u*w*> motion. by case, generated doubtful of both comparison laboratory equation on one make calculate and eddy many to 3 produce specified s t r a t i f i e d to to two relationship in also mixing measurements made velocity the the enough been of estuary. since stations direct and density river density and calculate not remaining (1959) in 1.0, collected to the diffuse turbulent equation and to profile Richardson sufficient Fraser were each in quite order the was listed was 0.5 velocity gradient N (z) , are that attempted damage Since completion were this in data determination profiles the of indicate momentum balance far on the Furthermore shears Ri currents the results order Furthermore, secondary straight density not meter. pycnocline expected considerable points. Fraser, of conductivity have coefficients the computed frequency, The velocity on be one u n t i l The Taylor to and complete, made 27. Values of is to 2 of A z meter. the 0.25. velocity suffered one numbers i n t e r n a l l y , a Brunt-Vaisal'a but those station averaged". not Figure observations less were The a at "time determinations p r o f i l i n g . 29 surface by Ellison jets 82 Table 3 Comparison of R i c h a r d s o n numbers o b t a i n e d from F r a s e r R i v e r and T a y l o r ( 1 9 3 1 ) . N (z) =-gA/o / p {\z i s t h e B r u n t - V a i s a l a f r e q u e n c y , R i = N ( z ) / ( A u / A z ) 2 t h e R i c h a r d s o n number and V the k i n e m a t i c eddy viscosity. € Depth (meters) March 1.5 2.5 3.5 4.5 5.5 March 0.5 1.5 2.5 3.5 4.5 5.5 Shultz• s 2.5 5.0 7.5 10.0 12.5 15.0 17.5 Au/ A z (sec - 1 N(z) (sec- ) ) 29, 1973 (0830 0.10 0.30 0.26 0.23 0.08 29, 0.03 0*10 0. 25 0.18 0.23 0.09 Grund -0.010. -0.017 -0.022 -0.024 -0.019 -0.008 0 Ri 1 0.0078 0.0176 0.0578 0.0392 0.0166 1973 (1552 0.0039 0.0127 0.0235 0.0461 0.0235 0.0539 Taylor 7.4x10-6 11.0 27.9 58.9 103.0 80.8 45.6 (cm /sec) 2 hours) station 2 station 2 0.78 0.20 0.85 0.74 2.77 hours) 4. 33 0.75 0.38 1.42 0.44 6.65 (1931) 7.14 3.85 5.88 10.2 28.6 125.0 3.1 3.1 2.7 2.2 1.9 3.8 data is 83 cr =( _ |.0) x I 0 t .5 /D 10 U 3 15 20 25 30 0 20 40 (cm/sec) 60 80 100 120 0 8 3 0 March 29 Station 2 Az= I m. u> 2 CD CD sz Q_ CD , 51 *>l.2 Q 10 20 30 N ( z ) = - x 10 10 20 40 I0 3 60 0 0.2 (Rad/sec) 15 20 30 40 N(Z) 50 0.4 0.6 0.8 Ri(z)=N(z)/(AUy2 U 1.0 12 100 120 1.0 1.2 (cm/sec) 25 30 0 20 40 60 80 50 60 0 0.2 0.4 0.6 0.8 Ri(z) Figure 27. P r o f i l e s o f °"t and v e l o c i t y on March 2 9 , 1973 a t s t a t i o n 2. D i s t r i b u t i o n s o f t h e B r u n t V a i s a l a f r e q u e n c y and g r a d i e n t R i c h a r d s o n number a r e shown. 84 and inclined number, the R i = Q to where 1/U as e f f e c t i v e l y R i Reynold's stress at not number characterize the beneath s t i l l at the interface and a inverse with g'= observed increase was primarily density The flows over velocity, plume. the both the and Since flow an s t r a t i f i e d can experimental an i s 0 and and and have results in overall the Fi did and the f l u i d be between • flow a appear to a series of flowing number salt layer. Froude The number, and ft w Lofguist's the attempt of was Richardson to layer a properties. almost developed Fraser estuary possible and derive confined v e l o c i t i e s , a study velocity well neither f a l l i n g stress to teen of shear Re. not have , water (1951)) integrated the In i n t e r f a c i a l s i g n i f i c a n t is showed -<u*w*> the ambient flows salt E, however, would '^2 of Farmer he would — with the experiments turbulence layers both 0 other work; flow. (1960) R i the the layer relating stress under) of to and 0 is series A relationship Ri or 1 increasing at laboratory (or R i with the _ 0 U Entrainment this associated (Stommel in between R i upon of aimed p r o f i l e s relation and e g 0.9. and two 0.3. from Lofquist Re, in interface turbulent depended root to Richardson c o e f f i c i e n t , related to properties water Fi=U/ J g • h, to a number, square 0.2 the overall thickness determined > 0.8 0 an entrainment non-linearly as mixing to layer The emerge such fresh Reynold's be R i experiments the was to for does is approached Q dimensionless flume h related velocity. found zero variables be [d(Uh)/dx], and sharply the g e h/U , layer experiments off could 2 average equal plumes to steady negligible only are in the unsteady extrapolating or reasonable. s 85 However the an an interfacial flows and the ratio terms i s internal gravity absence of relative upper waves cannot J number %r defined conditions shown of in correct under layer layer against the way (22) the the depths functional not form velocities. to simulate If ~ 0), a phase Fi=1, the speed of the be w i l l internal mixing improved The the arrested; complicated of as function possesses approach by Froude depict be Fi the is vigorous Instead the in U = u-u' can 9'V J infinitesimal accurately is and interface. g»i7 h * / h . waves speed be of and / to internal phase if has can u' the estimate meant the where current | / it discontinuity for Fi=U/ of number speed compares speed characterize terms where F i = 0 / y g , the , in on phase writing is waves velocity, to Froude density phase which equation the the i r fjords, the Then, and this in velocity, h'/h<1, h*/h, qq internal on layer and the approximate waves travel When using the seem stress, i n t e r f a c i a l (as currents. waves ensues. 1 the does The of h */h « 20) internal basis. in of (Figure number parameterizing observational interpreted Froude the c r i t i c a l conditions. Both assumed the expression Vreugdenhil interfacial stress which the dimensionless only the changes internal water has f r i c t i o n relative in layer waves. depth (1970) can which Fraser very Boulot of Such u-u* also stress a near a l . and to Kp and allows makes influence the (1967) formulation observations small et proportional dimensions velocity, thickness become is coefficient. layer The and show estuary no have U|U|, an for includes reference the speed that the mouth a and to of fresh that 86 the salt layer variations, mixing, Since be of various shape which can one thickness our the substitutions study for formulation was to examine form of the s a l t and water the using the Fi. influence predicted in promote wedge estuary, four made: (ii) T i = Ki p UJU| (39) (iii) T i = Ri p U I U I F i (40) i = Ki ^ U I D I F i T (i). In becomes what having a h may never role sensitive thickness i s t r a t i f i e d to be called when of an is often flows. the (41) 2 Ki a weak - h' shear a dimensionless model function = h/2. l i m i t i n g rapidly. assumed as two-layer In values amplification velocity decreases (38) preserves have the Fi no-mixing maximum 1 the a of salt p except T been speeds These = Ki formula since of toe. T i each on time wave stress the the (i) where and on have i T the objectives residence near i n t e r f a c i a l in functions (iv) V the included stress and reduce decreases and the the the numerical layer zero. making increasing Relation proportional denominator of of factor coefficent (i) to Thus the when has u-u' Fi depths solution Fi takes stress more either been in of layer included modelling 87 Chapter 5. SOLVING By recasting e x p l i c i t f i n i t e barotropic for the THE periods. of The specifying the free surface For example, currents channels in which of heavier was immeasurably f l u i d occupying about reasonable to salt Georgia and discharge the any only the from free the difference model, along half of the laboratory the free driven provides section experiments are by barotropic nearly tide Under free at this surface flows layer eguations. This fresh a discussion matched water This brief of discharge chapter independent of Strait of assumption the also of computational the be the net computed means that salt front either side presents description the is can on despite i t and across surface estuary the baroclinic model. and be the perfectly and to two allowing free the discharge. and the depth. In gravity removed water, the into, progress the the flume in flows. on current's surface only accuracy baroclinic long fresh water both lower was the the upstream a water, of suddenly surface with sea presence by the s t r a t i f i e d those the simulates of to under observation Observations water salt obtained the similar of a from and one equations principally model a flow the numerical in with were the dividing disturbed calculations since come to the at the during (14) them solutions barrier flows, model considering a a conditions. series expect water barotropic a wedge which eguations combining estuary, derived feels flow and salt densities fresh the the for barely in with boundary that form, the is MODEL s t r a t i f i e d entire of accuracy behaviour show the motions prototype flows the difference model t i d a l TWO-LAYER the the f i n i t e barotropic procedure and 88 application of motions are features of The Finite the boundary then the compared model three which and broad e x p l i c i t techniques, both differencing of wave (1967) have made (1967) central conditions. i m p l i c i t In to general, algorithmic The and (37) Fraser in the properties f i n i t e of problem. view Grubert scheme however, the salt some wedge essential and (1970) Explicit but suffer variable from (1972) Abbott the stratified flow time increments by implicit solving and schemes are Boulot in equations a l . and solve attractive a et time and the from a s t a b i l i t y successfully require kinds (Richtmyer to s t a b i l i t y central many restrictive have no differencing differences schemes are E x p l i c i t techniques spatial equations There f i n i t e in f a l l characteristics schemes. application forward the of weaknesses. Vreugdenhil equations d i f f e r e n t i a l the and to small of "Lax-Wendroff" in of method between u t i l i z i n g point and hyperbolic difference repeated while use observations solving strengths found ), flow programming confined have differences two-layer for choosing equations, Morton an has for computed examined. methods i m p l i c i t reasons The Eguations natural or with categories: u t i l i z e s dominant are Difference Approximate into conditions. which applied is not considerations. more involved structure. one-dimensional central estuary hydraulic difference including a l l form model was major using developed branches and equations for the Pitt (35) entire Lake. In 89 the discussion plane the and j to w i l l continuity bj (h refer i+i i-l -h 1 the that h |' = j 1 1 - 1 computation exactly what equation bj line in the p o s i t i o n . Consider difference form: j-l A x-t f i r s t (42) i - Sx they by are arithmetic )/2 = A); , )/2 = Vr\ the molecule is information i s replaced by the averaging, from the 1 average. Thus: (43) i l l u s t r a t e d known in and Figure 2 8 (a) u t i l i z e d for and shows advancing ( 4 3 ) •. Proceeding (35) time St Sx 1 J The 1 denoting h -: a i s : (Ij-jtA - here x -U Ajll obtained + — or central j-t (A]^ A;- 1 j+I overbar in unknown row; ' space (37) are preceding A a reference 2 values, A to > corresponding time w i l l S t A j j | , A j i | A i equation 2 Since follow (Figure b = r u-'j 2 8 (b) ) , Kb/0 u } 1 1 =< (43) 1 a similar where l u 1 ] the manner bottom for the and momentum | : 1 1 -ujj>) (44) equation stress i-l | i . ( u j ^ 2 Sx Equations in • 2 StKb comprise the lu'J 1 | + / h j barotropic (44) model. 90 initial conditions J" 2 J"' J j+l j+2 (a) advancing the continuity equations it initial conditions J*» J+2 - x (b) advancing The momentum equations h ,h'known ©u,u'known Qh.h' to be determined rju,u' to be determined Figure 28. molecules. Finite difference computation 91 For unit s i m p l i c i t y width written basis in a and for the form ! the bottom 1 1 stress, =iu» J i - l and U '. = F •ii oV i s = continuity d Since h j-i on Figure and t h e -!»._!,)+ X ( h j | , uij-1 - u ' i - ' = velocity V j the i n (14) are +h«) = _a_h = - a (ui? at in dx d h -= - a ( . . h ) - - u = barotropic b ax ^ " has equation f r i c t i o n equation eCh-jj, - h ' . j . , |/h» j constant of law i s : ) ) l / + 1 (46) shear, and Figure 28(b). s t r a t i f i e d / ax velocity. If the two summed: ) + and (UT/ (u»h') barotropic computations, ) + (u'h«) Thus solving f o r u't 1 : i4lri the been (45) Using 1 a h» j / h - molecule from on -1 quadratic St done (43): 28 ( a ) . momentum i d e n t i c a l b j-l J+I difference i s at where 1 / /g e equations (V at I ! (u-u*)^ computed equation IT i - l U ' T 'I |I u | F i - K b u» ' - ' | u « j S t 1 - u « .' , h» 8x 28t(Ki where u'.' . h i n are equation to stress the continuity analagous molecule i n t e r f a c i a l computations layer J+I computation u' '} lower j the f o r s t r a t i f i e d = h» T J (40) the difference h' '+ ' with the integration (47) being zero. The five equations (43) 92 to (U7) form the seen from can be grid lines basis required define the i s l i m i t a t i o n a minimum unfortunate one kilometers. is Sx structure. triangle this at point numerical flow be unique (1956) in characteristic as a the and must numerical dependence. Stated at in related 29 and other terms, characteristic must curves. the of spacings curvilinear dependence are for the on the to state (CFL) the 1928, what has s t a b i l i t y not follow the difference domain of the less In PR back they Lewy and the inside paper dates does the be for determined PQ are characteristic shaded which f i n i t e include 2.7 equations characteristics which least characteristics to is equations grid is i n i t i a l c in and only grid fundamental Lawy, This of the curves - to order is The The the 2 the the domain ). c+ the 1 and of Courant-Friedrichs- directions, dependence the the on of serves admitted. hyperbolic solution hyperbolic Friedrichs known difference of for Figure number differences are as 2. choice equations. treatment condition: of a (Crandall Courant, slope and station continuum characteristics, s t r a t i f i e d to P, at directly the be establishing the in can Sx and minimum which stations schemes in example, of the central for in f e l t are defines domain come error difference which For PQR dominant by , values algorithm six, that the separation any is length from immediately St solution the flow molecules computation reasonable r e s t r i c t i o n s to and a arising and E x p l i c i t s t r a t i f i e d computation for Thus conditions the penetration since kilometer subject the of continuum slope than Figure 29 domain of the or equal this of f i n i t e to the requires Figure 29. I l l u s t r a t i o n of r e l a t i o n s h i p between continuum and f i n i t e difference domains of dependence for a stable e x p l i c i t difference scheme. 94 that the f i n i t e information domain from (below we the points P). explanation: than difference This must maximum of before the < Sx / where max(c ) is the which w i l l St the + value of s t a b i l i t y (Roach the for the the need defined assess as equations difference whose is defined (Smith a in faster the would completed are physical equations solution is continuum simple waves the the the (1965)). has for to flow. be out within each ensured Sx obtain the f i n i t e bean i f gravity chosed as wave close we are of (46), and convergence systems dependent of on to and equations experiment numerical solutions and to serves f i n i t e the approach St solution accuracy, at exact through to underscore difference scheme solution zero. of Since a series of round-off errors are each point. growth or decay dissipative and stable the a for linear variables of In surface approaches as terms St convergent solution of the accuracy (43) A of theories that dependent in on practicable. only equation operations into errors study as the data. equations introduced usually value means to d i f f e r e n t i a l arithmetic this This one gravity advance advanced (48) developed f i e l d as has numerical of mathematical (1972)). such S, inside condition restrictions largest In are' well i n t u i t i o n l i e integration these / m a x (c+) Sx systems i s spatial must the to point max (c+) occur. Rigorous and used Quantitatively, R, s t a b i l i t y celerity information pass. Q and integrate Otherwise date solution S t a b i l i t y of these difference 95 scheme, numerical bounded schemes to always and constant coefficients, c r i t e r i a for deriving The the the simulation the and Sea an widths by Department river sounding. for linear to is within difference in systems derive with convergence in judged the are d i f f i c u l t i e s involved solutions of shown depth of this in study. terms assumptions model the river in branches the storage. depths Public Works 30. of the made in (3) obtained (Government was computed than two meters at 85 percent are not calculated Detailed bathymetric data over at low does areas, every data of width was at the notable which were sounding outlines most cross-sectional the into show The from and estuary heavy The and (1) mouths The lines scheme. evaluates partitioned The lighter branches Lake, influence. Figure the P i t t various t i d a l i n included greater barotropic major while conveyance depths at seven channel in or end between and those the having channel as appreciable except practice into not Reach point the the branches channels conveyance the the attempted starting to segments these is to equations data (44), schematized remaining have f i e l d upstream kilometer omission of not Unstable or Model (43) indicate have one-dimensional integrating one values. Due exponentially equations. The been small s t a b i l i t y non-linear the Barotropic has I accuracy of equations decay non-convergent. convergence Instead, either s u f f i c i e n t l y are proving errors grid provided Canada). the portion water of and the available In for of the greatest Pitt 96 Figure 30. used in the S c h e m a t i z a t i o n o f Lower Fraser barotropic hydraulic model. R iver 97 Lake, but so a shore depths and kilometer in the to programme The measured boundary the absence detailed s p a t i a l against of at stations data dispersion comparisons 30, lower the 1973 Main to along i s a crude of the elevations are accurately predicted centimeters of to lead the 40 minutes, 5 measure junction to response suggesting that Canoe the of below the at station depths The on were also after station 3. storage 3 the 4 order for the is the I capacity and the phase and (within 10 predictions the study additional just Both station 5 his Within station passage. elevation). at in agreement error on calibrated 32. at based positions phase water river of and the significant influence minutes 4) be surface provide and the can model surface the along calibration 31 In Kb (1974) To simulation the Arm. measured Joy the Agassiz extensively by higher-high Main used. were the points to measured station there bank was Figures model A similar Joy's and been coefficient River. from the various 6. feet in (below the at (1952,1953) plotted to and and Fraser following south 5 predicted however this the Baines Arm 1 calibrated 5000 the station one convenience has this was 4, seconds maps, equals for to f r i c t i o n 3, and of from §x applied section data taken Since 60 the predictions are ebb attribute of The satisfactory, turn of in incorporated. March model was (48) of St at discharge increments the a velocity which the elevations equation conditions f i n a l (from determined), by elevations at width estimated. bookkeeping, discharge estuary were seconds surface of conveyance areas < 83 St shore to appear 30 to 98 1.00 r Station 3 Barotropic prediction Sx - I Kilometer • Sx = 5000feet o observed G.D. G.D. -I.OOL 8 10 March 12 14 16 18 20 22 24 30,1973 Figure 31, Comparison of elevations with obervations at predicted surface stations 3 and 4. Hour, 99 i.oor Station 5 Barotropic prediction 0.75 8x = I Kilometer ~ • Bx- 5 0 0 0 feet o observed G.D. G.D. 8 10 March 12 14 16 18 20 22 3 0 , 1973 Piyuce 32. Comparison of elevations with obervations at predicted surface s t a t i o n s 5 and 6. 24 H o u r , 100 downstream (the are river water) is and the approximately The averaged 5 the phase may 10 the to area 33). is Computational Once flows were River storage covered only junctions are satisfactory are at areas at high poorly station 6,; over-estimated station predicted geometry the were an Control the and to with basic were in the Fortran (1974) necessary of the by 33 was and through station of by which that achieve the large 1. This ebb conveyance altering found of would the only the changes in the best As a barotropic calibrated, the A l l solved the limited, magnitude at 3 f i t tool model satisfactory. was interfacing IV sections Conditions model model. spatially very Reach to at schematization. flows, Boundary barotropic eguations available 31 the sea model s t r a t i f i e d Figures are overestimate Joy limitations the but in 2 were velocities especially this also 1 and measurements storage although by computer banks satisfactory calibrated in at the 1 or Station computed coded the of have as to the investigating calibrated complicated waters measured neglecting within Pitt underestimated, coefficients for the low seems f r i c t i o n possible extensive Although I channel the relationship - is and areas. the of that centimeters. agreement due and with compared currents into phase velocities (Figure be wide high and and large influence The however, ebb very the modelled. too lower f i n i t e using University the of the layer difference difference IBM 370 British s t r a t i f i e d eguations Model Columbia 168 101 Station l Barotropic prediction —'— Sx - I Kilometer 8 10 March 12 14 30, 1973 Figure 33. Comparison of predicted v e l o c i t i e s on March 3 0 , 1973 a t s t a t i o n s 1 and 2 . 16 18 with • 8x = 5000 feet o measure d 20 22 24 Houn observations 102 Computing Centre. evaluated throughout computation boundary turn water layer lower part to level a of p r o f i l e r s in is the the by If at flow was by domain 34 appropriate were used velocities pass. depth, datum model the the In is the ref.erred the s t r a t i f i e d and prototype three configuration. taking (47). h, for by in Finally equation and advancing the (46) were conductivity Model datum is of there and integration from the internal were domain. the three supercritical pass equation s u b c r i t i c a l and are the and flow and of inflow state was examining the at each everywhere (cj > 0; cJ each end of the at the toe front (h• imposed The states outflow (22) waves flow salt between nearest at water the depth velocity height moving section salt grid < downstream 0) of boundary. When x 22 interpolation meter) as between cf heights computation one serves March flow evaluating determined < 0; Figure direction and water (44) computation. complete i n t e r f a c i a l fixed (cf each the s t r a t i f i e d the in with and from and regular barotropic Figure their s u b c r i t i c a l propagation line. in depths total which . in barotropic following defined was shown (45) computed the (43) a seconds the relationship shown interest: from Arm defined are 60 layer were bottom The As and Main model parameters h, in equations lower depth, the = Next the equations estuary St velocities equations. used on update total upper based barotropic the conditions. to the The the > 0) the flows are i n t e r f a c i a l supercritical boundary out condition at h» the at mouth x = 0 is z = l6.84m(Geodetic datum) z = l4.24m(Sandheads datum) z = 4.25m (Model bottom) Deepest Channel Bottom z = 0 ( Model datum) 8 10 J 12 L 14 16 18 Figure 34. Relationship between the estuary Conductivity p r o f i l e r s at stations 1, 2 and configuration. 20 and 3 are J 22 L 24 model shown i n J 26 Kilometers parameters. their March o 104 released. no Physically this means t h a t longer be maintained at conditions in the are structure of throughout x = 0 a between river control the corresponding enters the f i n i t e 22) will occur flows the positive computations mouth. was and Throughout flooding supercritical suhcritical in the i n the conditions would interface propagating numerical scheme i t be n e g l e c t e d . t h i s reason during requires u using The wave no once the in the velocity layer the field flows were Flows were The The unsteady weak s u r g e waves on inflows, flux (Figure s e c t i o n s near layer. s o l u t i o n s may the b a r o t r o p i c side waves. the boundary longer t o advance mouth, the and in the lost i n such w e l l be i n e r r o r f o r however the additional t h e domain from the seaward velocity stratified characteristic that the energy reasonable. entering a assumed supercritical appears characteristic evaluating was boundary near the t o e i n the upper upper from seaward the the entire p r o b a b l y produce upstream column Somewhere only upper and water imposed. interfacial a transition flow simulation to layer implying the boundary the the lower layer waves c o u l d and with respect flow to the v e l o c i t y the lower estuary upstream since the s e a w a r d occured were c o n f i n e d boundary internal T h e r e f o r e h' a t x = 0 i s n o t inflows can' the normal Since d i f f e r e n c e domain from Supercritical water marking and of G e o r g i a . to of s a l t domain. i n f o r m a t i o n c a n n o t be drawn f r o m t h i s solution. 22) determining dominated c o n d i t i o n s i n the S t r a i t curve seaward the c a l c u l a t i o n section river the the head condition, side overall internal (Figure supplied i n eguation (47). by 105 I n i t i a l i z a t i o n and observations The completely washed out this feature. computation concerned, Wash-Oat the out i s defined, when of section 6.' the toe position T h e wedge r e m o v a l I n the more u s u a l floods. tidal fairly convergent, i t w i l l o v e r c o m e the e f f e c t s o f bad crudely and e v e n t u a l l y approach a r e "run-in" the I n t h i s case 2 and The 26, surface initialization scheme i s s t a r t i n g values these Normally cycles t o eliminate from for (28) eguation between grid from discharge. initialization the validity procedure requires o f the s t a r t i n g values be unacceptably large kilometers criteria can t o o small and vice penetration length exceeds 7 kilometers 5 slope u ' i s s e t e q u a l t o z e r o and u i s c a l c u l a t e d example, i f the s u r f a c e slope becomes below and by a m e a s u r e d v a l u e o f h ' a t x = 0. T h e r e q u i r e d v a l u e s o f h the barotropic will large ebb the s t a r t i n g v a l u e s calculated computed by assuming a u n i f o r m which solution. f o r twoo r three t i d a l 1 lines flow s t u d i e s , correct effects. has retreated and i f t h e numerical the i n t e r f a c i a l height, h ,are are include models, can b e done using must must be r e - i n i t i a l i z e d i nthe other s t r a t i f i e d the i n i t i a l i z a t i o n c a n be on each implication models wedge a s f a r a s t h e model i s t i d e a l s o means the s t r a t i f i e d c o m p u t a t i o n on s u b s e q u e n t salt past s t a t i o n 1 a n dthe model as occuring downstream that s i x g r i d l i n e s are reguired for an advancing Since wash imply versa. (grid line against For be judged. the intrusion I f the 8) the s t a r t i n g values are r e j e c t e d . or initial falls Further if 106 the value of h» i n i t i a l i z a t i o n what can values only are with was not Since this every 25 for penetrated reasonable to affected bad by The with the scheme that the into flux front assumes that CoBiparincj centred on those by the the 10 time the or 12 of start to at that least effects The bad validity predictions t i d a l cycle to when kilometers. at once of overall the arrival move cycle. repeated of inserted suggesting flood was met, beginning was would comparing parts than has position of salt or during the basic been where salt Predictions The the solutions. judged wedge flood, computation, the a layer procedure in more toe increasing moving into are salt It profiler 3 i s to be i n i t i a l i z a t i o n . wedge toe be expect position the late meters reasonable such the two r e s t r i c t i o n s as lower to of felt observations these after the too hours only has practice entire are exceeds i n t u i t i v e l y reversing can water go In toe ensuring zero, before method wedge judged to i n i t i a l i z a t i o n the By be i n i t i a l i z a t i o n the f a i l s . equal downstream of the obtained. u' within at has = 1 been water each with the In or downstream the storage computation water defined meter. advanced just decreasing problem finding h* a r b i t r a r i l y discharge is as this coinciding computational retreated of the toe, associated interval constant assuming of for w i l l with 2 St. 2 a l l the This St. Observations in applying correct the balance numerical between the algorithm two stress 107 T± terms and the solutions: the greatest cycle, and the for and Kb Ki "Th. the phase of salt water magnitude the velocities. stress layer by comparing with for of found periods. Kb=0.0055 duration three during and f i t and affected distance coefficients overall imbalances penetration were The Large systematically solutions formulation f i n a l the a in to £§rticular at data particular (40) values barotropic two measuring gave of values the both 3, t i d a l Optimum from of station altering equation coefficient aspects the best Ki=0.0075 solution and discussed previously. Two-layer results The numerical solutions observations using data velocities 35 and the solutions together model the with effect the i s worst predicted both stations 1 solutions except agreement is peak salt salt station and 2 the for and due maximum the low zero wash-out second agrees is flood at within on station 40 of the 30th. have the in the almost become this data. In reasonably well 17th. both the at earlier. March of l i n e ; to simultaneously is minutes plotted February defined for Figure that height 3 In relative probe to p r o f i l e r been errors on as water compared observations Contain to salt and 17 particularly goes to 29 Harch thickness water 3, satisfactory intrusion March observations the at on 10 layer conveniently parameterization recorded interface modelled the two-layer February The when The both for bottom. appreciable the are The records, phase where observations. Observations x Station I 0 Station 2 + Stalion 3 1 MARCH 17, 1973 Hours Figure 35. Comparison of typical i n t e r f a c i a l p o s i t i o n s p r e d i c t e d by t h e s t r a t i f i e d flow model with two-layer parameterization of observations at stations 1, 2 a n d 3 . 109 In station 1700 a l l 2. The hours stations slope on March 2 near i n i t i a l i z a t i o n , into i s the when compared The the ebb 1. At this numerical between (x=9 tide point model stations kilometers) horizontal length of rapidly whole In a the than of the salt model. On during March, the at the a the rounded model) which hand predicted of is Canoe water lowering the advect measurements at station and: water This of shorter f a l l s junction i s the nearly penetration slope increases flows along freshwater to the layer supercritical height is the heights Passage on the turn out at interface solution interface contour velocities released s u p e r c r i t i c a l the a such fresh the i n t e r f a c i a l salt with of of depending response. must The i n t e r f a c i a l the meters the measured other 10th (4.1 and for to following layer from The u n t i l nose upper condition the between reproduce s u p e r c r i t i c a l v i c i n i t y toe and solution. to height February thin water the the rapidly Near relatively by and f a l l toe. wedge. predicted volume 1 boundary not mixing diverge changes 10th separation effect consistently. located forming remains slowly and the the also at February accurate. the the early .immediately that of too corresponding least no-mixing state behaves is have the on could except suggest solutions flow model reversal would hours meters, end 14 flood i n t e r f a c i a l 2 solution and with an about during model when show to 0000 numerical the and tends near seaward 13 layer considerable interface the Figures salt 17th The 3 in model averaging 0.7x10~ . slopes charts the observations 1 and of large cases due the f a l l s to more the estuary as large in the penetration lenghts away rapidly very 110 from the measurements, wedge behaviour To February check 8th It this The supercritical water thickness was l i k e l y barotropic spike from this point lower level promoted the the and salt the Consequently remained until The to since March i t had but 17th. closely by The the similar the matched are only loss to tidal turn 25 to to in 30 salt measurements. associated u , 0 a heights ebb 90 near allowing or 100 curve outflow adjustment with the March 17th conditions. At 1 collapsed of layer the imposition flows on station centimeters supercritical data upper regions layer velocity, 1 supercritical flow, flows. the from layer p r o f i l e r s , enough station water some velocity conductivity to the were a velocites of above to a measured the previous re-established and wash-out. predicted passed the s u b c r i t i c a l . lower on more resulting level. the of predictions, observations differences turn condition deep simulation Harch occurred the 60 also in boundary with to the computed lead the poor model. The resulted of trend 50 a phase. was outflow with provides aspect same compared seems this solution conditions. minutes during and velocity of and in 30th Figure measurements the estuary To compute which 29 velocities i n t e r f a c i a l subroutine March height to at integrated 36. were provide the are a the As not good observed each compared with the made in picture upper of layer applicable time was measurements over the Ill March 2 9 , 1973 — prediction section 5 O observation March 10 12 14 Time ( Hours) 30,1973 prediction section 3 — prediction section 5 A observation O observation .... 8 station 2 16 18 station I station 20 Figure 36. Comparison o f p r e d i c t e d and measured upper layer v e l o c i t i e s at s t a t i o n s 1 and 2 f o r March 29 and 3 0 , 1 9 7 3 . 22 2 24 112 upper layer; u where to that yJ = 0 u (z) 7) = compare velocity i i s , u(z)dz h measured velocities phase varies on a section 3 and 2 with kilometers 2.8 only two velocities agree the solutions model station 2. Qualitative been in Figures derived and 14 from using horizontal indicate above column the the due cm/sec to in more along since the estuary compared is section 5 which in predictions the The for the part to with measured both the the and is with reflects a compared and predicted stations. observed the d i f f i c u l t depths 1 lead consistent and during and 38. i s time in in meters However, flows especially distance from i n t e r f a c i a l three the The and to exactly of data 1 is in the response. data. assumed supercritical of constant the imposed outflow in were °j Figures before columns river two-layer of As axes clearly the measuring contoured vertical the each terms v e r t i c a l show the in charts densities temperature and days contour The station follows periods on probes. relation at for conductivity background bottom line solutions same operative i n t e r f a c i a l except is 37 the monitored condition ±15 is Station estuary. superimposed axis model the It layer distance with appear numerical have density than grid. 2 in also way z. Comparisons The period i s height kilometers within This but with station of at this kilometer separation boundary, velocity the computed at (49) of give the zeros distance extent bed. 13 of water The solid seaward boundary parameterization which have been o 2 o g u> o inittobzation • O m«osurad boundary condition STN.I c,'<0 o o o »s ^ CO o . o . STN.2 Model Bottom o o o CO o 10 o o FEBRUARY 1973 Figure 37. I n t e r f a c i a l s o l u t i o n s from the s t r a t i f i e d f l o w model a r e shown s u p e r i m p o s e d on c o n t o u r c h a r t s o f c o n s t a n t d e n s i t y ( Ct) for three days in February 1 9 7 3 . T h e p e r i o d s o f s u p e r c r i t i c a l o u t f l o w a r e i n d i c a t e d b y c ~ <0 on t h e s t a t i o n 1 c o n t o u r chart. + r— LO 1 o J I MARCH F i g u r e 38. Interfacial so superimposed on charts 1973. P e r i o d s of s u p e r c r i t station 1 contour chart, s 1973 l u t i o n s from the s t r a t i f i e d flow model are shown of c o n s t a n t d e n s i t y ( Ct) f o r three days in March ical outflow are indicated by <0 on the u p e r c r i t i c a l i n f l o w s by c f >0. M 115 indicated have by also cj been These barotropic with the The solution model water figures the at outflow occurs. as shown salt to be judging by accurate within series of longitudinal in time on computed layer Until turn the isohaline, s a l i n i t y flow out minutes of was for to February the of computation, and the river the duration the previously, the model for once tides 10 has is least small diurnal allows the Steveston, the 1 salt predicted model above station of supercritical of numerical mouth, upstream. in at s a l i n i t y the predictions. at s u p e r c r i t i c a l which the the kilometers estuary sections s a l i n i t y structure. at using confidence The charts velocites after condition worst the the to s t r a t i f i e d of timing and appears minutes. solution superimposed 150 38. contour ±30 interpolating must Figure of capable several measurements outflow. thicknesses is The corresponds layer out two-layer is estimate effect washed the for noted the in the allows As This model boundary and simulating inequality the reasonable lengths. in water a station accurate that flows The supercritical i n i t i a l i z e water provides penetration show to charts. during internal salt each the indicated measured calculate on <0 time In the estuary reguired i t in data, 2 and interface appears the of to Figure the f i n a l section and have by been show the near the wedge toe. l i e s near in a l l lower 12 a also rise model in Each 39. sections station within plotted isohalines The the been Figure profiles numerical beyond also relation of the layer section the in and salt a Figure 15%o to the water further 39 116 x ( kilometers ) x ( ki lome te r s ) Figure 39. Interfacial solutions f o r the t i d a l cycle on February 10, 1973. Isohalines interpolated f r o m t h e d a t a i n F i g u r e 12 a r e s h o w n in each s e c t i o n . 117 for this water to masses estuary, in occur. the in giving model on each layer rise to a found sections ebb downstream - of that plays different an mixing between important removal the ebb. the tendency for 3 and numerical which an role mechanism reduced could i n t e r f a c i a l slope due the solutions computed pronounced change behaviour. This (1970) which near to the in than the maximum e b b the salt account for they layer although the occurs about a retain data is a no level off upstream. I junction 10 per change the although exhibit a same less overall Vreugenhil's distinct comment at cent in and the in numerical to the velocity forming there by Passage limited the slope flow Canoe of interface firm decreased slope, contrasts the influenced Main without in shows was the effect behaviour increasing model This even turbulent i l l u s t r a t e the station Passage on contrast, model. These Canoe In paper wedge shape the flow on state. One excursion piece of the March tides above Steveston kilometers. greatest New crabs which indirect data wedge produced The very (36 Westminster are I and 1) unable this to would those collect have (station in caught such a water New long the maximum valuable. 18 The kilometers were February would Salt near been February on which 4). was averaging ineguality kilometers) support to lengths while large occasionally evidence was penetration (station excursion above of 11 about gave put salt fish species the water Westminster penetration. 27 and provide I would 118 expect the two-layer lengths due layer the in the of to well water on As scheme and the detailed outflow. The early which becomes Vreugdenhil's where the minutes solutions each values which and the ebb severe model to salt hydraulics the duration does not perform to during ebb peak and s u p e r c r i t i c a l characteristic upstream, water ty turn seems (Vreugdenhil appear of a number February range be of of to (1970), be the shared figure approximately 40 is wedge procedure dissipation of by the in numerical was is 7/) to If 60 The definite stress washed out i n t e r f a c i a l errors and the varying stress the of investigated and a i n t e r f a c i a l repeatedly f a i l s . 29 turn, There fixed. is characteristics March constant values. assumed condition of 10 a n d parameter i n i t i a l i z e d i n i t i a l i z a t i o n provides a can boundary the for stress through large, less It thickness the gross judged predictions. flood s e n s i t i v i t y other the the satisfactory, especially on penetration Analysis The holding mixing modelling layer two-layer of the early. Sensitivity model salt predictions too as aspects, the overestimate effect velocity of by far seems maintenance solutions, to d i l u t i n g estuary. numerical salt the model cannot the limit T i by to since becomes too until the stress also assume a zero value. A of the mean velocity s t r a t i f i e d shear, flows and U=u-u', of 0.300 corresponds to m/sec a is stress typical of 2.44 119 dynes/cm for 2 Ki=0.0075. r and Three were The 3. in Kb which 10th ^"i. is is The solutions, a bottom stress b±50% and T for for shall On the 40%, from r i+50%, of also 4.95 typical dynes/cm . 2 b=0. T 10 refer to the other hand a zero bottom provides a poor simulation form of the penetration i s per almost only the ±6 are of and The is February variation characteristic this zero to outflow time of bottom this cent solution more about described solutions such significant possibly to apparent i n s e n s i t i v i t y long stresses only the per ±6 stress that at T sensitive delays cent. outflows errors the affect the In the b to salt this time February range of turning point 37 thicknesses the the the February and i s the for Compared on in stress solutions minutes layer penetration, to the occurs. stress on 5 of f i r s t varied about produce Both I s u p e r c r i t i c a l the coefficient K i . effect the a parameter. the confined by clear s u p e r c r i t i c a l minutes. 1 (as important However, the computed m/sec, lengths i , showing than solutions were and u'=0.300 investigated: section). It An at represents excursion important changes velocity, solution the station an T previous increases i s of standard the solutions penetration independent the water Kb=0.0055 values meters) i + 30055. r salt for C7 = h ' = 6 Numerical i + 100% and A in Fi=0.36 at with may the 10th layer station March do not depth, explain due the parameters. wash-out times at station 1; in 120 this i+300% r T case, the wash-out of 35 produce f a i r l y the (0.0075) seems station increase The to in 3, did of back allow the 0.007. upper onto upper this sensitive Some the near of the station 3. a l i m i t . wash-out time and higher values of trends are Ki not Lower large the ebb remains between u-u . Since 1 depths values h' are not of Ki value produced flood-ebb about do level standard the lack coupling layer The i-503L but in stress with delays T ^"i very reducing solution, lower to Increases increased effect each at the for general the is only minutes u n t i l L it stress i n t e r f a c i a l but coupling the upper the phase for layer barotropic layer to is flood not in the basis i t Variations layer the increased Increases on l i e T as With behaviour same percentage not. velocity and has except most analysis. in minutes, 60 solutions. cent) in 60 important. bottom about appear average per whereas slowing them the by zero with changes imposed changes effect various becomes reduced the rate velocities affected, stress conclusive (+10 i d e n t i c a l l y at a the similar marked and Rather layer i s compared proportionate greatly The time in currents. is minutes prevents apparent time comparison removal data i n t e r f a c i a l removal By b-5Q%. The the of velocity and higher velocities solution) ebb noticeably bottom is ±50% r b compared (in while with of Ki fact, has the collapsing decreases higher in Ki v e l o c i t i e s . changed. stress possible in values to delay the reject have almost with the ebb values no at station of effect measurements. Kb 3 above on As the b T 121 decreases reduced 7 to 10 the peak since u' per cent Based discussed stress extent of of are 0.010 smaller (41) solutions for the to s e n s i t i v i t y optimum the solutions that greatly from largest located stress forms be the 0.006 the order and the estimated both the of Ki and stress model for the accuracy influence for are unaffected. reflect bottom and Fi=0.362, common the the same This Ki in of a the maximum would occupy a stress numerical The as equivalent does each of not form, longitudinal form standard. salt kilometers providing the equations model stress the (40) values necessarily but was and coefficient equation to (38), for used in represent designed to give basis. overall in forms, evaluated. the for stress into give value a were analysis. difference 10 of alternate 17th Superposition revealed on layer Forms substituted March m/sec the can and The Stress three were calculated u-u^O.300 w i l l value i s observations monitoring A minimum upper appears limits values the reduction phase section in Kb=0.0055±0.0010. of and The between These Interfacial Each currents The appropriate. range: Alternate the f i t t i n g f i e l d model. flood b-50%. previous barotropic was T the the and increased. coefficients. and (39), i s for on in ebb On water above the of sections the both wedge flood thickness the weakest from boundary coupling, each did and was at solution not early 30 ebb, the centimeters station KiyOFi d i f f e r and 1. The K i p U | U |, 122 did not allow forms, the and wedge in to general be removed were as rapidly associated with as greater the other lower layer depths. The ±4 per penetration from the standard, coupling delayed the turn minutes. The the cent length lower solution stress stations. for Kip U|U|Fi once the change coupling; lowest levels Conversely, The but 2 of the stress upper layer stress form the relative does the stress forms were was most the numerical Equations and with also produced closer appears and one outflow. I match to removal had the form varied providing outflow a longest salt was water of 56 f i r s t , but duration delayed was at the the only greater total s u p e r c r i t i c a l flow a l l longest most rapid place. i s also forms in equations affected by (40) the and (41) degree of produce the velocities and greatest salt not change the phase the velocities, only u and u'. numerical procedures a l l of tried and (41) the of calibrated. could are chosen of however which greatest have in f i e l d exception, the went of each stresses Fi taken development solution the s u p e r c r i t i c a l satisfactory, (40) Kip resulted the magnitude During but by s u p e r c r i t i c a l for state velocity The to predicted the each be most water Overall stress f i t t e d responsive to supercritical delay the KyOU|0|Fi to observations have reasonable than the turn since the theoretical it a observations. changes inflows. to i n U They s u p e r c r i t i c a l provided alternative validity. (40) permitted the prevented for eguation form to currents. a s l i g h t l y forms and Unfortunately, 123 the observations to provide the pressure which, water several flows required for by and lower a barotropic surface slopes layer) formulation solution (entering prevent for pressure hydraulic water w i l l for be low the the a more i n t e r f a c i a l within percent 10 agreement within excursion average layer of ±40 the assumptions, succeeds the the is total at distance. The velocities which observed model neglects the depth river and boundary can draws from a condition i s neglects mixing of but includes the model predicts that relation. the estuary of on of each and the approximately also agree is daily predicted phase one-half provides within large r e - i n i t i a l i z a t i o n penetration depth model the conditions model capable extent minutes and interface, of of The boundary empirical The chapter assumes A further the and this width observations, flows, wash-out. and Finally, out in estuary. uniform model. an broad velocity, forces flushed following of across with even average and channel described characteristics density Consistent ebb, f a i r l y Fraser using water some the stresses salt been important in a has measurements. fresh turbulent on in by one-dimensional the the the Model model variations supplied The based approximated salt in of and concerning of numerical simulating data use flows term Features although l a t e r a l be the term. A salt with layer statement Essential in upper gradient definitive stress coupled ±15 shews of estimates cm/sec of the of the 124 observations. On removal good. the other mechanism This is The insensitive expected shape of the to both appears to be I found barotropic depths the estuary previously expected effects would along be a improvements, monitoring the phase independent due to during to the the use that of the the south the bank of the and to properly done, measurements. In in summary, s t r a t i f i e d calculation accurately as that of Main influence boundary the warrant is the simulation model The to the model and price be 1 and and described for could and careful the condition. the be storage for model. and emphasizing essential barotropic of velocities computer a .fieid s t r a t i f i e d delta Arm. and assumptions. improvements estuary i t velocity obtainable expensive the i n t e r f a c i a l layer f i t Further representation relatively barotropic best complex programme the not is the the is and effects. the one-dimensional more be both of reached stress measured depths mixing the of the of of The about better the a phase accuracy of over-riding development geometry. a of are wedge addition, schematization. with salt In represents particular calculated layer without form and upon model and models, depend a the flows magnitude are model in ebb of the almost results simulation s u p e r c r i t i c a l be stresses. barotropic once the to bottom These hand, success this Such detailed velocity of calibrated the as possible. Currents in the upper fresh water layer of the estuary 125 are affected along the both by the interface. the and of Figure together The phases u*, of f a i r l y bottom makes stress bottom i s For the values of can be explained in near the interface due The 10 to 12 is the forcing upstream, and the estuary depends condition a l . (1967) downstream is 80 those for the turbulent height the In two in 4 stresses for the flows in with have terms of remains type of ebb the during ^ ~ i . an arrested case. This stresses layer. at salt the river water layer throughout which studies gave compared 2 Reynold's the this both formulated river stresses dynes/cm simulation previous i analyses condition drives the in for each and variation This than in a l l Also but A nearly unsteady increased which (1970) to the plotted i n t e r f a c i a l the accuracy condition 2 boundary of both wedge approximately of is calculated stationary Vreugdenhil boundary larger unsteady 2 17th that generalize, of modelled. outflows. percent than accuracy specified. and to mechanism upon is stress. terms i n t e r f a c i a l in i n t e r f a c i a l dynes/cm to March mixing velocities value well follows maximum of by for turbulent layer which the stresses with must observation to greater example, i n t e r f a c i a l mouth 60 to total variations d i f f i c u l t addition, the s u p e r c r i t i c a l about considerably wedge. time due correct and stress, the i t the solutions the during flows stresses important than constant In with the larger variation magnitude wedge most flow i s are salt water calculate bottom sequence u-u'. To relative i n t e r f a c i a l 40 salt flow boundary Boulot the the et internal parameters. 126 Distance above Station I ( kilometers) F i g u r e 40. Tidal variations i n the interfacial and bottom stresses and t h e mean l a y e r v e l o c i t y s h e a r a t s t a t i o n 2 f o r March 17, 1973 (upper). Six l o n g i t u d i n a l s e c t i o n s a r e shown f o r f l o o d and ebb p h a s e s (lower). 127 Basically that the they postulate, a control fresh water section layer hydraulic conditions outflowing upper further and waves equation (22) where define a i s one flow conditions that salt questioned tendency a velocities layer generality since during positive each evaluated for values h 1 the and momentum the determined by the presence an cj" of ct and both solving (47): of this inflow and eguation no layer in flow to for mechanism Rigter velocity Figure (41). the discharge in hydraulic must River, be the with upstream for arresting conditions with must to has the calculated It Then (1970) Fraser existed compared the tends arrests assumption the in where optimum boundary and (1953) velocity maximum of assumption direction. corresponded These tide This in 0. the (51) flow, layer kind (50) Schb'nfeld layer corresponding 17th lower and -c~—-*• gives goes inflow = 0 width. upper that Vreugdenhil opposite lower where wave. March and be exchange calculations layer internal mouth h (0,t)/2 Schijf the the s u p e r c r i t i c a l in g e unit but situation The to for such + / by layer and case water conditions. each a equation c r i t i c a l " in producing In setting per work equal wave will analysis, + q ( 0 , t ) / ( 2 J g e h (0 , t ) ) "double internal river supercritical by using the they the u' and wedge assumed. during discharge from suggested from is net follow other, the that and to unique the = 0 = g(0,t)/(2h(0,t)) discharge arrest c"| h(0,t)/2 the the estuary. the u'(0,t) = near within stationary h' stationary form = appears for w i l l h»(0,t) q which for the there layer are in thickness assumes internal as be were measured directly emphasized 128 .5r- \> f N 2 \ v o w \ ®0.5 / E \ I 1 > 1 4 1 6 / / I 8 *^-<S 10 I 12 v\ boundary x ^ \ ./ «L Supercritical / \ i 14 16 inflow condition Computed boundary velocity 18 20 JL 22 March 17, 1973 F i g u r e 4 1 . C o m p a r i s o n o f t h e measured boundary c o n d i t i o n f o r h' a t s t a t i o n 1 w i t h t h e t h e o r e t i c a l condition of Vreugdenhil (1970) (upper). Comparison o f u' c a l c u l a t e d from the s t r a t i f i e d flow model and t h e t h e o r e t i c a l r e l a t i o n of V r e u g d e n h i l (lower) . 24 Hours 129 that the Fraser Vreugdenhil applies The observed water, h very u' is 1 (50) to are model destroyed tests where flows, and the poor is the a two internal boundary flood estuaries with specification the developed of flow as part of this was flow are w i l l the to for in of but Such the a that behave similarly at river large numerical be used mouth an can measuring to estuary column other of i . T Fraser and the series cannot water both largely lowering the entire straightforward work. by salt meter. depend during assumption the phase matched, condition the high one apart. induced and corresponding the model cm/sec expect of time closely conditions conditions relatively the (50) within Since calculation reasonable tides in boundary conditions large 80 equation a and case. duration at g(0,t). to a agree h' they inflow c r i t i c a l is in s t r a t i f i e d doubly It heights 40 The under as supercritically such from calculated as to h* calculation used flood between maximum s u p e r c r i t i c a l upstream. with (51) not only maximum consistently water since the the did (51) maximum predicts salt provide the barotropic velocities equation agreement equation the flows particularly closely from on phase however Equation model flows shallow accurate be made techniques 130 Chapter into 6. SUMMARY The work two programme water AND carried d i s t i n c t of f i e l d intrusion relationship important between of changes touched upon by series for very i n s t a l l e d at three water tides. tides duration. (upstream of the intrusions low large salt of Steveston, The fresh water absence of mixing took large place a the study a salt into the and some wedge motions. The for predicting the tool an aspect which is only were discharges estuary of detected, the and nature or also on the winter tides of large instruments were monitored the days. Significant extent and of Strait the more having removed each in which several the kilometers B.C.) out Self-contained periods was carried large were a duration of Georgia produced long high from the daily ebb, of by water estuary in spite discharges. conductivity were salt inequality wedge of the the by diurnal The winter in 15 nature f i r s t l y conditions estuary, water were of the f a l l s examples. for determined thesis catagories, theoretical observations points this discharge ineguality. Penetrations of of the two structure were a and fresh diurnal conductivity which of in reveal provide to low to secondly t i d a l of reported complementary also way Two small salt and characteristics outcome and but and models 1973 out measurements mathematical of CONCLUSIONS profiles mixed density within across indicate the gradients each layer. that i n t e r f a c i a l suggested Surface both salt region that and and the turbulent s a l i n i t i e s usually 131 exceeding 10 % longitudinal s a l i n i t y surface and Fraser River (Cameron accompanied B at and since In estuaries the i t horizontal advection and The simulated were salt the a in fresh turbulent momentum was in a barotropic measured reasonable in the currents effects were The magnitude accuracy of of Vreugdenhil's Waterway were of as of a the function the of by the and salt the conclusion water in (1970)). The included. in been layers mixing neglected but The The water model use depth of of the conjunction with of a enabled salt water tide at Steveston. flows on the predicting penetration for vertical the duration the by fresh The water model. model barotropic was salt and of with which estuary. extent cycle. in the the unique have form for a estuary difference entire estuaries governed structure. empirically lower t i d a l is the layers. model fluxes over the of each and the of along Fraser interface condition (Vreugdenhil the the currents the between mathematical f i n i t e salt water across predicted success of class 1 near place s a l i n i t y density predictions modifying salt of the e x p l i c i t estuary of both somewhat of Calculation lower flushed diffusion terms boundary be dynamics water although of two-layer station present s t r a t i f i e d " d i s t r i b u t i o n advection unsteady with solved the to near characteristics (1966)), appears tide were "moderately turbulent defined and These Pritchard example these gradients depth. into high depended calculation. a Of the similar nearly phase primarily This model equal of on was the and the also Rotterdam importance in 132 terms the of the measured duration boundary of salt condition water for throughout the interface at the estuary the was river mouth. The also a duration function i n t e r f a c i a l had maximum stress energy values in the of to the the in to r i g i d of in the mixing was The stress near modelled calibrated mean the and greater, the were bottom i n t e r f a c i a l 2 in magnitudes the dynes/cm , significant the namely and stress the bottom 18 to dissipation shear condition for i t was the same form mainly of the on to the predicted to small were the magnitude not and number the supercritical 20 of coefficient of water could the Fi f i n a l to has of and a calibrated of measured included increased bottom KbyOu'|u'| positions make the influence were depth choice been The layers. to be were degrees the possible flows. relation interfacial changes salt relation represent each between the stress increasing correspondence Froude quadratic for interfacial expressing Each onset the velocity i n t e r f a c i a l using for model, data, formulation The in between percent relations insensitive seen 10 them. made values Kb=0.0055. of among much was velocities. are current typically 80 numerical the to in about and balance order boundary choice KioU|U|Fi the the conclusive data water stresses; stresses the resolution the correct empirical s e n s i t i v i t y Due salt flows. Four substituted on usually Both 2 the turbulent was dynes/cm . of of stress and the Ki=0.0075 and were relatively differences in these coefficients; the layer velocities. Using mainly 133 the correspondence velocities and following between the measured and interfacial ranges for predictions each estimated: 0.010 < Ki < 0.006 and the coefficients within stress predicted water salt depth minutes and a compared kilometers showed ebb currents £2l!£ludin,g and these models mouth. the ±15 c m / s e c on the order theoretical the only of of 2 were ranges If the of model the intrusion obtained total within ±40 approximately 10 The f r e s h of 3 the 10 p e r c e n t maximum values station < Kb < 0 . 0 0 4 5 . these within at water water velocities the observations. Maximum meters/sec. Remarks i n In agreement at fresh coefficient 0.0065 measured within were Two neglect with were thicknesses phase upstream agreement reported water predicted the past, mixing one case of solved of both which salt were measurements were studies i n of unsteady and f r e s h are occupied based water the predictions less salt e x p l i c i t difference monitoring programme the with one t i d a l form have been on two l a y e r s across compared than wedges and interface. observations cycle. using Both Lax-Wendroff techniques. present salt The f i e l d work succeeded wedge motions different t i d a l to between be model made i n i n the producing Fraser conditions. and the a c t u a l hydraulic detailed River This the predictions a forming over allowed from behaviour a a of description several the of days rigorous two-layer in part the and comparison "no-mixing" the estuary. I found 134 such a model phase of the i f the the provides penetration, correct layer as boundary i n t e r f a c i a l measurements. the reasonable height The near the does the outflows, however even velocities are modelled. some i t of Two examples the more relates hydraulic in the well to salt throughout guantitative through the aspects of serve to use the of salt and provide for dispersion water mouth mouth in a was good state layer this study found from simulation the upper layer of the s a l i n i t y intrusion water quality. Basically is found in in of the each layer to make or water the more the as variations reguired sedimentation Some i l l u s t r a t e the velocities which models. which on of supercritical Appendix the A and each In during flow extent in and intrusion the applied. information information predictions are this of currents provide river aspects location estuary, not discussed important water the are the river during sedimentation models as conditions at model thicknesses well estimates guality important examples are: (i) D r e d g i n g o f t h e s h i p p i n g c h a n n e l t o p r o v i d e an a d d i t i o n a l 3 meters o f c l e a r a n c e w o u l d i n c r e a s e maximum p e n e t r a t i o n s a b o u t 20 percent. This would r e s u l t i n s a l t water l o c a t e d in and above the t r i f u r c a t i o n a t New W e s t m i n s t e r f o r much g r e a t e r p e r i o d s o f time than at p r e s e n t and would i n c r e a s e the s e d i m e n t a t i o n i n this r e g i o n w h i c h i s a l r e a d y d r e d g e d on a c o n t i n u a l b a s i s . (ii) The t i m e r e q u i r e d t o f l u s h p o l l u t a n t s c o n f i n e d t o t h e fresh w a t e r l a y e r i s s i g n i f i c a n t l y d e c r e a s e d by t h e s a l t wedge presence compared with times computed using the unstratified velocity f i e l d . (iii) The distribution of p a r c e l s of contaminated water within the estuary is s i g n i f i c a n t l y changed by the baroclinic flows compared with the unstratified distribution. In g e n e r a l , the s t r a t i f i e d computation shows that water p a r c e l s o r i g i n a t i n g both from Gilbert Road and Annacis Island pass l e s s often through o u t f a l l r e g i o n s , w h i c h w o u l d t e n d t o i n c r e a s e e f f l u e n t l o a d i n g on 135 the f r e s h water l a y e r , barotropic velocities. than those water parcels computed with the (iv) Host high tides during the measuring periods produce predicted excursions exceeding 18 k i l o m e t e r s a b o v e s t a t i o n 1, thereby bringing s t r a t i f i e d flows into the vicinity of the Annacis Island sewage treatment plant. The suppression of v e r t i c a l mixing associated with the s t r a t i f i c a t i o n means that effluents discharged into either layer might tend to remain in t h a t l a y e r r e s u l t i n g i n higher c o n c e n t r a t i o n s than would be the case i n u n s t r a t i f i e d r i v e r s . (v) Increased salt water penetration associated with further d r e d g i n g would i n c r e a s e the d u r a t i o n of s t r a t i f i e d flews around Annacis Island, thereby i n c r e a s i n g e f f l u e n t c o n c e n t r a t i o n s due t o reduced rates of v e r t i c a l mixing. It is clear that circulation in which be may water the must Recommendations this across on (Rossiter and the i n t e r f a c i a l hydraulic turbulent step i s the diffusion the of ) in hydraulic in on models sedimentation of however wedge or two main discussed fresh water longitudinal is be usually an terms in mixed negligible to of in the influence a Froude development mixing across entrainment term d i f f i c u l t y additional the in density variations expected in step incorporate of and the can next flows salt motion terms The of of parameterized to term. introduction effects flows. s t r a t i f i e d logical is formulated changes effect the when the model subsequent effects The along stress important baroclinic for (1960) Therefore interface, model Lennon that has Research equations contrast number. the the the Future interface. gradients wedge predicting include neglects the density for and for numerical thesis salt estuary used quality, The the involved empirical in of the plus a this coefficients 136 for the mixing by obtaining coefficients were not and to f i e l d on determination of station. to provide due depth and the would probably model also the There requires density at river suitable parameterization the the the of but in at least specification this of data each balance across the currents by the a and bends. the maximum f i r s t station can such of of salt the one permit loss location near additional type the the the to stations between although coefficients example, proper located adeguate, is extensive produced l o g i s t i c s mouth, of a average with make to the effects introduce For to the they mixing enough one simultaneously channel. and part part mid-way be of in currents located problem operating mixing in derive insufficient Fraser, width, banks shipping due require two the and secondary across the were cross-sectional to model to however, Mixing since predictions. the resolved estuary study determine 1973 2 other stations a l i k e the be calculation. rates, probably a to 30, can numerical the the appreciate the both March rivers from present the 1 and stations the to stations Three and the verify w i l l s a l i n i t i e s in mixing In which balance the calculation width data salt data, properly at d i f f i c u l t y complexity observations probes a included for a -sufficient from considerable demands terms, immediately project! four Six located in consideration of can the be that s a l i n i t y obtained collected or by in a this project. Calibration need to include diffusion terms of numerical empirical and in relations this models for regard, is necessary turbulent velocity because stresses data from we or the 137 prototype be is collected allow part across of i t the A problem should of the of project. The three but station 1 failed clamps and submerged located as similar the c o i l s estuary If close could from be as this where only one data should feasible station possible anchor could more inch to tube fame. wire be to to can be the deepest for future along To exceeding another units platforms or be on 300 here. s i g n i f i c a n t l y sealed 3/8 angles made reported or durable fatigue be one plastic hollow made 1/4 weights loss can the triangular through steel to in the pile constant recommended. probe than thickness maintaining the recommendations probe rather designed of Furthermore averaging. conductivity compound are width programmes casting clamp be valuable. channel. number monitoring as the cross-sectional occupied by particularly by 1/2 in this satisfactory increasing inch. reduced waterproof used were The The the pile clamps the weld between certain of eliminating the pounds at the or instrumentation, on the guide wires 138 BIBLIOGRAPHY Abbott, P a r t I", M . , 1 9 6 1 . 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" D e t e r m i n a t i o n Num^rigue des Mouvements d'un Coin Sale", La Houille Blanche, V o l . 2 2 , No. 8, p. 871 - 8 7 7 . Cameron, W. a n d P r i t c h a r d , D . (1963). "Estuaries", i n T h e S e a ( e d . M. H i l l ) , V o l . 2 , J o h n W i l e y & Sons, p. 3 0 6 - 3 2 4 . C h a p t e r 15 New York, Courant, R., Friedrichs, K. a n d L e w y , H., 1928. "Uber die Partiellen Differenzengleichurgen der Mathematischen Physik", M a t h e m a t i s c h e A n n a l e n , V o l . 1 0 0 , p. 32 - 7 4 . Dronkers, J . , Waters^ North Netherlands. 1964. Holland Tidal Computations i n R i v e r s and C o a s t a l Publishing Company, Amsterdam, The Dronkers, J . , 1969. "Tidal Computations Areas, and Seas", Journal of the Hydraulics No. 6 3 4 1 , H Y 1 , p. 29 - 7 7 . E l l i s o n , T. S t r a t i f i e d 423 - 4 4 8 . and Turner, J . , Flows", Journal f o r Rivers, Coastal Division, ASCE, Paper 1959. "Turbulent Entrainment of Fluid Mechanics, V o l . 6, F a r m e r , D. a n d O s b o r n , T . , 1 9 7 3 . "An Instrument Conductivity Profiles i n Inlets", Journal of Research B o a r d , Canada, 2 9 ( 1 2 ) , p. 1767 -1 7 6 9 . Farmer, H. a n d M o r g a n , G . , 1 9 5 3 . "The Salt of the Third Coastal Engineering Conference, f o r the i n p. Measuring Fisheries Wedge", Proceedings p. 54 - 6 4 . Grubert, H. a n d A b b o t t , M., 1972. "Numerical Computation of S t r a t i f i e d Nearly Horizontal Flows", Journal of the Hydraulics D i v i s i o n , ASCE, Paper No. 9 3 0 0 , H Y 1 0 , p. 1847 - 1 8 6 5 . 139 Hodgins, D. a n d Quick, M., 1 9 7 2 . "Computer Studies of Estuary Water Q u a l i t y " , Proceedings 13th Coastal Engineering Conference, July 10 - 1 4 , 1 9 7 2 , V a n c o u v e r , C a n a d a , p. 2327 - 2338. Joy, C. , 1974. Thesis, University Keulegan, G., Hydrodynamics 574? Water finality M o n i t o r i n g i n E s t u a r i e s ^ , of B r i t i s h Columbia, Vancouver, Canada. 1966. Chapter 11 in Estuary and (ed. A. I p p e n ) , M c G r a w - H i l l , New Y o r k , L a f o n d , E., 1951. EE2£§§§iS9. 2 2 § i . n o g r a p h i c Office Publication No. 6 1 4 , U. S Navy W a s h i n g t o n , D. C . , p. 9 1. L o f q u i s t , K., 1960. Stratified Fluids", p. 158 - 1 7 5 . Miles, Flows", "Flow The J . , 1 9 6 1 . "On Journal of Fluid Pritchard, D., 1956. Estuary", Journal of p. 33 - 4 2 . Ph.D. Coastline p. 546 - Cata Hydrographic Hydrographic Office, x and S t r e s s Near an Interface Physics of Fluids, V o l . 3, Eetween No. 2., The S t a b i l i t y of Heterogeneous Shear Mechanics, V o l . 1 0 , p. 496 - 5 0 8 . "The Dynamic S t r u c t u r e o f a C o a s t a l Marine Research, V o l . 15, No. Plain 1, R a t t r a y , M . , 1 9 6 4 . " t i m e - D e p e n d e n t Motion i n an Ocean; A U n i f i e d Two-Layer, Beta-Plane Approximation", Studies i n Oceanography^ (ed. K. Yoshida), University of Washington Press, Seattle, Washington, p. 19 - 2 9 . Richtmyer, R. a n d Morton, K. 1 9 6 6 . Difference Methods Initia1^value Problems^ 2nd e d i t i o n , Interscience Publishers, York7 p . ~ 2 8 8 . Rigter, B., 1970. "Density Induced Return Currents in Channels", Journal of the Hydaulics Division, ASCE, No. 7 0 8 6 , H Y 2 , p. 529 - 5 4 6 . Roach, p., Publishers, 1972. Computational A l b u g u e r g u e , New M e x i c o , Fluid U.S.A. for New Outlet Paper Dynamics^ Hermosa Rossiter, J . and Lennon, G., 1965. "Computation of C o n d i t i o n s i n t h e Thames E s t u a r y by t h e I n i t i a l Value Proceedings of the Institution of C i v i l Engineers, 6 8 5 5 , p. 25, 56. the Tidal Method", Paper No. Schijf, J . and S c h o n f e l d , J . , 1 9 5 3 . " T h e o r e t i c a l Considerations on the Motion of S a l t and Fresh Water", P r o c e e d i n g s Minnesota International Hydraulics Convention, I.A.H.R., September 1-4, 1953, Minneapolis, Minnesota. Smith, G., 1965. Numerical Solution of J. O x f o r d U n i v e r s i t y P r e s s , Oxford. Partial Differential 140 S t o m m e l , H. a n d F a r m e r , H., 1952. "Abrupt Change in Width in Two-Layer Open C h a n n e l F l o w " , J o u r n a l o f M a r i n e R e s e a r c h , Volume XI, N o . 2 , p. 2 0 5 - 2 1 4 . Taylor, G., 1931. "Internal Waves and T u r b u l e n c e i n a Fluid Variable Density", Conseil. Perm. Intern. Pour L ' E x p l . De Mer, Rapp. E t P r o c - V e r b . , V o l . 7 6 , p. 33 - 4 2 . Turner, J . , 1973. Buoyancy University Press, Cambridge. Vreugdenhil, an E s t u a r y " , C , 1970. La H o u i l l e Effects "Two - L a y e r Blanche, Vol. in Fluids^ of la Cambridge Model of S t r a t i f i e d Flow 2 5 , N o . 1, p . 3 5 - 4 0 . in Waldichuk, M., M a r k e r t , J . and M e i k l e , J . , 1968. "Fraser River Estuary, Burrard Inlet, Howe S o u n d a n d M a l a s p i n a S t r a i t Physical and C h e m i c a l o c e a n o g r a p h i c D a t a , 1957 - 1 9 6 6 " , M a n u s c r i p t Report Series No. 939, Fisheries Research Board of Canada, Pacific O c e a n o g r a p h i c G r o u p , N a n a i m o , B. C. 141 APPENDIX A. ENGINEERING The to provide outcome the numerical part of changes present produces with of effects speaking velocity fields dispersion be models i s of derived before possible considering to resulting which contaminants and in a used predictive i l l u s t r a t e only the to some of information the in intrusion problems dealing lower estuary. time varying the of salt water sedimentation or the velocity with be the used - predict extent the can be modifications the the conjunction capacity in in relate can s a l i n i t y provide and possible to from The models layer thesis required quality hydraulic each this considered water Submodels of be STUDY in exploitation. and in THE developed estuary must the OF information the which Generally must in sedimentation penetration. models the forms ASPECTS the information basic realized. salt provided However wedge by hydraulic effects the i t by hydraulic models. Sedimentation produces the may a region v e l o c i t i e s be duration next The a meters to estuary to to bottom by and in mouth examine the effects dredging to i t s near of depth are the or, natural salt the promoting toe the return the flocculation variations average by mixing of further the accentuated turbulent the upstream interest estuary: of accompanied sedimentation. of is which toe, important two the state and down salt changes to hand, (reducing This increases parameters. channel other i t slowing further imagined shipping since deposition. position of on water water It in add allowing the depth is the three the by 142 about 2 meters February the 10th total using results penetration time. expected the shallowest boundary two over A l l showed the basis of three the have evaluated boundary the conditions order of magnitude two i s and shipping to 15 not a l l and present mean model but for altering expect the would salt would channel also usually be the occupies time. the measured arise depth much solution. On dredging about for in very 20 in depths penetration decreased changes percent on by of estuary 15 of percent predicted the than As wedge; water additional in less the the duration case and differences depth altered the cycle, fresh the accompany s i g n i f i c a n t l y the Since reduction water of longest penetration A terms same i n t e r f a c i a l distances. The the the similar might in t i d a l at runs, "standard" percent meters. this for the we the admitted increase excursion the model values in 4 penetration. remained the Table i n i t i a l i z e d used with in times channel of meters present were was these three shortest compared approximately the for wedges of the summarized runs extrapolation or are condition penetration the measured deepest various an I the lengths wash-out as average). depths. The along on this since of the width. The deepening. cycles, the significance The increased presence New Westminster this area. This does of w i l l part of in the penetration salt be l i e water increased the river, in changes means the and that brought over which many t r i f u r c a t i o n sedimentation presently about t i d a l area enhanced receives by at in 143 Table 4 S a l t wedge i n t r u s i o n c h a r a c t e r i s t i c s i n the F r a s e r R i v e r v a r i o u s model d e p t h s . The deep c h a n n e l i s 3 m e t e r s below p r e s e n t and the s h a l l o w i s 2 meters above the present. PENETRATION (KILOMETERS) ESTUARI TYPE Deep Present Shallow Time Feb. 10, 1973 0300 hours 0500 1200 21.6 21.0 32.0 17.4 16.2 27.2 14.3 12.9 23. 5 Wash-out 17h53m 17h43m 17h27m for the 144 continual dredging, deposition have to and be and and been In neglected examined with the lower the introduced of and i s for a been using a course followed relation to particles the fresh of the velocity f i e l d , paths. The upstream on Arm would the f i e l d baroclinic this Fraser monitoring models (Joy effects are assumption far ebb the and as can be flushing in and plant can be Two Main salt seen particle s i g n i f i c a n t l y water (1) flows: one barotropic near an I runs 1 and treatment were plant the on a proposed tide. in Figure have have 2 ebb sketched The 42 assumed in the flows. layer compared in us separate River. Arm let the Numbers during is water into released Fraser the the one sewage 4 mixing, fresh days. Road velocities this but 3 the in of vertical particle of " s t r a t i f i e d " flood on dispersion particles. treatment effect and of maintenance. both as rates shipping issue by least by two Gilbert remain water of four each Main main at model particles by a l l of the sewage w i l l The period total and Island an of and advected f i e l d Annacis recently longitudinal velocity tide channel v a l i d i t y two-layer flooding expanded becoming model, increased concerned. particles offshore of studies, the the injected by one-dimensional into made cost rapidly two-layer estuary two the dispersion Neglecting follow is to generated investigated these usually subjected against development (1974)). be revenues quality has the the balanced Hater River would the with to the particle advects further is increase barotropic 1 s l i g h t l y downstream on and 2 further the 145 Figure 42. Advection paths of four particles r e l e a s e d i n t o t h e M a i n Arm o f the Fraser River. The small numbers along each path i n d i c a t e the time i n hours f o l l o w i n g r e l e a s e . 146 subsequent i t does ebb. not pass flood a second about 3 hours appear in the tidal cycle salt back time Annacis beyond to wedge, the with Island model that flush the return o u t f a l l and area and number 1. Much does not paths flush number in the 3. consequence,' Particle flushing the and i t s In fresh reduction of region. o u t f a l l of of modified particle particles extent is into, the into barotropic required i t s compared the that Also i t does is delayed same trends is to be noted particle u n t i l general the water depending 2 i s one time reduced by the the point of there would be upon release. These particle paths considerable differences contaminants between s t r a t i f i e d on the particle the the the f i e l d and released Annacis Road s t r a t i f i e d fresh effects. water o u t f a l l particle near the dispersion The both at same released baroclinic flows purely advective account in do than one apparent dispersion be in models. barotopic through higher the from salt on a water (1) and show that on the taken into results influence be for loading particles must the passes effluent much on times three for s t r i c t l y the five These and case based including significant dispersion one example, with would a case, predicted Road. in passes mouth Gilbert have For compared also concentrations based other (4) Thus river of the Island (3). is models f i e l d . region from part numerical in model trend that predicted dispersion velocity Gilbert (2), in barotropic barotropic the velocity imply 147 The Effects of The region deleterious end from the the dispersion incorporation s t r a t i f i e d of the improved model mixing however, the i t i s layers salt wedge the river is and effluents result tend to than compensated the on they the be for the the salt suffer rate of confined in some to from of motions. or that the once the measured model basic rates for i t s e l f use can be vary. important each the thinner degree dispersion provide been vertical effluent wedge to within corresponding loading The from the In the layer. surface one considerable to flushed models. also depth being some dispersion clear either in the within at whole the flush influences of the s t r a t i f i e d concentrations to discharges over a mixing that require have is means a therefore hydraulic intrusion v e r t i c a l mixed as layer the produces w i l l , effluent used densities and knowledge be the usually these could layer of the across This before would into and mass simulation by river, required water the unstratified i s other studies, allowing wedge either dispersion of This into terms between salt diffusion properties. contaminants diffusion standpoint release the information, The are in turbulent the released A complete flow vertical in water of of that of up estuary. show along substances proportion, S t r a t i f i c a t i o n occurs transfer hydraulic and observations i n t e r f a c i a l two-way Mixing to or two hours d i l u t i o n . mixing i s layers by the the estuary. of When suppressed with unstratified contaminants bottom higher situation. decreased time Predicting relies on a
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Salinity intrusion in the Fraser River, British Columbia Hodgins, Donald Ormond 1974
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Title | Salinity intrusion in the Fraser River, British Columbia |
Creator |
Hodgins, Donald Ormond |
Date Issued | 1974 |
Description | The dynamics of salt water intrusion in the tidal Fraser estuary was studied by both a programme of field measurements and the use of numerical solutions of the equations of motion. Time series conductivity measurements spanning several tidal cycles indicated significant penetrations exceeding an estimated 15 kilometers above Steveston for tides of large diurnal inequality. Large ebb tides washed salt water out of the river despite low winter discharges averaging 1100 m³/sec. Mixing sufficient to disperse the salt water throughout the water column was not observed although surface currents typically ebb between 2 and 3 meters/second, and the salt wedge appeared to flood and ebb in a fairly well-defined layer. Longitudinal salinity gradients were detectable in each layer, indicating that two-way mixing took place during flood and ebb periods. Both conductivity and velocity data revealed that maximum intrusion lagged high water by 60 to 80 minutes near the river mouth. A numerical two-layer model predicted the salt water thickness within 10 per cent of the total depth and a phase agreement of ± 40 minutes at maximum intrusion. Velocities were comparable to measurements within 15 cm/sec. The model neglected mixing across the interface but included the Reynold's stress formulated as KipU|U|Fi where Ki=0.0075, U is the relative layer velocity and Fi is an interfacial Froude number. The bottom stress was included as Kbp¹u¹|u¹| where Kb=0.0055, and both stresses were found to be significant in the dissipation of energy in the flows. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2010-01-25 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0064165 |
URI | http://hdl.handle.net/2429/19137 |
Degree |
Doctor of Philosophy - PhD |
Program |
Civil Engineering |
Affiliation |
Applied Science, Faculty of Civil Engineering, Department of |
Degree Grantor | University of British Columbia |
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UBCV |
Scholarly Level | Graduate |
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