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A laboratory study of slope flow induced by a surface salt flux Hardenberg, Bon J. van 1987-07-14

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A LABORATORY STUDY OF SLOPE FLOW INDUCED BY A SURFACE SALT FLUX by Bon J. van Hardenberg B . Sc . ,University of British Columbia, 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE DEPARTMENT OF OCEANOGRAPHY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1987 (c)Bon J. van Hardenberg, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Oceanography The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 15 April 1987 Date nF-firt/ft-n ABSTRACT The salt expulsion caused by the freezing of seawater and the drainage of brine from the ice creates a convectively mixed layer, which extends to the bottom in shallow coastal regions. This buoyancy flux at the surface was simulated in laboratory experiments by percolating salt water through a porous membrane into a tank. Shadowgraph images show that a down-slope flow is induced when the bottom of the tank is set at an angle. Velocity maxima in the slope flow, measured from the movement of injected dye ranged from 0.09 to 0.66 cm/s. Fluid densities were determined using thermistors and small-volume conductivity micro-cells developed for this purpose. For bottom slope angles between 2.2° and 5.5°, and at computed salt fluxes between 1.82*10_5and 1 . 63* 10_& g/cm2/s, the salinity profiles showed slope flow depths between 7 and 17 mm with a rise in salinity of 0.24 to 0.92 ppt above those in the mixed layer. Entrainment at a density interface without shear, using this experimental arrangement, agreed closely with predicted results by Bo Pedersen. Using the entrainment model for a turbulent gravity current, entrainment factors computed from the data of the slope flow experiments were up to two orders of magnitude larger than those predicted for flows in a quiescent environ ment. This is contrary to visual evidence of the experiments or to Arctic field data, which indicate low rates of entrainment. This suggests that a different model is required to explain the interaction between such flows and the turbulent environment. i i TABLE OF CONTENTS Abstract i i Table of contents iii List of f i gure s v i List of photos x List of tables x i Acknowledgements xii 1 - INTRODUCTION 1 1.1 Arctic subsurface intrusions and slope flow 1 1.2 Laboratory study 3 2 - EXPERIMENTAL METHODS 5 2.1 Tank and tray arrangement 5 2.2 Flow visualization 7 2.3 Instrumentation for density determination 9 2.3.1 Thermistors and micro-cells 9 2.3.2 Calibration of cell constants 12 2.3.3 Time response characteristics 13 2.3.4 Spatial resolution 15 2.4 Data acquisition 17 2.5 Experimental procedure 19 2.6 Determination of membrane salt flux 21 2.6.1 Salt- and volume fluxes 22.6.2 Salt flux calibration 2 2.6.3 Membrane salt flux determination 24 2.6.4 Salt flux and entrainment 28 2.6.5 Arctic salt flux and convection depth 37 i i i 3 - EXPERIMENTAL RESULTS AND INTERPRETATION 40 3.1 Slope angles, starting salinities and salt flux 40 3.2 Shadowgraph observations 41 3.3 Injected dye 44 3.4 Salinities and salinity profiles 50 3.5 Salt fluxes and flow velocities 57 3.6 Interpretation 62 4 - SUMMARY AND CONCLUSIONS 7 BIBLIOGRAPHY 70 Appendix A - SALINITY AND DENSITY CALCULATION 73 A.l Sa Unity 74 A. 2 Density 6 Appendix B - CONDUCTIVITY MICRO-CELLS 79 B. l Cell construction 80 B.2 Micro-cell electronics 81 B.3 AM/CT Datalogger conductivity electronics 82 B.4 Determinattion of calibration constants 83 B.5 Micro-cell time response 91 B. 6 Spatial resolution of the micro-cells 102 Appendix C - THERMISTORS 105 Cl Thermistor use 106 C. 2 Leaks 107 C.3 Re-calibration for extended range 108 C.4 Datalogger calibration correction 109 i v Appendix D - DATALOGGERS 114 D.l Applied Microsystems datalogger 115 D. 2 HP-Data Acquisition System 118 Appendix E - MEMBRANE FLUX CALIBRATION 119 E. l Salt and volume flux and driving pressure 120 E. 2 Flux calibration experiments 121 Appendix F - DESCRIPTION OF EXPERIMENTS 127 F. l Slope flow experiment #1 129 F.2 Slope flow experiment #2 137 F.3 Slope flow experiment #3 144 F.4 Slope flow experiment #4 149 F.5 Slope flow experiment #5 154 F.6 Slope flow experiment #6 159 F.7 Slope flow experiment #7 164 F.8 Slope flow experiment #8 170 v LIST OF FIGURES Fig.1-1 Typical Arctic profiles in winter 2 Fig.2-1 Apparatus for slope flow experiments 7 2-2 Diagram of arrangement for shadowgraphs 7 2-3 Micro-cell with thermistors 10 2-4 Micro-cells in experiments 1 2-5 Volume required to flush cell 14 2-6 Micro-cell spatial resolution 6 2-8 Data acquisition - manual input 17 2-9 Data acquisition: AM/CT datalogger 18 2-10 Data acquisition: HP-3497A data system 19 2-11 Flux - driving force ... 23 2-12 Salinity profile in tank/tray edge 25 2-13 Salinity profile in the tray 26 2-15 Membrane volume flux vs. pressure 27 2-16 Diagram of interface entrainment definitions 29 2-17 Entrainment at interface of 2-layer system 31 2-18 Time series plot of interface depth and mixed layer salinity 34 2-19 Interface depth vs. mixed layer salinity, and initial stratification 35 2-20 Entrainment by penetrative convection 36 2- 21 Profiles and ice thickness - field data 39 Fig.3-1 Sketch of typical shadowgraph pattern 42 3- 2 Sketch of downhi11/ups1 ope flow cells 43 3-3 Mixed layer time-series and linear fit 52 v i 3-4 Actual and adjusted salinity profiles 53 3-5 Micro-cell time-series - slope flow exp#3 54 3-6 Salinity rate of change in mixed layer and bottm flow 56 3-7 Slope flow velocity vs. salt flux 60 3-8 Flow velocity vs. slope angle 61 3-9 Slope flow diagram 62 Fig.A-1 Conductivity ratio vs. salinity 77 A-2 Density vs. salinity 78 Fig.B-1 Diagram of micro-cell assembly 81 B-2 Micro-cell constants vs. temperature 85 B-3 Time-series of micro-cell calibration constants ... 89 B-4 Cell calibration constants vs. salinity 90 B-5 Time response - experimental arrangement 91 B-6 Micro-cell time response - C#l time-series 96 B-7 Micro-cell time response - C#2 time-series 97 B-8 Micro-cell time response - C#3 time-series 98 B-9 Micro-cell response curve - C#l 99 B-10 Micro-cell response curve - C#2 100 B-ll Micro-cell response curve - C#3 101 B-12 Resolution in 2-layer system - 5 PSS 103 B-13 Resolution in 2-layer system - 0.5 PSS 104 Fig.C-1 Thermistors at micro-cell inlet and outlet 107 C-2 Thermistor calibration curve 113 vii Flg.E-1 Membrane flux calibration - time-series 124 E-2 Membrane volume flux calibration before and after first slope flow experiment .... 125 E-3 Membrane volume flux calibration curves 126 Fig.F-1 Micro-cell time-series plot - experiment #1 ..... 131 F-2 Salinity profiles - slope flow exp #1 132 F-3 Time-series plot of profile points 133 F-4 Adjusted profiles - slope flow exp#l 134 F-5 Salinity distribution along the centerllne 135 F-6 Time-series plot of distribution data 136 Flg.F-7 Micro-cell time-series plot - experiment #2 139 F-8 Time-series plot and linear fit 140 F-9 Salinity profiles - slope flow exp#2 141 F-10 Time-series plot and linear fit 142 F-ll Salinity profiles - slope flow exp #2 143 Fig.F-12 Micro-cell time-series plot - experiment #3 146 F-13 Time-series plot and linear fit 147 F-14 Salinity profiles - slope flow exp #3 148 Fig.F-15 Salinity profiles - slope flow exp#4 151 F-16 Salinity profiles - slope flow exp#4 152 F-17 Salinity distribution along bottom slope 153 viii Fig.F-18 Micro-cell time-series plot - experiment #5 156 F-19 Salinity profiles - slope flow exp#5 157 F-20 Salinity profiles - slope flow exp#5 158 Fig.F-21 Micro-cell time-series plot - experiment #6 163 Fig.F-22 Micro-cell time-series plot - experiment #7 166 F-23 Salinity profiles - slope flow exp#7 167 F-24 Salinity profiles - slope flow exp#7 168 F-25 Salinity profiles - slope flow exp#7 169 Fig.F-26 Arrangement of micro-cells - experiment #8 170 F-27 Micro-cell time-series plot - experiment #8 172 F-28 Expanded time-series and curve fit 173 F-29 Salinity profiles - slope flow exp#8 174 F-30 Salinity profiles - slope flow exp#8 175 F-31 Salinity profiles - slope flow exp#8 176 i x LIST OF PHOTOS Photo 1. Experimental tank and tray 5 Photo 2. Shadowgraph image of slope flow 8 Photo 3. Interface entrainment 28 Photo 4. Dye in the mixed layer and slope flow ... 45 Photo 5. Velocity maxima in dye 46 Photo 6. Dye at shallow end of tank 47 Photo 7. Bifurcation in slope flow 48 Photo 8. Waves in dye at lower end of slope 49 Photo 9. Dye in stably stratified region 49 Photo 10. Dye and shadowgraph 162 x LIST OF TABLES Table 2.0 Micro-cell calibration constant K 13 2.1 Entrainment in 2-layer system 32 2.2 Entrainment In linear stratification . .. 33 2.3 Entrainment from Arctic field data 38 Table 3.1 Starting conditions for slope flow experiments .. 41 3.2 Compiled results from slope flow experiments .... 58 Table Bl. Micro-cell calibration constants 87 Table Cl. Thermistor calibration constants 109 Table Dl. Clock board edge connector pin functions 117 Table D2. Multiplexer input channel cycling pattern 117 Table FI. Salt fluxes and flow velocities - sloperun#l ... 130 F2. Flow velocities from photos - sloperun#2 137 F3. Salinity of tray fluid - sloperun#2 138 F4. Saltfluxes and flow velocities - sloperun#2 .... 139 F5. Flow velocities from photos - sloperun#3 145 F6. Salt fluxes and flow velocities - sloperun#3 ... 145 F7. Salinities in the tray - sloperun#4 149 F8. Salt fluxes and flow velocities - sloperun#4 ... 150 F9. Salinities in the tray during sloperun#5 154 F10. Flow velocities and salt fluxes - sloperun#5 ... 156 Fll. Slope flow velocities - sloperun#6 160 F12. Salinities ln tray and tank - sloperun#6 161 F13. Flow velocities and salt fluxes - sloperun#6 ... 162 F14. Flow velocity and salt flux - sloperun#7 165 x i ACKNOWLEDGEMENTS The author is grateful to Dr. D. R. Topham of the Institute of Ocean Sciences in Sidney, who suggested this problem and provided the required equipment, advice and much of the funding for the experimental work, and to Dr P.H. LeBlond of U.B.C. who provided encouragement, further funding and the academic advice required to successfully complete the project. The late R.B. Sudar provided invaluable guidance in the development of the salinity measurement system. Special thanks also goes to the technical staff of the Frozen Seas group of Ocean Physics at the Institute of Ocean Sciences in Sidney, B.C. who helped to get the experimental system operational. This work was partially funded under Government of Canada contracts nr. FP941-4-1919 and FP941-5-1290. x i i 1 - INTRODUCTION 1.1 Arctic subsurface intrusions and slope flow Typical oceanographic profiles taken during winter of the salinity and temperature under the ice in the Beaufort Sea (see figure 1-1) show a well-mixed surface layer extending to depths of up to 50 meters. This layer is isothermal, near the freezing point, and isohaline due to convective overturning caused by the expulsion of salt at the ice/water interface from the ice that forms as sea water freezes. The subsurface layer below this contains the pycnocline where a large increase in salinity generally is accompanied by a small rise in temperature. Below the thermocllne there is gradual mixing with water of Atlantic origin to form the Arctic Deep Water. In many of the profiles, intrusions into this sub-surface layer were found of up to 30 meters in thickness, characterized by temperature minima (see feature 'a' in figure 1-1). This colder water most likely was formed as a convectively mixed surface layer in some other location where water at the surface had a higher salinity or where a faster freezing rate caused a higher salt flux. The colder and saltier water moved to the depth of intrusion where it was found at the profiling station possibly as a slope current or shelf drainage flow. Such slope flows could be the cause of cold water intrusions penetrating out into the Arctic Ocean at depths up to 200 meters (see Perkin and Lewis (1979), Melling and Lewis (1982)). 1 -Q TJ -2 0 20 -\ 40 60 80 UJ fv ID to 100 u cr CL 120 14 0 -160 TEMP.°C. 1 32.7 temperatures STATION: 09 T S 29-11-79 30 31 32 —r~ 33 34 35 SALINITY Figure 1-1. Typical Arctic profiles in winter (Frozen Seas Research Group, IOS) As sea water freezes, some of the salt is expelled immedia tely from the ice which forms. Subsequently, more salt drains as brine from a system of dendritic channels that develops in the ice. The influx of salt causes a density increase at the ice/seawater interface and results in convective overturning of the water column below the ice. Laboratory studies by Foster (1969) and by Elliott (1972) looked at haline convection under sea ice. The rejected salt was seen to form a pattern of plumes or streamers with downward velocities ranging from 0.09 to 0.23 cm/s for ice growth rates from 0.3 to 7.8 cm/day. A 2 field study of salt rejection by sea ice during growth is described by Lake and Lewis (1970). In shallow seas, such as parts of the Beaufort Sea in the Canadian Arctic, the convecti-vely mixed layer which is driven by freezing may extend to the bottom. The density in this layer will vary with the amount of salt flowing into it and with the depth into which it is mixed. An uneven salt flux or a bottom slope will create horizontal gradients in the density which in turn can cause a downslope current along the bottom and intrusions at levels below that of normal mixing from surface effects; compensating currents will occur at higher levels. 1.2 Laboratory study A series of laboratory experiments was conducted under the auspices of the Ocean Physics Group at the Institute of Ocean Sciences in Sidney, British Columbia, to examine under control led conditions and on a small scale, slope flows induced by a surface salt flux over a sloping bottom. Slope flows were observed in each of the experiments, which were conducted in a plexiglass tank with the bottom set at some small slope angle. The surface salt flux was simulated by slow percolation of salt water through a membrane into the tank, and a simple formulation was developed to obtain estimates of the magnitude of the salt fluxes which generated and maintained the observed slope flows. Shadowgraph images and dye were used to visualize fluid motions in the convectively mixed layer and to determine velocities in the slope flow. A series of micro-cells 3 were developed to obtain the electrical conductivity of fluid withdrawn from points in the tank. The temperatures of fluid in the micro-cell and in the experimental tank, determined with micro-bead thermistors, were combined with the conductivity to compute the salinity and density of the fluid (appendix A). Patterns of motions in shadowgraphs show the slope flow and a weaker opposite flow in the mixed layer. Movement of injected dye shows a velocity distribution in the slope flow with a peak of 0.09 to 0.66 cm/s at about 0.5 cm above the bottom. Salinity profiles indicate slope flow depths of 7 to 17 mm in which the salinity rises 0.24 to 0.92 ppt above that in the convectively mixed layer. Estimates of salt fluxes in these experiments ranged from 1.82e-5 to 1.63e-6 g/cm'/s. The notation (e+n) is used in the following sections to denote (10 to the powertn). The computed salt flux estimates were several orders of magnitude larger than those found in Arctic field data, but mixing depths were several orders smaller. The buoyancy velocity scale W*, which can be used to characterize convection, was therefore nearly the same in both cases. When the slope flow was considered as a turbulent gravity current, entrainment factors calculated by inserting data from this series of slope flow experiments were up to two orders of magnitude larger than those predicted for a quiescent environ ment. This is also contrary to evidence from the experiments and to Arctic field data which show that such flows maintain their characteristics over great distances from the source. 4 2 - EXPERIMENTAL METHODS 2.1 Tank and tray arrangement A series of laboratory experiments was conducted in a tank made of 12 mm thick plexiglass. The inside dimensions were 87.5 cm long, 23cm wide and 25cm deep (see photo 1 and figure 2-1). The tank was raised at one end to create a sloping bottom and was partly filled with a mixture of fresh and sea water. Photo 1. Experimental tank and tray A tray was suspended level with the surface of the fluid in the tank, and the expulsion of salt from sea ice was simulated by a slow seepage of higher salinity water through the bottom of this tray. The tray bottom consisted of a porous membrane (a Mllllpore filter membrane, 0.8 micrometer pore size) mounted between two layers of fiberglass circuit boards, with aligned perforations. The tray was filled with sea water to several 5 millimeters above the height to which levelling slots in the sides were taped shut. In some of the experiments pure sea salt was added to increase the salt flux. When the high salinity fluid percolates through the membrane into the tank this causes an equal return flow of the lighter fluid to the tray. A small pump was used to stir the fluid in the tray, and exchange it with that in a back-up reservoir to help maintain the higher salinity in the tray. The volumes of fluid in tank, tray and reservoir were kept constant during each run and the system is self-levelling. A series of 6 cm long copper tubes of 1.6 mm inside diameter were mounted through the membrane in the bottom of the tray, at 10 cm intervals along the centre line, starting 7.5 cm from the shallow end of the tank. These access tubes or ports #1 to #8, numbered from the shallow end of the tank, were used to inject dye or to withdraw fluid from various locations and depths in the tank through conductivity micro-cells to determine salinity and dens i t y. Figure 2-1 shows a diagram of the arrangement of the tank, the tray with the sampling tubes and levelling slots, the added reservoir, and the circulation pump used to mix tray fluid and exchange it with that in the reservoir. The micro-cells are shown without the small pumps which return the syphoned fluid to tank and tray to maintain constant levels. 6 reservoir Figure 2-1. Apparatus for slope flow experiments. 2.2 Flow visualization Light from a source placed at a distance behind the tank was focused by cylindrical lenses into a nearly parallel beam (see figure 2-2). This beam was projected through the side of the tank onto a translucent mylar film on the opposite side to form shadowgraph Images. camera C approximately 7 meters tank cross-sect i on iiia r ID] a d pro j ector slot cy1i ndr lenses transp.film Figure 2-2. Diagram of arrangement for shadowgraphs 7 During the experiments, variations in the refractive index due convective overturning formed patterns of wrinkled lines in the shadowgraph image. The mean circulation pattern created by the bottom slope flow and the compensating flow in the mixed layer were visible as deflections in the line patterns (see photo 2). The image represents the motions of small streamers or parcels of fluid, integrated over the width of the tank and therefore can not show any cross-sectional circulation patterns. Photo 2. Shadowgraph image of slope flow The slope flow was also visualized by injecting dye, which was diluted with fluid from the mixed layer in an attempt to match the slope flow density. The dye was injected through one of the sampling tubes along the centerline of the tray. While some of the dye was entrained in the convective motions as it sank through the mixed layer, most of it was carried along as S dye streaks in the slope flow. The flow velocities at different slope angles over a range of salt fluxes were determined from the distance that the dye moved in a known time interval in photo and slide sequences or on video tape footage. 2.3 Instrumentation for density determination Several small-volume conductivity cells were developed for salinity determination and used in combination with thermistors to obtain a quantitative description of fluid densities in the slope flows and in the convectively mixed layer. The data were taken manually or with a datalogger and processed using a desk top computer. 2.3.1 Thermistors and micro-cells To determine the electrical conductivity of fluid taken from different points in the experimental tank, conductivity micro-cells were developed with a small internal volume of about 0.15 ml (figure 2-3). Fluid was sampled by syphoning it from a point in the tank or tray through one of the micro-cells. The micro-cells consisted of four platinum foil electrode rings (of 3 mm diameter by 5 mm long) separated by segments of glass tubing (of 1.8 mm inside and 3.0 mm outside diameter). Micro-bead thermistors were inserted in the flow at the inlet and outlet of each micro-cell. The average of the tempe ratures determined from their resistances was combined with the conductivity ratio to calculate the salinity using the polyno mials of the Practical Salinity scale (see appendix Al). 9 The density of the fluid at the intake point in the tank was computed by combining this salinity with the temperature from another thermistor located in the tank using the polynomials of the Unesco equation of State for seawater (appendix A2). Stable and repeatable readings were obtained with continuous slow syphoning of fluid through the micro-cells. The low rate of withdrawal from a point ln the tank did not perceptibly influence the general flow patterns. Dimensions and assembly details of the cells are described in appendix B. NEEDLE Figure 2-3. Micro-cell with thermistors One cell was mounted on a vertical traveller which was moved along a track over the tank to one of the sampling tubes spaced along the centerllne in the tray. Data points for salinity 10 profiles of fluid in the tank were obtained by lowering the tip of the intake tube to successive depths. A second cell was used for simultaneous readings at a fixed depth in the convectively mixed layer to determine the change ln background salinity and the third cell was used to monitor the slow change in tray salinity. Fluid was syphoned through the cells at a fixed rate of 0.05-0.15 ml/s (1 to 3 drops/sec). A small pump with two pump-heads was used to return fluid from the outlets of diffe rent cells to the tray and to the tank to maintain the fixed fluid levels and volumes used to calculate the salt fluxes, as shown ln figure 2-4. t— Figure 2-4. Micro-cells in experiments 1 1 2.3.2 Calibration of cell constants The electrical conductivity in the micro-cells changes with the salinity of the fluid. An electronic circuit was designed so the output voltage (VC) was a linear function of the micro-cell conductance (1/R) for fluid of a given temperature and salinity. A cell constant (K) was expressed in ohms resistance of the cell at S = 35 PSS and T=15 °C. The conductivity ratio (RR) is then computed from the micro-cell output voltage as the product of conductance and cell constant: (2.1) 1/R = A + B.VC A = -2.6008e-8 (2.2) RR = K.(A + B.VC) B = -4.5954e-4 The values of A and B were obtained by least squares linear fit through output voltages for.a series of high accuracy standard res i s tors . In a number of the experiments an Applied Microsystems C/T datalogger was used to take micro-cell and thermistor readings (see section 2.4)-. It was found that the different currents and voltages used by the internal conductivity circuit to drive the micro-cells required different values for the constants A and B and for the cell constant K to calculate the conductivity ratio from the datalogger numbers (NC): (2.3) RR = K'.(R'tB'.NC) A'= 5.53084e-5 B'= 1.3290e-7 The cell constants were chosen as those integer values for which the salinity of a fluid sample, calculated from the micro-cell conductivity ratio and temperature, was closest to 12 the value determined with a Guildline Autosal. This calibration was frequently repeated to ensure that no shifts had occurred due to aging or electrode fouling. The average values of the calibration constant for each of the micro-cells are listed in table 2.0 below (see appendix B table B.l for details). Table 2.0 Micro-cell calibration constant K Calibration constant K for: Cel1#1 Cel1#2 Cel 1#3 for the AM/CT datalogger: (std. dev. for 18 samples) for separate cond.circuit: (std.dev. for 12 samples) 1885 (6.3) 1803 (5.6) 1793 (4.2) 1752 (3.5) 182 1 (6.7) 1783 (6.7) 2.3.3 Time response characteristics As the salinity changes at the intake to a micro-cell, an amount of fluid must pass through the intake tubing and the cell to flush it, before a reading is taken. The time response to a sudden change in salinity at the intake point was determi ned for each of the cells, at flow rates ranging from about 1 to 3 drops per second (or 0.05 to 0.15 ml/s) and for salinity steps between 0.5 to 5 PSS. To obtain typical response curves for the micro-cells the results were normalized by plotting the change in the salinity as a fraction of the total salinity step against the volume required, which is the product of flow rate and time. For these syphon flow rates, the volume to flush the intake tubing and the micro-cell was found to be about 4 ml. The results are shown in figure 2-5. 13 MICRO-CELL TIME RESPONSE Fiqure 2~5. Volume required to flush the cell 2.3.4 Spatial resolution The fluid syphoned from the intake point to the micro-cell can be considered as a point sink in a flow, and the calculated salinity is an average of fluid drawn from a small region. Some measure of the spatial resolution is then the extent to which a sharp interface appears blurred in a salinity profile. A two-layer fluid system with a sharp density interface was obtained by partly filling a container with diluted sea water, then slowly piping water of a higher salinity to the bottom and sharpening the interface by syphoning fluid from a point just below it. The interface was visible as a bright line in a shadowgraph. Fluid was then syphoned through the micro-cell at a fixed flow rate of about 2 drops per second and readings were taken after 30 seconds at successive closely spaced depths. For such two-layer systems with a step in salinity between 0.5 and 5 ppt, salinity profiles plotted from data taken across the interface show a set of distinct steps over a few milli meters of depth (figure 2-6). A detailed description of the dimensions and assembly of the micro-cells, calibration of the cell constants and electronics, the time response characteristics and the spatial resolution is given in appendix B. 15 0 29.0 10 . 20 . 30 _ 40 _ | 50 5 60 J CL LU Q 70 J 80 90 100 _ 110 _ 120 _ 130 . 140 . 150 _ 160 SALINITY (PSS) J 1 i , i 29.5 —i 30.0 flow through cell: abt. 3 dr/aec Resolution of interface in 2~layer syst jystem 1— riqure 2-6. M icro-cell spa-tial resolution 16 2.4 Data acquisition In the initial tests, a small conductivity circuit was used with a switch to power each micro-cell In turn. The output vol tage from this circuit and the resistances of the thermistors were read from a set of digital voltmeters (DVM's). The numbers were entered via the keyboard into an HP-9825 desktop computer, which was programed to apply the calibration relations for the thermistors and micro-cells to the data, print the raw data and computed values, plot selected parameters and store the data on magnetic tape (see figure 2-8). SWITCH MICRO-CELL ELECTRONICS EXPERIMENTAL TANK 1 VC" DVM RT" DVM TAPP HP-7225 PLOTTER HP-9825 COMPUTER LINE PRINTER Figure 2-8. Data acquisition - manual input In most of the experiments, the micro-cells and thermistors were interfaced via an Applied Microsystems (AM/CT) datalogger to the HP-9825. The datalogger internal conductance circuit was modified for use with the micro-cells. The different driving voltage and sensing current used by this circuit required separate micro-cell calibration constants (see section 2.3.2). The AM/CT datalogger could be triggered manually or at a set clock interval to cycle through all sensors and then transmit 17 the data via a serial converter and an RS-232 interface module to the HP-9825 computer (see figure 2-9). The salinity range of the AM/CT datalogger was limited and when the conductivity of the tray fluid was out of range, the separate small circuit was used with the DVM's. T-TNK y EXPERIMENTAL TANK AM/CT DATA LOGGER SERIAL CONVERTER RS-232 TAPE HP-9825 COMPUTER HP-7225 PLOTTER 1 HP-LINE PRINTER Figure 2-9. Data acquisition: AM/CT datalogger In the last several experiments an HP-3497A Data Acquisition System was used, combined with a separate conductivity circuit for each micro-cell. This allowed a more rapid sampling rate, automatic averages of multiple readings for each sensor circuit (5 rapid readings were taken of each sensor), and also showed less variability because the cells were continuously powered. Some small shifts were found in data sequences from experiments and later testing revealed that any shift ln relative position of the micro-cell outlet tubes could cause a change in apparent conductivity. Data obtained with this arrangement (figure 2-10) provided the most detailed profiles of density distribution in the slope flow. 18 CIRCUIT "A" CIRCUIT "B" CIRCUIT "C" C#l t: C#2 C#3 ZZfcJ T-TNK J EXPERIMENTAL TANK CONDUCTIVITY ELECTRONICS HP-7225 PLOTTER HP-3497A DATA ACQUISITION SYSTEM TAPE HP-9825 COMPUTER LINE PRINTER Figure 2-10. Data acquisition: HP-3497A System The raw data from each sensor circuit and the computed values of temperatures, conductivity ratio, salinity and density for each of the cells were printed on a line-printer and saved on magnetic tape. Depths of the micro-cell intake during profiling were manually set and noted on the print-out. The salinity time series points were plotted during each experiment. Profiles of salinity in the tank were later plotted from these data, as is described with the experimental results (In section 3). 2.5 Experimental procedure Sea water was mixed with tap water in one tank to create low salinity fluid for the experimental tank, and salt was added to sea water in another tank for the high salinity fluid used in tray and reservoir in some runs. The fluids were pumped to the experimental tank or to reservoir and tray-filling pail through a 0.8 micron filter to remove most organic matter and were left 19 for at least one day to stabilize at ambient room temperature, and to de-gas to avoid the formation of bubbles on the sensor surfaces which would adversely affect readings during the expe riment. For the initial wetting of the membrane, the tank was filled to the top with low salinity fluid. The tray was lowered sideways into the tank and gently tapped to remove the air bubbles trapped in the perforated boards. The tray was then lowered horizontally to the desired depth and the tank drained until the fluid was level with the bottom of the tray. At the beginning of an experimental run, the tray was filled with high salinity fluid while low salinity fluid was added in the edge between tank and tray to keep the fluid levels at the same height. This was done to prevent a rapid initial flux due to pressure caused by a difference in fluid levels In excess of that due to the difference in density between the two fluids. The start of convection was seen in the shadowgraph image as a slowly and nearly evenly descending curtain of small plumes. Convective overturning produced a mixed layer which extended to the bottom of the tank. A down-slope bottom flow was seen to establish itself shortly after the start of each experiment and was maintained by the salt flux throughout each experiment. Observations were usually taken over a period of 3 to 5 hours, but in one case the slope flow was still seen about 15 hours later. The shadowgraph images and the movement of injected dye were recorded in photo and slide sequences or on video tape to study the flow patterns and to determine slope flow velocities. The experimental results are described in section 3. 20 2.6 Determination of membrane salt flux The salt flux through the porous membrane Is a function of the height of fluid in the tray, the density difference between the fluid in tank and that in the tray and the membrane charac teristics. The magnitude of this buoyancy flux determines the turbulence in the convectively mixed layer. 2.6.1 Salt- and volume fluxes Initial estimates of the net salt flux were obtained from the salinity time-series of fluid in the tray and the known volumes of fluid in tray and reservoir. The net salt flux is the rate of change in the total amount of salt in the combined tray and reservoir volume taken per unit of tray area: (2.4) Bn= d(S2*D2)*(V2+Vr) Bn = net salt flux (gr/cm2/s) dt 1000 A S2 = salinity (gr/kg or ppt) D2 = density (gr/cm3) V2 = tray fluid volume (cm3) Vr = reservoir volume (cm3) A = membrane area (cm2) Suffix 2 Is used for properties ln the tray and 1 for those In the tank. The net salt flux Is the rate at which salt flows Into the tank through the membrane in the tray bottom, reduced by that In the return flow through the levelling slots ln the tray, taken per unit surface area (see figure 2-11). The return flow forms a thin layer at the top of the tray which is only partly mixed into it by the pump which exchanges tray and reservoir fluid. Equation 2.4 will therefore only yield a rough 21 initial estimate of the net flux due to the incomplete mixing in tray and the slow exchange of tray and reservoir fluid. The amount of fluid entering the tank through the membrane must equal the return flow from the tank to the tray, and the volume flux F can be expressed in terms of the net salt flux: (2.5) Bn=F*(D2*S2-Dl*Sl) F= volume flux (cm3/cm2/s) 1000 The membrane salt flux B is then the product of volume flux and the amount of salt per unit volume of fluid from the tray: (2.6) B = F*(D2*S2) B= salt flux (gr/cm2/s) 1000 The convection is driven by this membrane salt flux. 2.6.2 Salt flux calibration To calibrate the membrane salt and volume fluxes, a series of experiments was done in which the bottom of the tank was kept horizontal. In these experiments the patterns of lines in shadowgraph images indicated a nearly uniform distribution of convective motions, with end effects of diminished activity near the end walls of the tank. The rate of change in salinity of fluid from a point near the center of the tank was then taken to represent the average change for the whole tank fluid volume. Estimates of the net salt flux were obtained from the rate of change in salinity and density in the tank: (2.7) Bn=_d (S1*D1)*V1 dt 1000 A 22 With the fluid In tank and tray at the same level, the salt flux through the membrane is driven by the pressure due to the density difference of fluid columns of equal height in the tray and in the edge space between tank and tray: (2.8) P = (D2-Dl)*g*h with: P = pressure (gr/cm/s2) D = density (gr/cm3) h = tray fluid height (cm) g = gravity = 981 (cm/s2) Ay LEVELLING SLOT me mbrane TANK Si, Dl Figure 2-11. Flux - driving force Salinity profiles of fluid in the edge space between tank and tray (figure 2-12) did show a stable stratification caused by the Increasing salinity of fluid rising from the mixed layer to return through the levelling slots to the tray, and profiles of salinity In the tray (figure 2-13) show that this return flow formed a light layer at the top in the tray. To calculate the driving pressure, a correction was made by approximating these stable stratifications with simple 2-layer systems and reducing the height of the fluid columns by the 2-3 mm of common upper layer sal ln 1 ty. 23 The driving pressures and corresponding volume fluxes were calculated from time series data for fluid in the tray and in the tank, using equations 2.6 to 2.8 and these approximations. A calibration curve was fitted through sets of membrane flux data obtained before and after the first slope flow experiment (figure 2-15). 2.6.3 Membrane salt flux determination To estimate the membrane salt flux at the time that a slope flow velocity was measured during an experiment, the salinities of fluid in the tray and in the mixed layer at that time were obtained by linear interpolation, when nearby data points were available from the time-series. Salinities were estimated from a least squares curve fit when only a few tray data points were taken, or when no nearby mixed layer data were available. The driving pressure was then calculated from the corresponding densities, computed from those salinities and the temperature in the tank, using the Unesco Equation of State (appendix A). The corresponding volume flux was obtained from the calibra tion graph of membrane flow (figure 2-15) and the membrane salt flux was calculated from equation 2.6. Several series of flux calibration experiments were done to develop the data acquisition methods. The rate of change in the tank and tray densities was always very similar, but individual numeric results for the volume flux varied, in part due to some clogging of the membrane in successive experiments or to poor readings of fluid depths in tank or tray. 24 25 22.0 Salinity (PSS) 2A, 5 0 4 E E 10 J Q-(U a 20 J 30 J 40 J 50 J 60 J L it J I I I L Profile in the "tray at the centre bottom of tray i 1 1 1 1 1 1 r 27. 0 Figure 2-13. Salinity profile in the tray. 26 Figure 2-15. MEMBRANE VOLUME-FLUX vs PRESSURE calibration data for sloperuns 2.6.4 Salt flux and entrainment Several separate experiments were conducted without a bottom slope, over a range of salt fluxes similar to those used In the slope flow experiments, to measure interface entrainment caused by convective turbulence In the absence of shear. The salt flux into either a 2-layer system or into a linear stratification created an upper well-mixed layer which slowly increased in density due to the salt flux and In depth due to entrainment. The interface was visible in the shadowgraph as a bright line separating the line patterns in the upper layer of convective turbulence from the clear quiescent region below (photo 3). This line slowly moved downward due to entrainment. In the 2-layer system, the line faded as the step in density across the interface became small and the individual convective elements penetrated through it. Photo 3. Interface entrainment 28 The entrainment velocity mixed layer with time: is measured as the deepening of the Ve = dY/dt (2.9) The following diagram defines the dimensions, velocities and densities used to formulate interface entrainment: Tank and tray 2-layer system D Dw I DL linear stratification Y = = mixed layer depth Ve = = entrainment velocity H = = depth of fluid ln tank Vw = = membrane volume flux L = = bottom of linear stratlf. Dw = = tray fluid density AW = = tray membrane area D = - mixed layer density Ae = = tank Interface area De = = density at Interface DL = = density at depth L Figure 2-16. Diagram of Interface entrainment definitions The intensity of the convective overturning can be expressed as a vertical velocity scale W* derived from the mixed layer depth Y and buoyancy flux Q using simple dimensional analysis: W* = (Y.Q)1^ = [Y.Vw.g.(Dw-D)\^ (2.10) L Dref' Dref= 1 gr/cm^ g = gravity acceleration 29 The ratio of the inertial force to the buoyancy force at the interface describes the relative Importance of penetrative convection versus a stabilizing density stratification and has been expressed either as a non-d1 menslonal overall Richardson number Ri by Kantha (1978) or as an internal Froude number Fr by Bo Pedersen ( 1980) : Fr2 = 1/Ri = W*2 (2.11) g.Y.(D-De)/Dref The entrainment hypothesis derived by Bo Pedersen predicts that the ratio of flux to entrainment, written as a bulk flux Richardson number RfT, is nearly constant: RfT = Ve.(De-D) * 0.20 (2.12) (Dw-D).Vw In these experiments, conservation of mass requires that the rate at which the salt flux adds mass to the volume in the tank equals the sum of changes In mixed layer and lower layer: In the 2-layer system, the lower layer density Is constant. The mass in the tank is: M '= Ae.tY.D + (H-Y).Del (2.13) and conservation of mass is described for the 2-layer system by: (Vw.Aw)(Dw-D) = Ae._dfY.D + De.(H-Y)] dtL J or Vw = Ae .fVe.(D-De) + Y.dD1 (2.14) Aw.(Dw-D) L dtJ The entrainment velocity was obtained from video observations of interface depth (figure 2-17). Table 2,1 lists the computed values for the scale velocity and non-d1 mens 1onal parameters. 30 Figure 2-17. Entrainment at interface of 2-layer system. 31 The analysis was done using the data of the 5-23-86 experiment. The ratio of tray to tank area was Aw/Ae=0.824, the lower layer density De=l.00926 (g/cm3) and the rate of change in the mixed layer density was nearly constant dD/dt=6.076e-4 g/cm3/s. Table 2.1 Entrainment in 2-layer system t Ve .e-4 Vw.e-4 W* Rf T Ve/W* Fr2 Ri min) < cm/s) (cm/s) (cm/s) .e-4 .e-3 42 1.3308 1 .0528 0. 157 0. 222 6.01 3.834 261 54 1 . 9600 1.0618 0. 196 0. 223 8.80 4. 495 223 66 2.5892 1.1035 0.217 0. 227 1 1 . 42 5. 265 190 75 3.0611 1.1631 0.214 0. 232 13.19 6 . 170 162 90 3. 8476 1.3334 0.169 0. 246 15.65 9. 275 108 In the case of a stratification which Is linear to a depth L the mass under the tray to that depth is: M = Ae.^Y.D + (L-Y).(DL+De)j (2.15) and conservation of mass for the linearly stratified case is: (Vw.AwXDw-D) = Ae. d [ Y . D+ (De +DL) . (H-Y ) 1 dtL 2 J The time-series plots for interface depth and salinity in the mixed layer (figure 2-18) were combined to show the Interface depths at the corresponding mixed layer salinity (figure 2-19). A profile of the initial stratification, plotted in this same graph, shows that the step in salinity across the interface is constant, or: De-D= const so _d.(De)= d(D) dt dt 32 or Vw = Ae .[Ve.(2D-De-DL) + (Y+L).dDl (2.16) Aw(Dw-D) L 2 2 dti A linear least-squares fit to the interface depths from video footage, for points In the nearly linear part of the profile, ylelded: Y = 5.30 + (t-24)*60*l.128e-3 (Y in cm, t in min) and thus a constant entrainment velocity: Ve = 1.128e-3 (cm/s) Values for flux, scale velocity and non-dimensional parameters were computed using the above derivations. The results for data from the linear stratification experiment are listed in table 2.2 be 1ow. Table 2.2 Entrainment in linear stratification t Vw.e-4 W*.e-2 RfT Ve/W* Fr2 Ri (min) (cm/s) (cm/s) .e-2 30 1 .686 2.58 0. 107 6.01 4 . 365 2. 46 40 1 .960 2 . 80 0. 094 8.80 4 .032 2. 34 50 2 . 246 3. 00 0. 084 1 1 . 42 3 .76 2. 25 60 2 . 550 3. 20 0. 076 13. 19 3 .52 2. 17 The computed results of these experiments show good agreement with the hypothesis for entrainment due to free penetrative convection by Bo Pedersen (1980) and agree with data from other sources when plotted in graphs of compiled field and laboratory results by Bo Pedersen and Jurgensen (1984) and by Kantha (1976), as shown in figure 2-20. 33 Entnainment by convection Linear- stratification 5-30-86 and mixed layer salini 34 Figure 2-19. Interface depth vs. mixed layer salinity, and initial stratification. 35 10 -1 10 -2 10 -3 10 -4 : ve i i i : i i! i 1 —.'. I 1.1 t a -• € A m x a , convect ior linear str 1 into-~atif. / * -, convectioi 2~layer e ,1 1 l l L1I l n into yetem 1_i—i i i 111 r 2 V\ Fr = Yg AD -/Dref -I • , 10 -3 10 -2 10 -1 10 10 Figure 2~20. Entrainment by penetrative convection Comparison with Bo Pedersen theory (1980) and with laboratory and field data by: ^ Bo Pedersen and JUrgensen (1984)- laboratory *PP Heidt (1975)- laboratory experiments si,si Willis and Deardorff (1974)- laboratory A Farmer (1975)- solar heating under lake ice + BvanH (1986) - laboratory salt flux 36 2.6.5 Arctic saltflux and convection depth To compare laboratory conditions with those encountered in the field, data from Cambridge Bay in the Canadian Arctic (Gade et al, 1974) were used to derive values for the buoyancy flux, entrainment and Froude number following the above notation. The data included ice thickness H, mixed layer salinity Sm and observed depth of convection Y between October 1971 and April 1972. The ice salinity Si was estimated as 3.0 ppt and ice density Di as 0.9 g/cm3. The ice growth was obtained by linear interpolation over the time between observations. The salt flux into the ice is the product of growth, density and salinity in the ice. Using a simplified model, the amount of salt expelled into the mixed layer can then be expressed as a salt flux F : F = (dH/dt).Di.tSm - Sil (2.17) The following table shows the field data and the derived values for entrainment velocity Ve= dY/dt, ice growth (dH/dt), salt flux F and buoyancy flux Q= F.g (g=gravity), convective scale velocity W*= CY.Q]1'3 and corresponding Froude number Fr. The salt flux from freezing estimated from these field data Is several orders of magnitude smaller than those used in the laboratory, however, the large depths of the mixed layer in the field bring the values for the scale velocity W* close to those in the experiments. 37 Table 2.3 Entrainnent from Arctic field data Mixed layer Ice Date Depth Incr Ve Sal in Dens Thk Incr Growth days (m) (m) (cm/s (ppt) (sigma) (cm) (cm) (cm/s .e-4) .e-5) 10/12 16 . 6 0 17 < 18 . 5> 3. 1 2. 1 1 <11.5> 23 1 . 566 10/29 19 . 7 26 .5 21 . 27 23 37 <20. 35> 1 . 3 0. 407 <27 . 15> <21 . 30> <37> 28 0. 876 12/5 21 . 0 27 .8 22 . 32 51 78 <24. 0> 6. 0 0. 890 <28 . 35> <22. 77> <95> 88 1 . 306 02/21 27 . 0 28 .9 23. 21 139 52 <30. 75> 7. 5 1 . 47 1 <29 . 1> <23. 38> <147.5> 17 0. 333 04/14 34. 5 29 . 3 23. 54 156 Values in brackets are linear interpolations between those from the dates of observation. Days Salt Buoyancy Flux (g/cm2/s) .e-7 Flux (g/cm/s3 .e-4 W* ) (cm/s) Ve /W* Fr2 RfT 17 3.31 3. 25 0. 839 2.517 1 .63 I .58 37 1 . 904 1 .87 0.724 0.561 1 .093 0.524 78 2.983 2.92 0.888 1 .002 3.586 0. 285 52 0.783 0.768 0.618 2 . 38 3. 960 0.61 The computed values for entrainment e f f lc iency agree with the 0.20 predicted by Bo Pedersen but there were few observations, spaced over a period of six months (figure 2-21), and the values for entrainment derived from these field data neglect any advection of salt by tidal flows or by the type of reverse estuarine flow suggested by the slope flow experiments, or any entrainment caused by Internal waves. 38 30 I f-CL ci 60 ~i r s. > 1 J i_ SEPT. 14.1971 OCT. 12.1971 OCT. 29.197! DEC . 5,1971 —«»» FEB .21 .1972 APR . 14.1972 J i ' « 26 28 30 SAL. (%o) -I +1 +3 TEMP. (°C) Seasonal changes in water column temperatures and salinities at Cambridge Bay, winter 1971 and 1972. 5 2.0 LU 1-5 Z U 1-0 I *~ 0.5 LU U 0 -i 1 r r\S.K£--J L O N 1971 J I L F M A 1972 M Sea ice thickness at Cambridge Bay according to Atmospheric Environmental Service and Frozen Sea Research Group measurements. Figure 2-21. Profiles and ice thickness - field data 39 3 - EXPERIMENTAL RESULTS AND INTERPRETATION Slope flows were Induced in a series of experiments conducted with different bottom slope angles, set between 2.2° and 5.5°. Salt flux estimates computed from micro-cell data taken during the experiments ranged from 1.82e-5 to 1.63e-6 gr/cm2/s. A slope flow was observed In each of the experiments. 3.1 Slope angles, starting salinities and salt fluxes The bottom slope angle of the tank was fixed before the start of each experiment. The salt flux range through the membrane during the experiment is determined by the height of fluid in the tray and by the difference in the initial salinities of the fluids in tank and tray. Sea water was used in the tray and reservoir for the lower salt fluxes, where conductivities were within range o-f the AM/CT Datalogger circuit. For the higher salt fluxes, pure sea salt was mixed into the sea water for tray and reservoir to obtain salinity differences of 40-60 ppt between the fluids in tank and tray. In these cases the tray salinities were monitored with a separate conductivity circuit and a digital voltmeter. Table 3.1 lists the bottom slope angle, the depths of fluids in and under the tray, the starting salinities for each of the slope flow experiments, and the range of computed membrane salt fluxes. 40 Table 3.1 Starting Conditions for Slope Flow Experiments Exp Angle Tray-h Tank-depth Sa1inity(ppt) Salt fluxes # (degr) (mm) Max(mm)Min Tray Tank (g/cm2/s*e-6) 1 3.3 34 63 7 59 15 17.80 -16.94 2 3.8 34 65 7 58 7 18 . 20 -17.12 3 2 . 2 34 51 20 58 8 14.18 - 9.46 4 5 . 2 34 100 20 53 7 21 .89 -13.64 5 5.2 34 100 20 52 13 12.67 - 5.51 6 2 . 3 34 57 20 30 16 2.21 - 1 .63 7 5.5 34 78 0 28 12 1.71 8 5 . 2 34 99 15 46 9 With the end of the tray resting on the bottom at the shallow end of the tank, the amount of fluid and the depths in the wedge-shaped volume below the tray became very small at small slope angles. In initial tests, neither the shadowgraph nor injected dye did show any distinct contribution to the slope flow near the shallow end. Therefore, the tray was raised so the fluid depth at the shallow end of the tank was 7 mm im the first and second slope flow experiments and 20 mm in nearly all subsequent experiments. 3.2 Shadowgraph observations When the tray was nearly filled with the denser fluid to the selected height, and the fluids in the tray and in the edge space between tank and tray reached almost the same level, salt began to percolate through the membrane in the tray bottom and convection started as a field of small plumes or streamers. It 41 became visible in the shadowgraph image as a curtain of small wrinkled line segments, slowly and fairly evenly descending at a speed estimated at less than one cm/sec, depending on the magnitude of the salt flux. A downslope flow was seen to start up shortly after part of this curtain reached the bottom at the shallow end of the tank: the mostly vertical orientation of the line segments in the shadowgraph image began to display a bend towards the shallow end of the tank in the mixed region, and near the bottom became parallel with it. The typical shadowgraph images seen during the experiments (seen in photo 2, page 8) show a deflection of the vertical line patterns from convective overturning by the general flow pattern imposed by the slope flow and associated return flow in the mixed region (see figure 3-1 below). Figure 3-1. Sketch of typical shadowgraph pattern The slope flow usually was seen to start up very close to the shallow end soon after the saltflux through the membrane became visible, but in several of the experiments it was seen to start initially at 20 to 30 cm from the shallow end of the 42 tank and to form a counter-rotating cell uphill from there (see figure 3-2). In these cases, the downslope/uph111 flow cells did re-establish themselves again after stirring the fluid under the tray to remove flow patterns which might have been introduced by uneven conditions while filling the tray. In some of the experiments, the initial descent of the curtain of lines in the shadowgraph was slightly faster in the area of the tray where the slope flow was seen to start. The starting point of the slope flow gradually moved toward the shallow end, while the uphill flow cell shortened and often disappeared over 8 to 20 minutes. In experiment #6, which had the lowest slope angle (2.3 degrees), the uphill flow cell decreased in length to the last 10 cm at the top of the slope, but persisted throughout the e xpe r i ment. Figure 3-2. Sketch of downs 1 ope/uphi11 flow cells The slope flow appeared to accelerate from the starting point but then to slown down and reach some equilibrium within about 43 20 to 30 cm down the slope, beyond which it was not possible to accurately measure any increase or decrease in the flow speed. As the experiments progressed and the heavier fluid collected at the deep end of the tank, the line patterns associated with convective turbulence did not penetrate into the deeper part of the tank. The slope flow was seen to separate from the bottom at an increasing distance from the end of the slope and move along the interface with the stably stratified fluid at the deep end. On several occasions, pinhole leaks were seen in the shadow graph Images at some of the points where sampling tubes cut through the membrane in the tray. The leaks showed as small streamers of denser fluid descending slightly faster through the mixed layer than the other motions observed and penetrating into the stably stratified layer which forms in the deeper part of the tank. While these contributed to the salt flux, they are believed to be minor. Some variability in the salinity profile points may have been caused when a streamer from a small leak intermittently was syphoned into a micro-cell during profiling, as was seen to occur in one instance on video footage. 3.3 Injected dye Small amounts of food dye were injected through one of the sampling tubes set along the centerline of the tray. The dye was mixed with some salt water to a density slightly above that of the fluid ln the tank. During injection, a line of dye was seen to sink through the convectively mixed layer, in which it 44 was deflected toward the shallow end of the tank by the overall flow pattern, similar to the lines seen in the shadowgraph. When the dye was more diluted and Its density was close to that in the mixed layer, the streaks made during descent through the mixed layer were distorted by the convective motions and moved toward the shallow end of the tank (photo 4). Photo 4. Dye in the mixed layer and slope flow Where the dye line sank through the bottom flow, vee-shaped features formed, showing a velocity maximum at about 3 to 6 mm above the bottom. These features were carried along much of the length of the tank bottom without noticeable dispersion from mixing, which indicates limited levels of turbulence in the slope flow. The vee-shaped features suggest a shear flow with a depth which would be twice that of the height of maximum velo city if the friction at the interface was equal to that at the bottom. The velocity shear and the penetration of convective 45 turbulence at the upper edge of the slopeflow entrained some of the dye from this edge while bottom friction stretches the lower part of the tongue of dye. (see photo 5). Photo 5. Velocity maxima in dye The maximum flow velocity was estimated at various times in each experiment from the distance that these dye tongues moved in timed photo or slide sequences, or in video tape footage. Velocities were generally determined from observations made between about 30 to 60 cm from the top of the slope, since the flow in this region appeared steady and not much affected by the conditions at the ends of the tank. The measured flow velocities ranged from 0.09 to 0.52 cm/s and decreased with time during each experiment as the salt flux diminished. In several of the experiments, dye which was injected In the 46 edge between tank and tray was slowly raised and carried to the slots into the tray by the return flow from the tank. This flow causes stable stratification in the edge space. Dye injected under the tray at the shallow end was seen to be mixed into the last 4 to 6 cm of the tank by the convection but did not flow down-slope for the slope angles and salt fluxes used in these experiments (see photo 6). Photo 6. Dye at shallow end of tank At the deep end of the tank the dye from the slope flow was slowly lifted and entrained into the mixed layer. When the slope flow velocities slowed down in the later part of an experiment, convective motions near the deep end of the tank did appear to penetrate closer to the bottom in the shadowgraph 47 edge between tank and tray was slowly raised and carried to the slots into the tray by the return flow from the tank. This flow causes stable stratification in the edge space. Dye injected under the tray at the shallow end was seen to be mixed into the last 4 to 6 cm of the tank by the convection but did not flow down-slope for the slope angles and salt fluxes used in these experiments (see photo 6). Photo 6. Dye at shallow end of tank At the deep end of the tank the dye from the slope flow was slowly lifted and entrained into the mixed layer. When the slope flow velocities slowed down in the later part of an experiment, convective motions near the deep end of the tank did appear to penetrate closer to the bottom in the shadowgraph 47 Image. In the course of an experiment, the heavier fluid from the slope flow accumulated at the deep end of the tank, where it formed a stably stratified region in which no convective penetration was seen, below a mixed layer of nearly uniform depth. In several of the experiments, the dye in the slope flow was seen to bifurcate where it reached this stable fluid (see arrows in photo 7). Photo 7. Bifurcation of slope flow The slope flow lifted off the bottom on reaching the stably stratified lower part of the tank. Dye travelling along the interface was often seen to climb up and over steep waves which were not visible in the shadowgraph (see photo 8). A cloud of dye, Injected in the centre of the stratified region, did not move but slowly diffused below the sharp interface with the mixed layer (see photo 9). 48 Along the part of the slope about 30 cm away from the ends of the tank, there were no perceptible changes In the depth of the slope flow or In the flow velocity, as seen ln the dye or shadowgraph images. Since the volume of fluid ln the tank is constant, there must be a return flow above the bottom slope flow for continuity. This was already seen to exist from the deflection of the lines in the shadowgraph image. After dye in the slope flow reached the deep end of the tank, it was seen to rise and be carried in the opposite direction at much slower velocities and in a much less organized manner, while being diffused by convective eddy motions. The flow velocity in the mixed layer increases as the depth in this layer decreases toward the top of the slope. 3.4 Salinities and salinity profiles During the experiments, data were taken from thermistors and micro-cells to determine temperatures, salinities and densities of fluid in the tray and at various locations and depths in the mixed layer and in the slope flow (as described in section 2). Fluid was syphoned through the cells at a constant rate of about 1 ml/s (2 drops per second),and the calibration constants for the micro-cells were usually checked before an experiment. Due to the salt flux, the salinity in the mixed layer slowly increased in the time needed to take a series of data points. 'Quas1-instantaneous' salinity profiles were obtained by sub tracting the change in salinity at a fixed point in the mixed layer from actual profile data: 50 S(profile) = S(actual) - S(mixed) + S(tl) (3.1) in which S(actual) is the salinity calculated from the data at the profile depth, S(mixed) and S(tl) are the salinities in the mixed layer at the same time that the profile data were taken and at the time (tl) that the first profile point was taken. The adjustment was made either by pointwise subtracting the change in the computed mixed layer salinity, or by subtracting a 'smoothed' value for this change using the slope of a least squares linear fit through the mixed layer salinities for short periods of time (figure 3-3). A line through the time-adjusted profile points in the mixed layer then became vertical (figure 3-4) which indicates that the layer was well mixed (except for points near the underside of the tray where the salt enters the tank). Time-series plots of salinity data taken in the mixed layer indicate that for longer observation times a second order curve gives a better approximation for the change in the mixed layer salinity during an experiment (figure 3-5). The slope flow was seen in the profiles as a 7 to 17 mm thick layer where the salinity rose by 0.24 to 0.92 PSS above the value in the mixed layer. Appendix F gives a brief description of each slope flow experiment with computed results, time-series plots and prof i1es. Excessive noise in some of the data was caused by faulty micro-bead thermistors at the micro-cells, and in some cases salinities were re-calculated using the temperature from the good thermistor, offset by half the averaged difference. 51 X ime (min) Figure 3~3. Time-series and linear fit Figure 3-4. Actual and adjusted salinity profiles 53 Figure 3~5. MICRO-CELL TIME-SERIES SLOPE FLOW EXP#3 In a separate slope flow experiment, successive profile data were taken by raising the Intakes of all three micro-cells to the same height above the bottom, but located near the middle of the tank and 20 cm to either side (figure F-26). The use of the HP-3497A Datalogger System allowed more frequent sampling, andiaveraging of rapid multiple readings for each sensor. Time series data from this (figure 3-6) and experiment #8 (figure F-27) indicate that the rate of change of salinity with time was the same at different locations along the slope In both mixed layer and slope flow. A curve fit through time-series data from the mixed layer can thus be used to correct for the change in salinity during the time required to collect profile data. When many points were taken, a second order curve was used (figure F-28) to obtain 'quas1- 1nstantaneous' profiles (figures F-30 and F-31) for which the mixed layer salinities at the end would match those at the start. A small but persistent weakening in the salinity gradient was seen near bottom in salinity profiles from locations spaced 20 cm apart down the slope. As heavy fluid from the slope flow collected in the bottom, a wedge of fluid formed at the deep end in which few convective motions were seen to penetrate in the shadowgraph images. A profile taken at port #7 in experiment #7, when this wedge was about 3 cm thick (figure F-25), shows the stable stratification of fluid at the deep end of the tank. Salinity profiles from data taken in the edge between tank and tray (figure 2-12) also was stably stratified: the return flow, rising from the tank, brought up fluid of increasing salinity from the mixed layer. 55 12.6 -I-CD CD a.' >-cn 11.6 CO CM C3 10. 6 TIME-SERIES-OF MICRO-CELLS SPACED 20 CM APART intake of Cl in port #7 (deepest) C2 tn port. #5 (middle) C3 in port #3 (shallowest) intakes at equal height above botto m intakes raised to 20 mm (mixed layer) ""V start of slope flow reaches: . ^v//* j lis C3; / • J r? :Cl if:" 4mm above bottor F i qure 3-6. TIME: 300SEC/DIV Salinity rate of change in mixed layer and bottom flo w. A sequence of micro-cell data taken during experiment #1 near the bottom and 6 mm below the tray in successive sampling ports did not show enough detail to see a distinct distribution in the salinity along the slope or under the tray (figure F-5), but data taken during experiment #4 show a higher salinity over the upper part of the slope, and at the deep end (figure F-17). 3.5 Salt fluxes and flow velocities The time after start, the raw data from thermistors and micro-cells and the calculated values of temperatures, conductivity ratios, salinities and densities (sigma-t) for each set of observations were listed on the line printer. These salinities were plotted as a time-series during each experiment to monitor the overall behaviour of the system. The salt flux slowly decreased during each experiment as the influx of salt into the tank reduced the difference in salinity between tank and tray fluids. For the times in an experiment at which slope flow velocities were determined, the salt flux was calculated from the time-series data of salinity in the tray and in the mixed layer in the tank, as outlined in section 2.6. The calculated results were tabulated for each experiment and included with the time-series plots and salinity profiles in the description of the individual experiments in appendix F. Table 3.2 below lists the compiled values from the slope flow experiments of slope angle 6, time t after starting the experi ment, slope flow velocity maxima Vmax measured from photo or slide sequences or from video footage of injected dye, computed 57 salt fluxes for times at which the velocity was determined, slope flow depth h and rise in salinity dS above that in the mixed layer (from profiles), and computed entrainment without (El) and with (E2) bottom drag Cd (see section 3.6) where: Cd= 4.2e-2/(h.Vmax) El= h.g'sinG/V2 and E2 = El - Cd Table 3.2 Compiled results of slope flow experiments slope t Vmax saltflx flow Salinity dS drag Entrainment # 6 (min) (gr/cm2/s depth (PSS) Cd El E2 (cm/s) *e-5) (mm)  1 3. 3 25 0. 51 1 . 780 14-17 20. 54 0. 68 0. 053 0. 217 0. 163 30 0. 46 1 . 694 2 3. 8 55 0. 42 1 . 820 9-9.5 15. 69 0. 57 0. 108 0. 183 0. 075 I 25 0 . 34 1 . 080 9- 1 1 25 . 01 0. 40 0. 124 0. 2 1 1 0. 087 3 2. 2 60 0. 26 1 . 418 8.5-9 21 . 56 0. 86 0. 185 0. 393 0. 208 1 35 0. 23 0. 946 4 5 . •2 20 0. 47 0. 498 50 0. 47 0. 436 102 0. 40 0. 373 16 ' 12. 72 0. 25 0. 066 0. 209 0. 144 1 38 0. 35 0. 332 5 5 . 2 71 0. 57 0. 310 11-13 15. 84 0. 26 0. 061 0. 080 0. 019 200 0. 28 0. 167 26 1 0. 28 0. 1 55 7-8 26. 41 0. 24 0. 200 0. 19 1 -0. 009 282 o. 26 0. 15 1 6 2. 3 1 38 0. 1 2 0. 0897 1 45 0. 1 2 0. 0796 216 0. 10 0. 0673 7 5 . 5 134 0. 10 0. 077 8-9.4 16 . 87 0. 24 0. 483 1. 844 1 . 36 1 8 5 . 1 13-17 13. 10 0. 34 58 The tabulated velocities have been plotted against both the corresponding angles and salt fluxes to check the dependence of the slope flow velocities on the magnitude of the salt fluxes (figure 3-7) and on the bottom slope angles (figure 3-8). Ver tical bars were used in the plots to indicate the range in the measured velocities. The relation between velocity and slope angle is not distinct for the range of angles used in the expe riments, but the relation describing the visible rise in slope flow velocity at increasing salt fluxes is further explored in the next section. The slope flow depths, estimated from the salinity profiles, ranged from 7 to 17 mm. There was no sharp interface between the flow and the convectively mixed layer: in the most detailed profiles the upper part of the bottom flow, where shear and penetrative convection dominate, shows a weak density gradient. The lower part of the slope flow is strongly stratified and dye 'tongues' associated with velocity maxima are carried along with little dispersion. The level of turbulence here is greatly reduced from that in the upper part of the slope flow and in the mixed region, where dye is more rapidly diffused. 59 CM in m co O CM a-8 3-rrr CM tn OJ in C3-Q OJ OJ in Q Q CM OJ OJ CM GTO 0 i—I a cn ai c 0 ai o Cu 0 0 •—I »—« V > £ c O •rt -P -P 0 o 01 _£> CP c 01 0 L L a 01 , a L L a ai -£> a E L 0 C _Q in i ai * OJ in i ai 4c OJ in 0—rrP OJ1-1^ in co OJ in in" CM IT) CD • 60 0. 70-0. 35H CO \ E 0 -P •|HJ 0 o I—I > 0. 00 + 0 numbers are salt fluxes (*e~5) bars indicate range in velocities 16. 94 17. 80 $18. 20 10. 80 14. 18 9. 46 1.95 1.63 T 12. 67 21.89 18. 72 * 15.59 $ 13. 64 1.71 T T gure 3-8. FI ow veloci vs. 4 6 Slope angle (degrees) slope angle 3.6 Interpretation Density currents and penetrative convection have been studied separately in geophysical fluid flows and in the laboratory by many researchers. In this series of laboratory experiments the two mechanisms are simultaneously involved: the surface salt flux induces a slope flow, which is driven by the component of (reduced) gravity along the slope. The flow is slowed down by friction at the bottom and by shear at the interface which is modified by convective turbulence in the overlying environment. The flow reaches a steady state when the gravitational force is balanced by the friction at the bottom and at the interface: h.g'sinG = (t i +tw) Ds K. V3 in which g' is the reduced gravity: g'= g.Ds-Do Dre f (3.1) (3.2) h = depth of the flow Ds= density in slope flow Do= density of environment g = gravity acceleration 9 = slope angle ti= friction at interface tw= friction at bottom K = drag factor V = averaged flow speed Ve= entrainment velocity 7 ->v Ve \ h w " / vmax ' n- e Figure 3-9. Slope flow diagram 62 Conventional turbulent density plumes have been characterized by an overall Richardson number Ri (Kantha, 1975) which is the inverse of the square of the densimetric Froude number Fr (Bo Pedersen, 1980) : Ri = 1 = h.q'cosG (3.3) Fr2 V2 Such gravity currents grow in depth with distance downstream as fluid from a quiescent environment is 'entrained* into the turbulent flow. This inflow is characterized by an entrainment velocity Ve. The linear spread with distance of free plumes led to the assumption by Morton, Taylor and Turner (1956) that Ve is proportional to the mean flow velocity V. The ratio (Ve/V) is the entrainment factor E. Gravity currents attain a constant mean velocity V and spread linearly with distance along the slope. Ellison and Turner (1959) modified the assumption for gravity currents to include a Richardson dependence of the en trainment factor, and described gravity driven turbulent slope currents in terms of variables integrated over the depth of the flow, specified by flow depth h and mean velocity V which are only dependent on downslope distance x and by the buoyancy flux A= h.V.g'. No assumptions were made about the distribution of properties in a cross section of the flow. The conservation equations could then be reduced to: mass _d(h.V) = E.V (3.4) dx momentum _d(h.V2) = h.g'sinG - Cd.V2 (3.5) dx buoyancy _d(h.V.g') = -h.V.N2(x) (3.6) dx 63 in which Cd is the coefficient of bottom friction (drag), N = (-_g_. d@)1/2 is the local buoyancy frequency and @o dz @o is the reference density. In these derivations it was assumed that the Reynolds numbers were high enough that any molecular effects could be ignored. The density differences were considered small enough to neglect inertia terms in the equations of motion (Boussinesq approxima tion), in which case the entrainment factor (E) only depends on the Richardson number. Algebraic manipulation of equation 3.5 and substitution of eqations 3.4 and 3.3 yields: _d(h.V2) = V._d(h.V) + h.V.dV = E.V2 = h.g'sinG - Cd.V2 dx dx dx or: E = h.g's in9 - Cd = Ri.tanG - Cd (3.7) V2 For slope currents dominated by turbulent entrainment at the interface, the bottom friction can be ignored and equation 3.7 is reduced to a simple relation: E(Ri)= Ri.tanG (3.8) In the present experiments with low levels of turbulence in the lower part of the observed flows, the bottom friction was estimated from: Tw = ji.dU = Cd.@.U2 (3.9) dy in which y/& = *? is the kinematic viscosity, about 1.4e-2 cm2/s and a first order approximation for dU/dy is the ratio of Vmax to height y of the maximum velocity above the bottom (about 1/3 of the flow depth, based on shadowgraph and dye observations), and thus: Cd = v. 1 = 4. 2e-2 (3.10) y.V h.V 64 The depth averaged velocity V, used in the computation of the entrainment factors, was estimated from velocity profiles for slope flows shown by LOfquist (I960): V = Vmax/1.12 (3.11) Field and laboratory data compiled by Bo Pedersen (1980) from the literature and from his own work indicate that the entrain ment factor for sub-critical flows can be approximated by: E = Ve/V = 0.072 sin9 (3.12) The predicted values for entrainment in a quiescent environment from equation 3.12 would range from 2.76e-3 to 6.9e-3 for slope angles between 2.2° and 5.5° used in the present experiments. The entrainment factors calculated from data of the slope flow experiments using equations 3.7 and 3.10 above (table 3.2) were 0.08 to 1.84 without bottom friction (El). While including the bottom friction (Cd) reduced these values (E2), in nearly every case the computed entrainment factor exceeded that predicted for the quiescent environment by up to two orders of magnitude. The formulation which describes gravity flows was used here to compare entrainment factors between flows in turbulent and in quiescent environments. The large values for calculated entrainment would indicate that the bottom flows would rapidly loose their density difference. This contradicts the present experimental findings as well as Arctic field data which show that such slope flows maintain their characteristics over great distances, and suggests that a different model is required to account for the interaction between the turbulence and shear. 65 The intensity of turbulent motions seen in the shadowgraph image appears much higher In the mixed layer than in the bottom slope, which could lead to net entrainment of mass and momentum upward out of the flow. The Richardson numbers calculated from data in table 3.2 using equation 3.3 range from 2.10 to 19.5 and would cause considerable damping of the turbulence at the i nterface. In a two-layer system, the velocity and density profiles are idealized by a discrete step at the Interface between the slope flow and the environment. In profiles from experimental data the density changed slowly with the depth in the slope flow and the velocity profile extended upward Into the mixed layer fluid since some of It is strained along by the friction. With the Instrumentation developed for these experiments more details of the growth or decay of such slope currents might be obtained if a longer slope was used. The change in the shape of salinity profiles taken at different locations along the slope shows the distribution of mass within the slope flow, and can be used to assess the down-slope change in mass when Integrated over the depth. 66 4 - SUMMARY AND CONCLUSIONS In a series of laboratory experiments, the salt flux due to the freezing of sea water was simulated by a percolation of sea water through a porous membrane into a plexiglass tank below. A two-dimensional bottom slope flow was Induced by the convection when the bottom of the tank was set at a small angle. Low values of salt fluxes, controlled by selected starting conditions, were calibrated from density differences across the membrane. In several interface entrainment experiments with two-layer and linear stratifications, this system confirmed that the constant entrainment efficiency for free penetrative convection as predicted by Bo Pedersen could be extended for these low salt fluxes. The interface entrainment assumptions were applied to a set of Arctic field data. The small values of computed entrainment did not agree closely with the predicted values, which may be due in part to salt advected into the bay by the reverse estua rine circulation caused by slope flow in the perimeter regions. Shadowgraph images of the fluid in the experimental tank did show patterns of convective motions in the mixed layer, which were carried along and smoothed out by a bottom slope flow. A weaker flow in the opposite direction was seen superimposed on the convective pattern. Velocity maxima in the slope flow of 0.09 to 0.66 cm/s were measured from the progress of tongue 67 features in injected dye, recorded in sequences of color slides and photographs and on videotape footage. Salinity profiles of fluid in the mixed layer and in the slope flow were plotted from data obtained from thermistors and from conductivity micro-cells developed for this purpose. These micro-cells have a resolution in calculated salinity of better than 0.05 ppt, require about 4 ml to flush and maintained stable readings over extended periods of use. The salinity profiles show a region well mixed by convective turbulence, and a rise in salinity in the slope flow of 0.24 to 0.92 ppt above the mixed layer value, for flow depths of 7 to 17 mm and calculated salt fluxes between 1.82e-5 and 1.63e-6 g/cm2/s. The spatial resolution achieved with the micro-cells allows a more detailed look at the density distribution within a slope flow, and with a longer slope it may be possible to model the down-slope behaviour of these bottom currents. The depth of the slope flow, the density difference between the flow and the mixed layer determined from the profiles, and the velocity maxima measured in the flow, were applied to the model for predicting entrainment of fluid from a quiescent environment by a turbulent gravity current. Entrainment factors computed by inserting data from the slope flow experiments were several orders of magnitude larger than the predicted values for the quiescent environment. 68 The conclusions from these experiments are: - Low calibrated salt fluxes to simulate salt expulsion due to freezing were achieved by percolating sea water through a porous membrane. The magnitude was controlled by selec ting starting depths and density differences. - Entrainment experiments across a density interface without shear confirmed that the constant entrainment efficiency predicted by Bo Pedersen applied to these low salt fluxes. - A surface salt flux over a sloping bottom always produced a slope flow. - Maxima in the slope flow velocity show an increase for higher salt fluxes (figure 3-5), but for bottom slopes of 2.2° to 5.5° in the experiments, there was no distinct re lation between flow velocity and slope angle (figure 3-6). - High resolution salinity profiles were obtained from data from small-volume conductivity micro-cells, developed for these experiments and used with micro-bead thermistors. - Entrainment factors calculated by inserting data from the slope flow experiments into a model for turbulent gravity flows were several orders of magnitude larger than those predicted for a quiescent environment, contrary to visual evidence from the experiments or from Arctic field data, which show that such flows under a turbulent environment maintain their characteristics over great distances. This suggests that a different model is required to describe the interaction between the slope flow and the turbulent env ironment. 69 BIBLIOGRAPHY Benjamin, T.B. 1968. Gravity currents and related phenomena. J.Fluid Mech. 31, 209-248 Bo Pedersen, F. 1980. A monograph on turbulent entrainment and friction in two-layer stratified flow. Paper 25, Inst.of Hydrodyn., Techn. Univ.of Denmark, 397 pp. Bo Pedersen, F. and C. Jurgensen, 1984. Laboratory experiments on entrainment due to free convection. Prog.Rep.61 Inst.of Hydrodyn., Techn.Univ.of Denmark, pp.47-54 Deardorff J.W., G.E. Willis and D.K. Lilly, 1969. Laboratory investigation of non-steady penetrative convection J.Fluid Mech. 35, 7-31 Deardorff J.W. 1980. Progress in understanding entrainment at the top of a mixed layer. Am.Meteorol.Soc. 1978 Workshop on the Planetary Boundary Layer, pp.33-66 Deardorff J.W,, G.E. Willis and B.H. Stockton 1980. Laboratory studies of the entrainment zone of a convectively mixed layer. J.Fluid Mech. 100, 41-64 Elliott, J.A. 1972. Convective motions under sea ice. Frozen Seas Research Group, Inst.of Ocean Sci. Sidney, B.C. Unpublished, 17 pp. Ellison, T.H. and Turner, J.S. 1959. Turbulent entrainment ln stratified flows. J.Fluid Mech. 6, 423-448 Fofonoff, N.P. and R.C. Millard Jr., 1983. Algorithms for com putation of fundamental properties of seawater. Unesco Techn. Papers in Marine Sci. 44, 53 pp. Foster, T.D. 1969. Experiments on haline convection induced by the freezing of seawater. J.Geop.Res. 74,6967-6974 Gade, H.G., R.A. Lake, E.L. Lewis and E.R. Walker, 1974 Oceanography of an Arctic Bay. Deep-Sea Res. 21, 547-571 70 Heidt, F.D. 1977. The growth of the mixed layer in a stratified fluid due to penetrative convection. Bdy.Layer Met. 12, 439-461 Kato, H. and O.M. Phillips, 1969. On the penetration of a turbulent layer into a stratified fluid. J.Fluid Mech. 37, 643-655 Kantha L.H. 1975. Turbulent entrainment at the density interface of a two-layer stably stratified fluid system. Techn.Report 75-1, Johns Hopkins Univ. 162pp. Kullenberg, G. 1977. Entrainment velocity In natural stratified shear flow. Estu.& Coast.Mar.Sci. 5, 329-338 Lake, R.A. and E.L. Lewis 1970. Salt rejection by sea ice during growth. J.Geophys.Res. 75, 583-597 Linden, P.F. 1975. The deepening of a mixed layer in a stratified fluid. J.Fluid Mech. 71, 385-405 LOfquist, K. 1960. Flow and stress near an interface between stratified liquids. Phys.of Fluids 3, 158-175 Long, R.R. 1975. The influence of shear on mixing across density interfaces. J.Fluid Mech. 70, 305-329 Meagher, T.B. A.M. Pederson and M.C. Gregg, 1982. A low-noise conductivity micro-structure Instrument. IEEE J.of Ocean.Eng, pp.283-290 Melling, H. and. E.L. Lewis 1982. Shelf drainage flows in the Beaufort Sea and their effect on the Arctic Ocean pycnocline. Deep-Sea Res. 29, 967-985 Millero, F.J., C.T. Chen, A. Bradshaw and K.Schleicher, 1980. A new high-pressure equation of state for seawater, Deep-Sea Res. 27A, 255-264 Moore, M.J. and R.R. Long 1971. An experimental Investigation of turbulent stratified shearing flow. J.Fluid Mech. 49, 635-655 71 Mowbray, D.E, 1967, The use of schlleren and shadowgraph tech niques ln the study of flow patterns in density stratified fluids. J.Fluid Mech. 27, 595-608 Perkin, R.G. and E.L. Lewis 1978. Mixing in an Arctic Fjord, J.Phys.Ocean. 8, 873-880 Perkin, R.G. and E.L. Lewis 1978. Salinity: Its definition and calculation. J.Geop.Res. 83, 466-478 Perkin, R.G. and E.L. Lewis 1980. The Practical Salinity Scale 1978:Fitting the Data. IEEE J.of Oceanic Eng. OE-5, 9-16 Phillips, O.M. 1972. T':>o entrainment interface J.Flu id Mech. 51, 97- 1 18 Thorpe, S.A. 1973. Turbulence. In stratified fluids: a review of laboratory experiments. Bdy.Layer Met. 4, 95-119 Turner, J.S. 1968. The influence of molecular diffusivity on turbulent entrainment across a density interface. J.Fluid Mech. 33, 639-656 Turner, J.S. 1973. "Buoyancy effects in fluids" Cambridge University Press, 367 pp. Turner, J.S. 1980. "Small scale mixing. In "Evolution of Physical Oceanography", edited by B.A. Warren & C. Wunsch, MIT Press, Cambridge, pp.236-262 Walin, G. 1971. Contained non-homogeneous flow under gravity or how to stratify a fluid in the lab. J.Fluid Mech. 48, 647-672 Wyatt, L.R. 1978. The entrainment interface in a stratified fluid. J.Fluid Mech. 86, 293-311 72 SALINITY AND DENSITY COMPUTATION APPKNDIX A 73 APPENDIX A SALINITY AND DENSITY CALCULATION A.l Sal in i ty The salinity of fluids used in the convection experiments is calculated from electrical conductivity, pressure and tempera ture using a standard set of polynomials known as the Practical Salinity Scale (Lewis and Perkin, 1980). If R is the conductivity ratio of the fluid (i.e. the ratio of the conductance at temperature T and pressure P to that at atmospheric pressure and 15 °C) then the salinity S in units of the Practical Salinity Scale is calculated from: Q = 1+P(A1+P(A2+P*A3))/(1+T(B1+T*B2)+R(B3+T*B4)) U = C0+T(C1+T(C2+T(C3+T*C4))) W = R/(Q*U) Y =W"2 F=(T-15)/(1+.0162(T-15)) S=E0+F*F0+Y(E1+F*F1+Y(E2+F*F2+Y(E3+F*F3+Y(E4+F*F4+Y(E5+F*F5))))) in which P is the pressure in bars, T the temperature in °C, S is the salinity in PSS (units are close to the formerly used grams/ki1ogram or parts-per-thousand), Q, U, W, Y, F are inter mediate results, and Ai through Fi are constants with values: Al=2.070e-5 C0=0.6766097 E0=0.0080 F0=0.0005 A2=0.637e-9 C1=0.0200564 El=-0.1692 Fl=-0.0056 A3 = 3.989e-15 C2=1. 104259e-4 E2 = 25.3851 F2 = -0.0066 B1=0.03426 C3=-6.9698e-7 E3=14.0941 F3=-0.0375 B2=4.464e-4 C4=1.0031e-9 E4=-7.0261 F4=0.0636 B3=0.4215 E5=2.7081 F5=-0.0144 B4=-0.003107 74 For laboratory experiments these calculations are simplified since P=0 at atmospheric pressure. These polynomials are defined for a range of salinities from 2 to 42 parts-per-thousand. Although PSS units are not defined outside this range, a graph of the conductivity ratio over an extended range of salinity and for laboratory temperatures from 17 to 25 °C shows that these polynomials smoothly extend to higher values of S (see figure A-1). To create higher salt fluxes, pure sea salt was added to sea water. Salinity values of this fluid, obtained with an optical refractometer, from the Guildline Autosal after a 2-to-l volume dilution and doubling the result, and from the output of the calibrated micro-cell were found to agree within several ppt, indicating that values computed from the above formulas for the Practical Salinity Scale may be used with caution as reasonable est i mates. 75 A.2 Density The Unesco Equation of State for sea water (Millero, 1980) is used to calculate fluid densities D in g/cm3 or in units of sigma-t =(D-1)*1000 from salinity S (PSS), temperature T (°C) and pressure P (bars) from the following set of polynomials: A= 8.50935e-5+T(-6.1 2293e-6 + T*5.2787e-8) B= 3.2399Q3-rTC 1 . 437 1 3e-3i-T( 1 . 1 6092e-4-T *5 . 779G5e-7 ) ) C=1965 2.21+T<148.4206+T(-2.327105+T(1.360477e-2-T*5.155 288e-5))) E= A+S(-9.9348e-7+T(2.0816e-8+T*9.1697e-10)) F= B+S(2.2838e-3+T(-l.0981e-5-T*l . 6078e-6 ) ) +S3/2* 1 .9 1075e-4 G= C+S(54.6746+T(-0.603459+T(0.0109987-T*6.167e-5) ) ) H= G + S3,2(0.079 44 + T(0.016483-T*5 . 3009e-4) ) +P(F+P*E) J=999.8 42594+T(0.0679 395 2+T(-9.09*29e-3+T*1.001685e-4)) K= J + T«(-l . 1 20083e-6+T*6.536332e-9) L=0.8 2 449 3+T(-4.0899e-3+T(7.6 438e-5+T(-8.2 467e-7+T*5.3875e-9)) ) M=-5.7 2 466e-3+T(1.02 27e-4-T*l.65 46e-6) N= J+S*K+S:"2*M+S2*4.8314e-4 D= N/1000/(1-P/H) = density in gr/cm3 Similar to the polynomials of the Practical Salinity Scale, these are valid for salinities ranging from 0 to 42 PSS. They also simplify since P=0 for laboratory (atmospheric pressure). The relation between salinity and density, plotted from the above polynomials, is nearly linear over the extended range of salinities for the temperatures used in laboratory experiments (see figure A-2). Densities so determined were used to compute estimates of the membrane salt flux during the experiments. 76 Figure A-l. CONDUCTIVITY RATIO vs SALINITY for laboratory temperatures T-25 22 21 20 Salini ty 0 15 30 45 E0 75 Salini ty CONDUCTIVITY MICRO-CELLS APPENDIX B 79 APPENDIX B MICRO-CELLS A set of small volume four-electrode conductivity cells was developed to determine the salinity of fluid In an experimental tank. As fluid is syphoned through one of these micro-cells, at a flow rate of about 2 drops/sec (0.15 ml/s), the electrical conductance inside the cell changes with the salinity of the fluid. A small electronic circuit converts this conductance into an output voltage, which was calibrated to yield the conductivity ratio of the fluid. Thermistors were added at the inlet and outlet of the micro-cell, and the salinity of fluid in the micro-cell is calculated from the conductivity ratio and the average temperature of the thermistors, using the polynomials of the Practical Salinity Scale (see appendix A.l). The fluid density at the intake point in the tank is computed from this salinity and the temperature from another thermistor located in the tank, using the Unesco Equation of State for Sea Water (appendix A.2). B.l Cell construction The micro-cells, constructed by technical support staff at the Institute of Ocean Sciences, consist of four ring-shaped electrodes made of 0.002" thick platinum foil and separated by segments of 1.8 mm l.D. glass tubing of 0.6 mm wall thickness. Figure B-1 shows a diagram of the cell with the principal d i mens 1ons. 80 GLASS TUBING SECTIONS 1 .8mm I.D. - 3mm O.D, COLOR CODED LEADS FROM ELECTRODES 0.002" PLATINUM FOIL ELECTRODES, EACH 5mm WIDE PVC TUBING COVER Figure B-l. Diagram of micro-cell assembly The electrodes and glass spacers were held in place by sections of heat shrink tubing, and color coded electrical leads were soldered to the electrodes. The completed assembly was sealed with epoxy in a protective PVC sleeve. Three such micro-cells were made, using the same materials and physical dimensions. B.2 Micro-cell electronics The four electrodes of the micro-cell were connected to an electronic circuit which converts the conductance (1/R) of the microcell into a linear function of the output voltage (VC). Fluid samples of a known salinity, determined with a Guild-line Autosal bench salinometer, were used to obtain values for micro-cells calibration constants K, expressed in ohms of cell resistance at a salinity of 35 ppt and a temperature of 15 °C. 8 1 The conductivity ratio (RR) obtained from the micro-cell is the product of conductance and cell constant: 1/R = = A + B.VC 1/R = = cell conductance VC = = output voltage RR = = K.(A + B.VC) RR = = conductivity ratio K = cell constant and coe f f lc ients: A = -2.6008e-8 B = -4.5954e-4 The coefficients A and B were determined with a high precision decade resistor box, and checked after about 6 months of use. There was no drift or temperature dependence found in the output voltage of the circuit. A least squares linear fit to the data was used to calculate A and B. The standard deviation was 2.2065e-4 with a correlation factor better than 0.9999 . B.3 AM/CT Datalogger conductivity electronics The AM/CT Datalogger had a slightly different conductivity circuit. It was originally designed for cells with a constant of about 100 ohms but was modified for use with the micro-cells which have a much higher cell constant of about 1800 ohms. The relation between N-number and conductivity ratio is given by: RR = K'.(A + B.NC) with NC = AM/CT datalogger output K'= cell constant and coefficients: A = 5.53084e-5 B = 1 .3290e-7 82 A number of trial runs were done to determine the stability and variability of measurements at several constant salinities. In several of the tests, the variability of the raw temperature data was less than + 2 in the last digit (+0.007 °C>, and for raw conductivity about + 3 units (corresponding to +0.025 PSS). As a larger range of conductivities was used with the three micro-cells, the variability in the output of the datalogger conductivity circuit Increased. Several series of observations were taken over longer periods of time, using three micro-cells simultaneously. Deviations in the observations could be caused by sudden variations in the flow rate caused by small particles obstructing the flow. Filtering all fluids did not eliminate the problem. Small bubbles adhering to a micro-cell electrode could change the conductance in the cell. The tests did show that any abrupt change In the flow causes an immediate change in the computed salinity which in about 5 to 20 seconds returns to the previous level. The computed value of salinity and the variability did not depend on the magnitude of the flow through the micro-cells. The use of a peristaltic pump to draw the fluid through the cells more than doubles the variability, possibly due to shocks which cause small particles or bubbles to disrupt the potential or the current pattern ins ide the ce11 . B.4 Determination of calibration constants The micro-cells were calibrated by using fluid samples of known salinity. Cell constants were then chosen which yield a calculated salinity equal to that determined with a Guildline 83 Autosal bench salinometer. The fluid was syphoned through each micro-cell at several different steady flow rates counted to be between 1 and 4 drops per second (about 0.05 to 0.20 ml/s). An Integer value was chosen for K to make the calculated 3 agree with the value determined using the Autosal. These calibrations were repeated at several temperatures and salinities. The values of K were plotted against ^temperature at which they were calculated to check for temperature dependence (figure B-2). Shifts In conductivity were found to occur when the cell outlet tubing made electrical contact with the fluid which was pumped back to the tank instead of dripping to break the flow. An external current loop formed via the pump or one of the other cells and caused a change in apparent conductivity and thus in the cell constant. For cell #2, the data without an external loop had an average value for K of 1765 with a stan dard deviation of 1.89 , which changes the calculated salinity by 0.024 at a salinity of 20 PSS and a temperature of 20 °C. Initially, the current electrodes were those closest to the centre of the cell, but exchanging the leads of potential and current electrodes reduced the variability in the calculated salinity from the Datalogger to nearly half the initial value. This exchange of electrodes changed the effective potential path inside the cell and caused a small change in the values of cell constants. 84 MICRO-CELL CALIBRATION , CELL#2 T = TEMP <°C> 21.0 1790 _J 22.0 I 23.0 1 jM.0 1770 J x x X X x x XXx *x x x< oell outlet drip©, no external loop 1750 J 1730 J 1710 x X X oell outlet immereed, external eleo. loop x x 1590 iqure B-2. Micro-cell constants vs. temp. 85 Cells have been reported t© 'age' In successive cycles of wetting and drying. This may alter the surface characteristics of the electrodes of the new cells, and cause some shift in K. No significant change was found in the constant of the first cell in more than a year. The conductance in the cell is strongly affected by minute particles or bubbles due to the small size of the cell. In some instances, using a well mixed fluid of constant salinity, the time-series plot of calculated values of S from the Datalogger output did show a drift down in salinity, followed by a jump back to the former constant value. This apparent drop in salinity could be caused by a decreasing contact surface at an electrode due to trapped and coalescing bubbles. Occasional light tapping on the cell may dislodge any particle or bubble trapped in the cell and restore the correct calibration value. The AM/CT datalogger conductivity circuit used different current and voltage values for the cell electrodes, resulting in values for the cell constants K which differ significantly from those obtained with the small electronic circuits as was explained previously. Calibration checks were frequently done for both systems to track the long term behaviour of the micro-cells. Print-outs of each date are Included In this appendix and the averaged value of calibration constants for each cell are shown in table B.l below. Each calibration constant listed below is an average of 4 to 8 observations. 86 Table B.l Micro-cell calibration constants Day Date Sal Temp. dataloqqer small ' e 1 ectr. # (PSS) (°C) KI K2 K3 KI K2 K3 1 1 85-12 -1 1 31 . 15 22.0 1879 1787 1815 1799 1749 1783 1 1 12- 1 1 1878 1789 18 15 12 12- 12 31 . 34 21.7 1882 1791 18 16 1801 1753 1786 13 12- 13 31 . 50 21.8 1885 1792 1818 1802 1753 1787 13 12- 1 3 31 . 34 21.8 1876 1784 1811 1796 1746 1779 20 12- 20 7 . 83 21.1 1886 1790 1823 28 12- 28 7. 52 20. 7 1891 1802 1831 34 86-1- 3 2. 74 19. 1 1897 1796 1826 34 1 -3 4. 83 19.2 1897 1793 ( 1837) 34 1-3 30. 3 20.5 1888 1796 1826 37 1-6 4. 97 20.5 1885 (1818) 1832 5 1 1 -20 5 . 95 21.0 1878 1794 1832 53 1-22 31 . 5 21.0 1808 1754 (1738) 53 1 -22 6. 10 20.5 (1771)(1717)(1755) 54 1-23 6. 1 1 2 1.1 (1709) 1748 (1763) 55 1-24 33. 66 20.0 (1816 1758 1793 55 1-24 6 . 59 20.0 (1767) ( 171 1 )( 1753) 62 1-31 20. 56 21.6 1884 1795 1822 1799 1750 1785 66 2- 4 22. 60 20.9 1801 1748 1787 8 1 2- 19 25. 85 21.1 1884 1792 1816 1803 1752 1786 8 1 2- 19 25. 94 21.3 1798 1752 1782 86 2- 24 27. 40 21.3 1802 1751 1786 89 2- 27 35. 56 21.6 (1811) 1758 1790 99 3-9 28 . 02 2 1.9 1877 1792 18 14 1800 1751 1782 106 3- 16 28 . 36 21.4 (1845)(1774) — — 1785 143 4-22 31 . 60 21.3 1888 1798 18 25 159 5- 8 16 . 40 20. 4 1892 1795 1817 165 5- 14 28 . 49 19.6 1884 1793 1818 196 6-27 26 . 83 21.3 1885 1795 1821 1803 17 46 1782 Average eel 1 constants: 1885 1793 1821 1801 1752 1785 w i th standard de v i at i on: 6.34 4.20 6.70 5.64 3. 50 6.63 The constants in brackets differed substantially from the expected value and were not Included in determining the average values and standard deviations. Some of these differences could be caused by contamination of the electrodes Inside a cell by particles or bubbles. A time-series plot of the cell constant values (figure B-3) shows that any drift Is much less than the 87 variability In the observations. The conductivity may affect the field distribution and current path In the cell and thus alter the cell constant. Some dependence is seen in a plot of cell constant versus salinity during calibration (figure B-4). 88 1900 -l 17 CO (0 -p c 0 -p (0 c o 0 01 G • Q 1800 - X X — I. Xa X Q X Qa Q Qy—_a-X Ax a x Xv X-X-X I X 0 o • X OG11#1 cell#2 cel103 1700 —r 90 T r 120 i r 150 T T 1 180 0 30 60 days after 85-12-1 Figure B~3 Time-series of micro-cell calibration constants Salinity (PSS) Figure E>-4\Cell calibration constants vs. Salinity B.5 Micro-cell time response The response of the cell to an abrupt change in salinity has been investigated to determine the volume required (or the time required at a selected flow rate) before the calculated salini ty reaches the new value. After a step-change in the salinity at the intake point, the length of time for the cell to respond depends on the flushing characteristics of the cell. In initial attempts to determine the time response of the micro-cell with the AM/CT datalogger, the minimum sampling was about 4 seconds and the output showed excessive variability caused by problems with the A/D converter of the conductivity circuit. To get more accurate data and faster sampling, an HP-3497A Data Acquisition System was used. The arrangement is shown in figure B-5. •T-TOP CELL OUTLET SYPHON TUBE MICRO-CELL ELECTRONICS T-BOTTOM VALVE JAR S-l -PAIL •CH9 -HP-7225A PLOTTER HP-9825 COMPUTER HP-3497A DATA ACQUISITION SYSTEM Figure B-5. Time Response - Experimental Arrangement The intake of the micro-cell was connected to a valve which could switch the flow from a jar of one salinity 91 to a pall of another. The jar was floated ln the larger pall to minimize temperature differences and to get a nearly constant drop in height between the fluid levels and the cell outlet. The gravity-driven flow through the cell did remain nearly constant when switching between salinities. Actual flow rates during each run were measured by counting the number of drops over time at the outlet for different settings. These ranged from about 0.5 to 4 drops per second. Counting showed about 825 drops in 50 ml. Each cell was connected to a micro-cell conductivity circuit and continuously powered during a run, which avoids transients caused by switching. The output of this circuit and of the micro-cell thermistors were then connected to the HP-Datalogger System, which was controlled by an HP-9825 computer. A program for this system was modified to use the average temperature from both thermistors for calculating the salinity and to store the calculated values on tape. The computed salinities were plotted during each run and the observed flow rates were marked on the plots in number of drops counted per stopwatch seconds. At low flows, the difference ln fluid levels of pail and jar resulted in a change in flow when switching between salinities. Flow rates were counted and marked for both heights. The time to adjust to this change is unknown but believed to have a negligible effect on the response time. From the first time-series at constant salinity it was found that the overall variability of this system was about 0.01 S. 92 The next series of runs was done to look at the characteristics of the response for a range of salinity values and at flowrates used in experiments. The output of these runs consists of plots of calculated salinity for each of the three cells at different but steady flow rates from 0.5 to 4 drops per second, and for steps of 0.5 to 4.0 S in the salinity. These time-series plots are included in this appendix. The typical shape of the response curves consist of: a nearly horizontal part after switching the intake, a steep linear section of rapid change In salinity an exponential tail approaching the final salinity The time required after a switch in salinity at the intake, for the calculated salinity to reach 90% or 95% of the final value, was graphically determined from this first set of plots: On these plots, the time at which the intake was switched was marked as tO and the start of rapid change as tc; t90 and t95 were the times at which the calculated value had changed by 90% or 95% of the step in salinity. The rapid change starting at t=tc appears linear over part of the change, except at flows of less than about 1 drop per 2 seconds (.03 ml/sec). This is fol lowed by a curve as the calculated value approaches the final salinity. Distances measured along the time axis were converted to volume by multiplying with the flow rate. For obtaining density profiles in the tank a reasonable flow rate is needed to take successive readings at different depths within the time in which larger patterns In the convection tatik change. A steady slow flow through the micro-cell minimizes the disturbance at the intake point. The length of time before the rapid change (tO-tc) depends on the length and diameter of the tube through which the fluid moves before reaching the cell and on the flow rate. The volume of fluid entering the cell in time (tO-tc) should be constant for steady flow, but the flow is briefly Interrupted while switching salinity at the Intake. The starting point and flow rate are approximate which explains the range in initial volume from 0.28 to 0.66 ml. The plotted data show that for a change to 95% of the final value takes 30 to 90 seconds and between 2 and 7 ml of fluid. The shape of the response curve changes with the flow rate. In a next set of runs the calculated temperatures, conductivity ratios and salinities were recorded. The time-series plots show a series of calculated salinity curves at different flow rates. These have been normalized for salinity change and each section has been replotted in terms of volume required from the time of a switch in salinity. A plot of normalized salinity change vs. volume (text fig. 2-5) shows that the response curves collapse Into a single curve at higher flow rates. The flow rate and the start and end time for each segment are also marked on the plots. Several time-series of computed salinities, temperatures and conductivity ratios were plotted at the same time-scale to check their relative effect. At the higher flow rates (40/15 dr/s or 0.16 ml/s) It takes 2 to 3 ml of fluid for a change of 90% to 95% of the new value over respectively 12 to 19 seconds. To get a density profile of 94 fluid in the experimental tank, the flow rate is set by adjus ting the drop in height between the fluid level in the tank and the cell outlet. If the Datalogger multiplexer cycle is started 20 seconds after the intake is moved to the next height, then the calculated salinity <Sc) will be close to 95% of the change in salinity or, assuming Si < S2: Sc=Sl + 0.95CS2-S1) which yields: S2 = (Sc - .05SD/.95 For continuous monitoring of the salinity in the tray or in the mixed layer below it at a fixed point, a much slower flow rate can be used since the average changes over time are much smaller and slower than those observed in the test profiles. 95 96 , SALINITY (PSS) iFO I 0.100/DIV 2B 500 29 r00 —I 1 1 HH 1 1 1 1 1 1 1 1 1 1 1 1 1 ,—— CD c i fD CO 1 CD 3 fD fD Salinity (PSS) o m 0 ;. ro 0 • .1 I 0 < fD co ca ro -J ( •-+> n> / cT ® '•• * ^3 a, 0 w cn 4> • ca ca 0- D_ \ \ 1— • >—• : ui cn V © 03 (D ft) 0 0 (0 ID O a. L6 SALINITY (PSS) &RL* I 0.100/DIV f-rH 1 CD. C "5 fD 00 ! O "5 0 I O fD M-3 fD CO TJ 0 (0 fD 2D. m 29.SB0 H 1 o m ro ro cn i *—* i 00 cn OJ o cn ra D_ T ro co o E3 CO m n *^ CJ 0 0 OJ a>' co © cn -~i —• OJ \ V. L f. -si- %r GO o 00 LO CD I C3 «—i I LO ro LU 0) CO c o Q_ CO CU L CU e CU O I 0 L 0 •I-I CO I CD CU L D Ul my EI H h rx. UJ cr>-> 1 1 1 1 1 h^-H h—I f— 005"BZ Aia/001-0 i ring (SSd) A1INI1VS 98 Fiaure B-9. MICRO-CELL TIME RESPONSE CELL01 25-10/0.4 Figure B-10. MICRO-CELL TIME RESPONSE CELL#2 25-10-85/1. 1 -1.2 S1-S2 = 27.85-29.02 1 2 3 4 5 6 Vol ume (ml) Figure B—11. MICRO-CELL TIME RESPONSE CELL#3 25-10/ FILES F1.7-F1. 10 S1-S2 = 27.97-29.13 1 2 3 4 5 6 Volume(ml) B.6 Spatial resolution of the micro-cells A two-layer system was used to check how well an apparently sharp step in salinity at the interface is represented in a salinity profile from micro-cells data taken at closely spaced po ints. The lighter fluid of lower salinity was first placed in the container and the heavier fluid was then slowly added at the bottom. The density interface was visible in the shadowgraph image as a narrow bright line of light which slowly broadened due to diffusion and turbulence from filling. It was sharpened by withdrawing fluid from a point below the line. Fluid was then syphoned through the micro-cell at about 2 to 3 drops per second in several runs with different steps in salinity. Measurements were while syphoning fluid through the micro-cell at a fixed rate, lowering the cell intake to a depth and taking a reading after allowing enough time to flush the cell (30 sec), then moving the intake to the next depth. Salinity profiles were obtained by plotting the calculated salinities against depth (figures B-6,7 ). Several plots show a spread ln depth between the layers of constant salinity. This can indicate either a lack of resolution or the actual shape of the interface which showed long period oscillations ln one case. In the profile dated 15-4-86 a sharp interface is seen of 0.5 PSS over 3 mm thickness, in which the salinity increases in 8 steps of 0.4 mm each. 102 SALINITY PROFILE 11-4-86 CELL SPATIAL RESOLUTION 30.0 103 SALINITY PROFILE 15-4-86 MICRO-CELL SPATIAL RESOLUTION 29.0 SALINITY (PSS) 2G. 5 0 J i 1 1 i 1 10 . 20 _ 30 _ 40 _ | 50 f 60 . CL. UJ Q 70 J 80 90 100 . 110 -120 _ 130 _ 140 . 150 _ 30.0 I I L 1 1 •* e-flow through oell abt. 3 dr/8ec Figure B*I3. Resolution in 2-layer system. 104 Therm i stors APPENDIX 1C5 APPENDIX C THERMISTORS Cl Thermistor use Thermistors were used to determine the temperature of fluid inside each micro-cell and in the experimental tank, to enable accurate calculation of the salinity and density of the fluid. The type of thermistor used in these experiments consisted of a small bead mounted in the tip of a hollow needle, and placed in in the tank and at the inlet and outlet of each cell. Initially, a single thermistor was inserted in the flow at the outlet of the micro-cells through a small glass tee. The difference between the temperature of fluid in the experimental tank and ambient room temperature caused the value determined from this thermistor to differ from that at the centre of the cell by some amount which depends on the rate of flow through the cell and on the magnitude of the temperature difference. To reduce this error and to check on the output of these older thermistors (some of which were found to develop electrical leaks over time) a second thermistor was installed at the inlet of each cell. The average of the temperatures at the inlet and outlet of the cell was used in the calculation of salinity (see appendix A.l). This was then combined with the temperature in the experimental tank to determine the density of fluid at the intake point (see appendix A.2). Figure C-1 below shows the micro-cell with the two thermistors. 106 Figure C-1 . Thermistors at micro-cell Inlet and outlet. Temperatures are calculated from the measured resistance of calibrated thermistors. The temperature T (In °C> for a given resistance RT (in ohms) and calibration constants A, B and C is then computed from: T = 1/1A + B*ln(RT) + C*(ln(RT>>3] - 273.15 I.1 Leaks In initial tests with the thermistors at top and bottom of each cell, significant differences were found in several cases between the calculated temperatures above and below the cell. Electrical leaks were found In some thermistors. These leaks form an external current path parallel to the Internal path, 107 with a resistance which may vary with the conductivity of the fluid or with variations in temperature, which can change the contact-surface resistance in minute cracks. Any current leak lowers the true resistance value as a parallel resistance, which corresponds to a higher apparent temperature: 1/Rapparent = 1/Rtrue + 1/Rleak For a leak of 1 megohm and a true resistance of 2000 ohm, the apparent resistance becomes 1996 ohm. For thermistor #31 the calculated temperature would change from 20.281 to 20.338 °C and the salinity at 20-30 PSS would change by 0.3-0.4 PSS. The discrepancies in temperatures were reduced by replacing the thermistors which were found to have leaks. C.2 Re-calibration for extended range The thermistors were originally calibrated at temperatures close to 0 °C. For laboratory use, the resistance of the needle mounted thermistors was determined at temperatures up to 25 °C in a controlled temperature bath against recently calibrated thermistors. The HP utility-program FITTER was used to generate a new set of calibration constants for these thermistors, which are listed in table C.1 below. Some typical examples of the output from the curve fitting program for the re-calibrated thermistors is included at the end of this appendix. This lists date, data used for the fit, generated calibration constants, and the maximum error and standard error of the estimate. 108 Table Cl Thermistor Calibration Constants Therm# A = B = C = 17 0.928120e-3 3 .216646e-4 3 .286378e-7 20 1.072391e-3 2 .936491e-4 1 .741109e-7 22 1.060989e-3 2 .973808e-4 1 .586510e-7 23 1 .076479e-3 2 . 937859e-4 1 .670782e-7 34 1.053861e-3 2 .975737e-4 1 .544686e-7 37 1 .015587e-3 3 .013717e-4 1 .391556e-7 40 1 . 143266e-3 2 .841332e-4 2 . 267124e-7 44 1 .027313e-3 2 . 924027e-4 1 .616634e-7 526 1 .3262863e-3 2 .5896285e-4 1 .3697736e-7 T (<*C> = 1/CA + Bxln(RT) + C*(ln(RT))» ] - 273.15 C.3 Datalogger calibration correction Recalibration did correct the error in observations when a digital voltmeter was used but temperatures determined from the datalogger input still did not agree for different thermistors. The conversion from datalogger N-number to resistance value was done with a linear fit for the resistance values for a range of laboratory operating temperatures returned by thermistor #41, (used initially at the exit of the first cell but replaced due to an electrical leak). This linear fit was given by: RT = 2526 - NT*0.25373 where RT = resistance value (ohm) NT = datalogger N-number 109 Many of the thermistors cover a slightly lower range of values. A second order fit to the datalogger output NT-numbers yields a better fit over the range of resistance values from 1600 to 2500 ohms, with a standard error of 0.854221 : RT = 2527.62 + NT*(-0.261192 + NT*4.771296E-6> A thermistor resistance of 1800 ohms corresponds to an N-number of 2861 when using the coefficients of the linear fit, but with the second order fit this N-number (2861) yields a resistance of 1818.4 ohms. Using the calibration constants for thermistor #40, 1800 ohms corresponds to a temperature of 23.72 °C while 1818 ohms would be 23.44 °C. After implementing the above corrections, the values of the observed temperatures were found to be in good agreement with expected values for fluid in the tank and for ambient air temperatures. 110 4 Title: THERM* 31 X-Variable: R Y-Variabie: T Created 07-04-85 Observa 11 on ! : x/ A * 3961 . 72 Y -- 1.953 Observa tion 9 • • \/ A = 3854 .75 Y = = 2.B48 Ubservation 3: X = = 3580 . 44 y = = 4.539 Observa 11 on 4: V A * 3101 .18 Y = = 8.282 Obse rvat i on 5: V = /\ s 2692 o -> . _> ._ Y = - 12.053 Observa 11 on 6: \/ A - ")0''Q .38 Y = = 1b.009 Observa tion 7: X * = 2155 .63 Y = - 18.157 Observa t ion 3: X = •• 1943 .39 Y = = 21.097 Observa 11on 9: \/ A " - 1G91 .93 Y = - 25. 1 F I NHL RESULT OF CURVE FIT Dataset title: THERM* 31 Mode] used: Thermistor Equation: F(X ) - 1/(A1+ A2*1n (X)+A3*ln (X)*3)-273.15 The estimated parameter values after 7 iterations'. AM J = 1 .03541 /e-03 AI2]= 3.033537e-04 A13 J = 1.520697e-07 Maximum error is 1.220309e-03 Ihe overall standard error of estimate is 8.155511e-04 111 Tjtie: IHE.RMI::. FOR* 37 X Variable: R Y~\> a r i ;b i e : T Created 08- 1 3 86 Gbserva t ion i • 1 . X = = 3694 •' i . i T Observa t ion '} • V -/\ = 3309 .9; v •• 9.96 Observa t Iori j • X = * 3IIU6 .112 r ^ •  12.612 Gbserva tion 4: \/ A " = 2646 i i v i - 16.971 Gbserva t ion V A " - 24 15 . 65 / - 18.483 Gbserva 11on IS: X = - 2322 .26 Y - 19.682 Gbserva t ion 7: X = 2111 . <- V 1 < 22.27 Gbserva t ion 8: X -- 1986 . 76 V = - 24.022 Gbserva ti on 9: X = = 1913 .41 V 1 26.091 Gbserva 11on 1 ii: X = =• 1864 t = = 26.002 I- iiirii ••:! t ii i nf (' IJRVL 611 bataset titl.?: THth'M IS TOR* 37 Model used: Thermistor L'q'.u-i t ion: F f X ) = 1 / ( M 1 • H2 • i u (XMHJ'ln ( X ) ' 3 > - 2 7 3 . 1 5 fh>- estimated parameter values a t U-r 6 i tor a t ions : fH i J= 1.U16687e-03 M 21= 3.013717e-0^ M31 = 1 .331666e-07 Ua;< imuni er roi is 1 . 324976,.. • U :'. the overall standard error ot tr. ti'-iate is 8 . U 1623lle-U4 112 Dataloggers APPENDIX D APPENDIX D DATALOGGERS In this series of experiments, two types of datalogger were used at different times. The first was an Applied Microsystems C/T datalogger, modified to bring the digitized output in range for input from the thermistors and micro-cells. When available, an HP-3497A Data Acquisition System was used with individual conductivity circuits for the micro-cells. The output in both cases was directed to an HP-9825 computer. D.l Applied Microsystems C/T Datalogger An Applied Microsystems Datalogger (S/N 170) was adapted for use with the micro-cells: an input panel allows a number of cells and thermistors to be connected to designated channels. The temperature and conductivity electronics in this AM/CT Datalogger were modified for the range of conditions expected to be used in laboratory experiments. Triggered manually or at some pre-set clock rate, the multi plexer cycles through the pre-set pattern of input channels. Analog input signals are converted into a digital output line which contains serial number, time, and numbers for temperature and conductivity. This line Is translated by an A.M. serial converter and entered into the HP-9825 via an RS-232 interface. The sampling cycle frequency or clock rate is set by connec ting pin #32 of the edge-connector on the Sequencer board to the appropriate pin on the Clock board edge connector. Table D.l lists the function for each pin of the Clock board. After switching on the datalogger, the sampling cycles are initiated 115 automatically at the rate set on the clock or can be triggered manually by pressing the button marked "start". The pattern of C and T channels which the sequencer cycles through was programmed on a ROM-chip in the Datalogger. Up to four different micro-cells can be selected, each with two thermistors, and up to four additional thermistor inputs can be added to determine the temperature at points in the tank. These patterns are listed in table D.2 . Dip-switches S1-S5 of SW1 on the multiplexer (MUX) board are pre-set to the desired pattern number: MUX# = 1 +S1 +S2 +S3 +S4 +S5 Here and in the following dip-switch patterns, Si=0 if open and Si = 2<1-" if closed. Dip-switches S6-S8 of MUX-SW1 should be closed for 12-bit data. The number of channels output by the Datalogger to the Serial Converter is set with switches S1-S5 of SW1 on on the Storage Formatter (FMT) board: #CHNLS = 1 +S1 +S2 +S3 +S4 +S5 The first two channels are instrument serial number and time in seconds (approx1 mate 1y),and each temperature and conductance requires an additional channel. The HP-9825 programs prompt for number of cells and extra thermistors and display settings for MUX-SW and FMT-SW1. Dip-switches S6-S8 of FMT-SW1 set the number of times that the data words are output (once if all are open). Dipswitches S1-S6 of FMT-SW2 set the data output rate in m i11i seconds: Time/bit = 5.15*(1 +S1 +S2 +S3 +S4 +S5) For 12-bit word output S7 of FMT-SW2 is closed (10-bit If open). 116 Table D.l. Clock Board Edge Connector Pin Functions Pin# Function Pin# Function 1 o/p 256 hours 18 o/p 30 minutes 2 o/p 128 hours 19 o/p 56.25 seconds 3 parallel transfer pulse 20 o/p 28.125 seconds 4 serial data output 21 serial data Input 5 o/p 32 hours 22 o/p 112.5 seconds 6 o/p 16 hours 23 o/p 1.75 seconds 7 o/p 8 hours 24 o/p 3.51 seconds 8 o/p 64 hours 25 o/p 7.03 9 o/p 27.466 microseconds 26 o/p 14.0625 10 o/p 1 hour 27 o/p 429.153522 microsec 1 1 shift clock 28 o/p 6.86 msec 12 o/p 2 hours 29 o/p 3.43 msec 13 o/p 4 hours 30 cl'ock reset pulse out 14 o/p 15 minutes 31 clock reset 15 o/p 225 seconds 32 parallel transfer 16 o/p 7.5 minutes 33 Vss 17 time code Increment o/p 34 Vdd 35 Vss Table D.2. Multiplexer Input Channel Cycling Pattern MUX# = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 CHANNELS: T1-C1-T6 x x x x x xx xxxxxxxxxxxxx T2-C2-T7 xxx xxx xxx xxxxxx T3-C3-T8 xx xx xx xx xx T4-C4-T9 xxx x x Til XXXXXX XXX XX XX xxx T12 xxxxxxxxxxxT13 xxxxxxxx T14 x x x x 117 The datalogger greatly simplified the nearly simultaneous collection of data from all thermistors and conductivity cells during the slope flow experiments. However, while the data from the temperature circuit gave very stable output,there were some spurious jumps in the output from the conductivity circuit. The N-numbers did jump at times by up to 10 or more units, which corresponds to a variability of almost 0.1 PSS. Several efforts were made to improve the reliability by replacing components in the datalogger and by increasing the delay between switching a cell on and reading the output, but the conductivity readings still became noisy occasionally without known cause. D.2 HP-3497A Data Acquisition System The HP-3497A System was only available on occasion. It was used in determining the time response characteristics of the micro-cells and to obtain data for simultaneous profiles in the last two slope flow experiments. When using this system, each micro-cell was continuously powered by a separate conductivity circuit. This reduced any transients caused by switching the cells on but caused some cross-talk between the cells which was eliminated by shifting the individual operating frequencies. Small shifts found after collecting experimental data were seen to occur when the syphon outlets of the micro-cells were moved relative to each other. The HP-datalogger allowed much higher sampling frequencies as well as averaging of rapid multiple readings of each sensor, which further reduced the noise in the data. 118 Membrane Salt Flux Calibration APPENDIX 119 APPENDIX E MEMBRANE FLUX CALIBRATION E.l Salt and volume flux and driving pressure The surface salt flux due to the freezing of sea water was simulated in these experiments by a percolation of sea water through a porous membrane in a tray. This membrane was mounted between two layers of circuit board, with perforations of about 1 mm diameter spaced uniformly at 4 per cm along and across the tray. The tray was suspended level with the surface of fluid in the experimental tank, which was partly filled with a mixture of sea water and filtered tap water. The method used for estimating the magnitude of the volume and salt flux through the membrane is detailed in section 2.6 in the text. In a series of flux calibration runs, in which the bottom of the tank was kept hor1zontal,the salinity of fluid at the center of the tank was taken as average for the whole tank since the mixed layer extends to the bottom. The net salt flux is the high salinity inflow reduced by the low salinity return flow to the tray, per unit time and unit area. It was expressed as : Bn = Vw.(S2.D2-S1.Dl) = dlSl.Dl1.VI (E-l) 1000 dt 1000 A Bn= net salt flux (g/cm2/s) Vw= volume flux (cm3/cm2/s) Si= salinity in tray(2) and tank(l) (g/kg or PSS) Di= density in tray(2) and tank(l) (g/cm3) Vl= volume of fluid in the tank (cm3) A = area of the tray bottom (cm2) 120 The flux is driven by the pressure caused by the difference in density between the fluid in the tank and that in the tray or rather, the weight of a column of fluid In the tray and that of a column of the same height in the edge between tank and tray: P = (D2-D1).g.h (E-2) P = pressure (g/cm/s2) Di= density <g/cm3) g = gravity = 981 (cm/s*) h = effective height of fluid (cm) The fluid in the edge space between tank and tray became stably stratified as the return flow which rises from the mixed layer in the tank slowly Increases in salinity. The less saline fluid formed a surface layer of about 2 mm in the tray, which can not be mixed well without disturbing the surface (and thus the pressure and associated flux). Fluid in the tray and in the edge space were approximated as 2-layer systems with the same salinity in the upper 2 mm layer, and the effective height used to compute pressures was the tray fluid height reduced by 2 mm. E.2 Flux calibration experiments To estimate the magnitude of the salt flux, time-series data of conductivity and temperature were collected from tank and tray in a series of calibration experiments without a bottom slope. The salt flux was varied by using different starting salinities and depths of fluid In the tray. The meniscus in the 121 edge space made It difficult to determine the exact height of the fluid. Shadowgraph patterns during these runs show a nearly uniform distribution of convective motions in the tank except near the tank end-walls where these motions appear reduced in a triangular section widening with depth. This Is caused by the small downflow under the end-walls of the tray and the very slow upward motion in the edge space. Any similar effect at the side walls cannot be distinguished since the shadowgraph image integrates over the width of the tank, but injected dye did not show any mean circulation in a cross-section of the tank. Salinity profiles were plotted from data taken during several salt flux calibration runs, along the centerline and in the edge space between the tank and tray,(figures E-1 to E-3). Vertical salinity gradients were found just below the membrane and in some cases close to the bottom, possibly due to incom plete mixing after a local spill. The profiles indicate that salinity of fluid sampled at a point near the centre of the tank may be taken as a reasonable estimate of the average for the tank. The initial series of calibration runs did show a general similarity ln the shape of the time-series plots of calculated salinities. Estimated values for volume fluxes were obtained with the expressions formulated above, using a finite differen ces method: the rate of change in salinity and in density was approximated by the difference between successive observations divided by the time interval. Interpolated time, salinity and density are taken as the average of each pair. The volume 122 fluxes and pressures found by substituting these values into the above expressions were plotted for successive runs to obtain a single flux calibration graph for the system. There is a doubling of variability by using this method since a point too high in one step will be too low in the next. The plotted results from a first series of experiments did not form a single characteristic curve of volume flux versus pressure. The tray bottom was disassembled to inspect the membrane, which appeared to be clogged and discolored in spite of filtering through water-purifying cartridges. This could be caused by organic activity or mineral precipitation, and by dust from the laboratory ventilation system. A new membrane with 5 micron pore size was installed in the tray, and all fluids were pumped through a 0.45 micron filter. After adjusting the salinities, and adding a small amount of bleach to control biological activity, the fluids were pumped through a 0.8 or 5 micron filter into the tank and reservoirs before each calibration run. The salt flux plots from these experiments were combined in a single graph (figure E-3) . This shows that, with some scatter, repeatable results for salt flux estimates were obtained for a range of fluxes. Membrane volume flux calibrations were done before and after the first slope flow experiment and a curve through the combined plots (figure E-2, also in text) was used to compute salt flux estimates. The following pages contain a typical print-out of the data and calculated values, the time-series plot of salinities and the calibration plots of membrane volume flux versus pressure. 123 Figure E-l. MICRO-CELL TIME SERIES PLOT Membrane fl ux ca 11 brat. 1 on: 26-2-86 55.0-1 CO -P c salinity in the tray ro o CO 30. 0i salinity in the tank 5.0 —r— 90 —r :I0 Time (min) 1 30 150 270 Figure E~2. Membrane volume flux calibration before and after first slope flow experiment. 126 DESCRIPTION OF EXPERIMENTS APPENDI ZXi TT 127 APPENDIX F DESCRIPTION OF EXPERIMENTS This append IK contains a brief description of the individual slope flow experiments. Included are the slope angle, starting salinities of fluid in tank and tray, special features observed during the individual experiment, the tabulated values of tray salinities from the manually collected data, velocity maxima measured from dye features in the slope flow, the estimates of the membrane salt flux at the times that flow velocities were determined, time-series plots of salinities during the experi ments and the lineprlnter output of the raw data and computed values from the datalogger. 1.7.8 F. 1 SLOPE FLOW EXPERIMENT #1 In the first slope flow experiment, the bottom slope angle was 3.3 degrees and the depth in the tank under the tray was 7 mm at the raised end and 63 mm at the deep end. The tray was filled with fluid of 59 ppt to a height of about 34 mm, while 800 ml of fluid of 15 ppt was added to the edge between tank and tray to keep the levels equal. A bottom slope flow became visible on the shadowgraph before filling and levelling was completed. Velocity maxima in the slope flow were determined from color slide sequences of dye streaks. Salinity profiles were plotted from micro-cell data taken at port#6 over t=ll-38min (fig. F-2 ) . ' Quas i - i ns tantane ou s' profiles were obtained fitting a second order curve through the profile points in the mixed layer (figure F-3) and subtracting the fit from the profile points: S(instant)= S(profile)- S(fit)+ S(tl) The adjusted profiles (figure F-4) show a slope flow depth of 14 to 17 mm, with a rise in salinity of 0.6-0.7 PSS. Micro-cell data were also taken to check the distribution of salinity in the tank along the bottom slope and along the top under the tray (figure F-5), but a time-series plot of these points (figure F-6) gives insufficient detail about the lateral distribution. Table Fl lists the computed values of salinities, densities and driving pressures at those times that slope flow velocities were measured, and the volume and salt fluxes derived from them as described in the text (section 2.6). 1Z9 Table F1. Saltf1uxes and flow velocities - sloperun#l From dye seen in siide# 12-13 17-19,20-21 taken at time (min) t = = 25 30 (lineprinter time) max. velocity (cm/s) v : = 0.510 0.401-0. 519 salinity-tray (g/kg) S2 = = 57.926 57.676 from C#3 data fit salinity-mixed layer SI = = 20.541 21.395 from printer C#2 temperature CO T-tank = 21 .67 21.64 thermistor #526 tray density(sigma-t) D2 = = 41.867 41 .683 Unesco Eq.of State mixed layer density Dl : = 13.357 14.010 M n driving pressure P = = 89.50 86 .87 g*h*(D2-Dl)/1000 volume flux (cm/sec) Vw : = 2.95e-4 2.82e-4 from f ig.2-15 salt flux (g/cm2/s) B = 1.780e-5 1 .694e-5 130 Figure F-l. MICRO-CELL TIME SERIES PLOT SLOPE FLOW EXPERIMENT #1 60.01 co CO : : « z salinity in tray tit i i t II HI a co 35.0-salinity in tank (includes profiles) 10.0 Time (min) 1 20 "60" 100 140 180 F-2 SALINITY PROFILE SLOPE FLOW EXP#1 17.0 Salinity (PSS) 1Q 5 22. 0 1 I 1 1 I I I I I 1 PROFILES IN PORT #6 tell-27 min going down- 2 min intervale t=30-38 going up- 1 min intervale 132 time (min) Figure F-3. Time-series plot of profile points. Figure F~4. SALINITY PROFILE SLOPE FLOW EXP#1 16.90 Salinity CPSS)^ 30 40-J 1 L 17. 70 J I •Profilea in port #8 t=ll-27 going down (o) te30-38 going up (x) S <profile)-S (actual) - S(t) + S(t0) S(t) = 14.1185 +U.2S736 -t*.0021194) (2nd order fit to mixed layer data) (S(t0)- S(t-ll) 134 32.01 SLOPE FLOW EXP#1 Xs5 salinity at 2 mm above bottom o= salinity at 4 mm below tray samplinq interval 3 minutes &=r using 2nd order fit (fig. F~6).' 'quasi^inetantanous' points near tr< near bott om slope PORT #8 ~i— #7 n— #6 i—• #5 n— 0 20 40 §A n— #3 n— 60 80 Figure F~5. Distribution. Distance along tank (cm) 31.5 ON 29. 5-co CO CL •rt c 1 ( o LO 27.5 80 SLOPE FLOW EXP#1 time-series plot of data from successive party's: x = 5mm below the tray bottom, o = 2mm above the bottom slope X #8 S(t) =34. 2406+t (-0. 23219+t*l. 87359e-3) —r 90 100 110 Figure F~6. Time-series plot of distribution data time (min) F. 2 SLOPE FLOW EXPERIMENT #2 In slope flow experiment #2, the slope angle was 3.8 degrees and the fluid depth below the tray was 7 mm at the shallow end and 65 mm at the deep end. The AM/CT datalogger was used with micro-cells #1 and #2 to obtain data for fluid in the tank. Profile data were taken ln port #6 at t=39-56 min (figure F-9) and at t =112-130 min (figure F-ll) after the start. A least squares linear fit to data taken simultaneously with the second micro-cell at fixed depth in the mixed layer (figure F-8, F-10) was used to obtain the quasi-instantaneous profiles. Salinity maxima in the slope flow were 0.4 to 0.5 ppt above those in the mixed layer. Table F2. Flow velocities from photos - sloperun #2 Photos # : 7-10 14-17 min after start (clock time): 55 (15:25) 125 (16:35) scale : ports(cm)/photo(mm): 20/74 30/81.8 dye moved on photo(mm/1Osec): 16 8.5 flow velocity max. (cm/sec) : 0.43 0.312 Tray fluid data were only taken at the start and end of the run. Salinities at other times were estimated from conservation of volume and salt: V1*S1(t)*Dl(t)+V2*S2(t)*D2(t>= G(t) ln which VI and V2 were the tank and tray volumes, SI and S2 the salinity in the mixed layer and in the tray and DI and D2 corresponding densities. The arbitrary function G(t) represents 137 the salt loss to the bottom flow, arid was linearly proportioned over the profiling time. Table F3 shows the salinities computed from data of micro-cell #3, with Vl=7.08 and V2=26.5 liters. Table F4 lists the computed salinities, densities and pressures and the derived salt fluxes at the times that flow velocities were determined. Table F3. Salinity of tray fluid - sloperun #2 -VC#3 RT#22 RT#40 T(deg.C) S(ppt) start t = 55 t=125 end 2.217 1950 1883 (est i m.) (est i m.) 2.026 1956 1889 22. 45 22. 37 57.64 55.21 52 . 42 52 . 04 Table F4. Saltfluxes and slope flow velocities - sloperun#2 At time (min) ttprtl= 55 Sal.-mixed layer SI = 15.694 Sal in 1ty-tray S2 = 55.21 temp(deg.C) T-tnk = 21.286 tray dens(sigma-t) D2 = 39.890 dens mix.layer Dl = 9.794 driving pressure P = 94.48 volume flux (cm/s) Vw= 3.17e-4 membrane salt flux B = 1.820e-5 max.flow velocity v = 0.43 125 from: 25.006 C#2 print-out 52.04 estim.(table F3) 21.585 thermistor #526 37.652 Unesco polynom. 16.754 65.60 (D2-D1)/1000*g*h 2.00e-4 from figure 2-15 1.712e-5 B=F*S2*( D2 +1) 1000 1000 0.312 (cm/sec) 13B Figure F-7. MICRO-CELL TIME SERIES PLOT SLOPE FLOW EXPERIMENT #2 time (min) Figure F~B. Time-seriee and lineor fit Figure F-9. SALINITY PROFILE y 6-3-86 SLOPERUN §2 141 25. 80 24. 70-23. 60 Figure F_10. Time-series and linear fit Figure F-ll. SALINITY PROFILE a 6-3-86 SLOPERUN #2 23.60 SALINITY (PSS) 24<70 25 Q0 * t ' ' ' ' ' ' i f i i i t t » t i • ' • •„ " 10 J E E dl O 20 J 30 J 40 J 143 F. 3 SLOPE FLOW EXPERIMENT #3 In slope flow experiment #3 the slope angle was 2.2 degrees. The depth below the tray was 20 mm at the shallow end and 51 mm at the deep end. The AM/CT Datalogger was used with micro-cell #1 for profiles,with micro-cell #2 fixed at 15mm below the tray for salinities In the mixed layer and with thermistor #526 for temperatures in the tank. Salinities in the tray were computed from volt-meter readings of micro-cell #3. After filling the tray to start the experiment, the tank was briefly stirred to remove circulation patterns which might have been formed by uneven flux during the filling. The slope flow re-established itself within one minute, starting at about 30cm from the shallow end. A counter-rotating flow cell, also found in the previous experiment, was seen in the shadowgraph upslope from this point. This uphill flow disappeared when the starting point of the down-slope flow moved slowly towards the shallow end. Sketches of the typical flow patterns and the double flow cells are included in the text. Salinity profile data were taken in port #8 at t=105-129 min after the start. A linear fit to salinities computed from data taken at a fixed depth in the mixed layer during the profiling (figure F-13) was used to obtain 'quasI-instantaneous' profiles (figure F-14>. These show the convectively mixed layer and a sharp rise ln salinity of 0.8 PSS starting at 12-18 mm above the bottom. Maxima in the slopeflow velocity were measured from the distance dye moved in photo sequences. 144 Table F5. Flow velocities from photos - sloperun #3 min after start (clock time): 60 (10:30) 135 (11:45) dist. dye moved on photo (mm): 11-11.5 10.5-11.0 time between photos : 11.5 12.5 slopeflow velocity (cm/sec) : 0.259-0.270 0.227-0.238 Table F6. Saltflux and slopeflow velocity - sloperun #3 1inepr inter t ime = 60 135 min. after start mixed layer SI = 21 .561 29.106 (PSS)time-series fit tray salinity S2 = 54.583 52.695 (PSS)tIme-serles fit temperature T-tnk = 21.420 21.877 CO thermistor #526 tray density D2 = 39.366 37.775 (sigma-t)Unesco eqn. tank dens i ty DI = 14.192 19.781 M M pressure P = 81 .50 58.25 (gr/ct/s2) volume flux Vw = 2.50e-4 1.67e-4 (cm/s) flux cal.plot membr.salt flux B = 1.418e-5 0. 946e-5 gr/cm2/s slopeflow max . V = 0.259-0.270 0.2 27-0.2 38 cm/s from photos 145 igure F-14. SALINITY PROFILE 11-3-86 SLOPERUN #3 PORT #8 >5.80 SALINITY (PSS) 26.80 27. 80 i f tual profile* adjusted profiles by linear fit to data from fixed depth 148 F.4 SLOPE FLOW EXPERIMENT #4 In slope flow experiment #4, the slope angle was 5.2 degrees. The depth below the tray was 2 cm at the shallow end and 10 cm at the deep end. The AM/CT Datalogger was again used with micro-cells #1 and #2 and with the tank thermistor, and digital voltmeters were used with micro-cell #3 to monitor the salinity of fluid in the tray. Table F7. Salinities in the tray - sloperun #4 t i me m i n — VC#3 RT#22 --> TO °C> SCppt) 15:00 30 2 .012 2000 21 .746 52.381 15:23 53 1 .982 2006 21 .662 51 .585 15 : 37 68 1 .967 2008 21 .634 51.17 1 15:55 85 1 .947 201 1 21 .592 50.623 16:17 107 1 .927 2012 2 1 .578 50.043 16 : 40 130 1 .907 201 4 21 .550 49.480 16:55 205 1 .899 2013 21 .564 49.226 17: 25 235 1 . 880 2007 21 .648 48.566 Salinity profiles were plotted from data taken in port #5 over t=97-131 min after the start, corrected for the salinity change in the mixed layer (figure F-16). Data were also taken along the bottom of the tank at port #8 through #2 and back to port #7. Three data points were taken in rapid succession in each port at about 2 mm above the bottom, and the pointwise time-corrected averages were plotted (figure F-17>. 149 The slopeflow velocities were measured from video footage of dye carried along by the bottom flow, using the 10 cm spacing of sampling ports in the tray for scale where visible or taking the average of vertical lines at the back (spaced 5 cm) and the units on a scale along the front of the tank. Table F8. Flow velocities and saltfluxes - sloperun #4 At clock time = 1 4: 50 15:21 16:12 16: 48 hr:m i n 1i nepr i nter t = 20 50 102 138 m i n tray fluid S2= 52.708 51 .585 50.175 49.3445 ppt mixed layer Sl= 7.011 9.557 12.720 14.847 j ppt tank temp. T = 21 .053 21.392 2 1 .639 21.715 °C tray dens. D2 = 38.033 37.068 35.911 35.252 s i gma-1 tank dens. Dl = 3. 295 5. 138 7 . 464 9 .049 s i gma-1 pressure P = 112.5 103. 4 92.09 84.83 gr/cm/s2 volume flux Vw= 4.00e-4 3.50e-4 3.00e-4 2.67e-4 cm/s salt flux B = 2. 19e-5 1 . 87e-5 1 .56e-5 1 .36e-5 gr /cm2/ s max.f1owspeed = 0. 45-0,49 0. 45-0.49 0. 39-0.41 0. 33-0.36 cm/s 150 Figure F-15. SALINITY PROFILE SLOPE RUN #4 Port #5 t= 97-111 min K-AS=0- 24 —^ 151 FiqureF-16. SALINITY PROFILE SLOPE RUN #4 Port #5 t-ll1-126 min 3< 4 Salinity (PSS) i3. 9 J L • • • 1 1 L 14. 4 I 10 20 30 40 50 60 h=16mm >k Sm=13. 593 Q= actual C#l data Cueing 1 therm) X= linear fit to mixed lay«r data —= adjusted profile 152 13-6-86 SLOPE RUN #4: SALINITIES ALONG BOTTOM SLOPE pointwiee time-adjusted t=148-173 Figure F-17. Salinity distribution along bottom slope. F.5 SLOPE FLOW EXPERIMENT #5 In this experiment the slope angle was again 5.2 degrees and the depth 2 cm at the shallow end and 10 cm at the deep end. A new membrane was installed in the tray. Micro-cells #1 and #2 were connected to the AM/CT datalogger and cell #3 was used with the DVM's for tray. Starting salinities were 52 ppt in the tray and 13 ppt in the tank. Table F9. Salinities in the tray during sloperun #5 t i me m i n — VC3 RT#44 RT#23 T- avg S(K = 178: 12: 30 30 1 .9961 2497 2059 2 1 .644 52. 030 12: 40 40 1 . 9659 2496 2058 21 . 656 51 . 1 10 12: 50 50 1 .9336 2496 2058 21 .656 50. 1 47 13: 01 61 1 .9100 2494 2056 2 1 . 679 49 . 416 13: 10 70 1 . 8942 2494 2056 2 1 . 679 48 . 948 13: 30 90 1 .8610 2494 2056 21 . 679 47 . 967 13: 40 100 1 .8449 2494 2056 21 .679 47. 492 14: 03 123 1 .8160 2496 2057 21 . 663 46. 663 14: 20 1 40 1 .7971 2496 2058 21 .656 46 . 1 16 14: 50 170 1 .771 1 2496 2058 21 . 656 45. 356 15: 32 212 1 .7418 2498 2060 21 .631 44. 528 16: 20 260 1 .7222 2502 206 3 21 .589 44. 002 16: 30 270 1 .7203 2501 206 2 21 . 601 43. 934 17: 00 300 1 .7111 2500 2063 21 . 600 43. 668 Salinity profiles from data taken in port #5 at t=80-97 min (figure F-19) and in port #3 at t= 125-141 min after the start 154 (figure F-20) were made instantaneous by subtracting the change in simultaneously taken mixed layer salinities. They show a well mixed convective layer and a slope flow region of 9 to 15 mm thickness where the salinity increases by about 0.3 PSS. Another profile was plotted from data taken in the edge space between tank and tray (figure 2-12 in text). Shadowgraph images and motions of injected dye were recorded on videotape during part of this run. This includes footage of the counter-cell which formed upslope from the place where the bottom flow first established itself. Velocity maxima in the flow were measured from videotape footage, and the temperature and salinity of fluid in the mixed layer and in the tray at those times were obtained by linear interpolation of the time-series data of calculated values. Table F10. Flow velocities and salt f1uxes - sloperun #5 clock time t = 13:11 200(15:20)16:21 16:42 h r : m i n printer t(p) = 71 200 261 282 m i n trayfluid S2 = 48.948 44.765 43.995 43.828 PSS mix.layer S1 = 15.835 24.773 26.406 26.915 PSS temp T-tnk = 21.568 2 1 .843 21 .863 21 .872 deg. C tray dens D2 = 34.991 31.707 31.112 30.982 s i gma-1 tank dens Dl = 9.831 16.510 17.740 18.123 s i gma-1 pressure P = 81.45 49. 20 43.29 41 .63 g/cm/s2 vol.f1ux Vw = 2.50e-4 1.35e-4 1.25e-4 1 . 22e-4 cm/rain membr.flux B = 1.267e-5 0.623e-5 0.567e-5 0.551e-5 gr/cm2/s s1 ope flow v = 0.47 4-0.665 0.269-0.279 0.248-9.312 0.259-0.27 3 i cm/s 155 Figure F-18. MICRO-CELL TIMESERIES 18-3-86 SLOPERUN #5 d=2-10 Klf2=1878, 1793 new membr Ln 24.0n CO CO Q-o CO 14. H 4.0 30 120 210 300 Time (min) Fi aure f_ig: SALINITY PROFILE 18-3-86 SLOPERUN #5 0 16>5 SALINITY (PSS) 10 _ n. UJ o 30 _ 40 _ 50 _ 60 _ 17.5 i POUT iS t»80-97 (13.20-13i 37) x " actual profile data o - fixed depth backgnd £ - oorreoted profile (pointwiee diff.) 18.5 i 157 Figure F-20 : SALINITY PROFILE .18-3-86 SLOPERUN #5 158 F.6 SLOPE FLOW EXPERIMENT #6 In slope flow experiment #6, the slope angle was 2.3 degrees and the depth below the tray was 20 mm at the shallow end and 57 mm at the deep end. A convergence near the top of the mixed layer was seen to occur in several of the previous experiments. This convergence was centered near the point where the down-slope flow was separated from the uphill flow cell which formed during start-up. The object of this experiment was to check for variations in the mixed layer salinity along the length of the tank. Any sag in the bottom or a slight bow in the sides of the tray would increase the local height of the heavier fluid column and thus the saltflux. The AM/CT datalogger was used with all three micro-cells to sample fluid in the upper part of the mixed layer along the centerline, about 1 cm below the tray: micro-cell #1 was used at port #5 near the center, #2 at port #2 near the shallow end, and #3 was used at port #7 near the deep end but occasionally moved to the tray to determine the salinity there. The tray was filled between 11:10 to 11:20 to a height of 34 mm while fluid of 10 PSS was added to the edge space between tank and tray. The video timer was started at 11:23:30 but the time-series data are printed in minutes after 11:00 and thus: t<printer)= t(vldeo)+ 23.5 min. During the first 40 minutes in the time-series, the salinity was higher by 0.2 to 0.5 PSS near the center, and a convergence just below the tray was visible ln the shadowgraph. At t=29 or 159 t(vldeo)=5 min, the tank was stirred to remove patterns formed during filling. The downs 1 ope/uphi11 flow patterns re-formed in a short time and dye injected at points along the centerline confirmed this. In later measurements, the mixed layer salinity was higher towards the shallow end, explained by mixing of salt Into a smaller depth. The counter-cell which was visible ln the shadowgraph Image decreased to the shallowest 10 cm of the tank but persisted throughout the run. It might have been sustained by the difference In saltflux near the end wall due to the area without salt flux below the end of the tray. The shadowgraph images and streaks from injected dye were recorded on video tape during much of the run. Flow velocities determined from this are tabulated below: Table Fll. Slopeflow velocities - sloperun #6 dist video time-interval dt tCprtl velocity (cm) (h:min:sec) (s) (min) (mm/s) 2 1:36:49 - 1:37:21 = 32 1 20. 5 0.63 5 1:54:15 - 1:54:55 = 40 138 1 . 25 5 2:00:12 - 2:01:02 = 50 144 1 . 10 5 2:01:02 - 2:01:42 = 40 145 1 . 25 5 2:01:42 - 2:02:21 = 39 1 45 . 5 1 . 28 5 2:02:21 - 2:03:00 = 39 146 1 . 28 5 3:08:13 - 3:09:08 = 55 212 0.91 5 3:15:32 - 3:16:17 = 45 219 1.11 160 A third order polynomial fit was done to data from the tray fluid and from cell #1 to determine the salinity values at the times that flow velocities were measured, which were used to obtain saltflux estimates. Table F12. Salinities in tray and tank - sloperun #6 t(prt) S-C#3 t(prt) S-C#l 51 30.173 40 17.039 53 30.251 51 17.411 122 29.613 100 18.871 123 29.601 147 19.669 240 28.919 210 20.913 267 28.832 240 21.621 270 28.810 280 22.115 274 28.906 339 22.682 467 28.398 468 23.674 468 28.325 470 23.635 469 28.348 S2 = 30.779 +t(-0.1197 +t<2.3288E-5 -t*1.4454E-8)) (rms diff.= 0.0265) SI = 15.8225 +t(0.03325 +t(-4.4859E-5 +t*2.03725E-8)> (rms diff.= 0.0867) 161 Table F13. Flow velocities and saltfluxes - sloperun #6 video timer t(v) = 1:54:35 2:01:30 3:11:30 hr:min:sec pr int-out t(p) = 1 38 145 216 m i n S-tray fluid S2 = 29.495 29.447 29.041 PSS S-mixed layer SI = 19.610 19.763 2 1.117 PSS tank temp T- tnk = 22.291 22.325 22.574 °C tray dens i ty D2 = 19.963 19.917 19.541 s igma-t tank density Dl = 12.494 12.601 13.556 s igma-t pressure P = 24.18 23.68 19 . 37 g/cm/s2 volume flux Vw = 7.33e-5 6.50e-5 5.50e-5 cm/s membr.salt flux = 2.205e-6 1 . 952e-6 1 .628e-6 gr /cm2/s flow velocity V = Q.123 0.1 1-0.1 3 0.09-0.1 1 cm / s 162 Figure F~2 1 MICRO-CELL TIMESERIES 8-5-86 SLOPERUN #6 d=20-57 h=34 K=1892, 1795, 1817 Time (min) F.7 SLOPE FLOW EXPERIMENT #7 In this experiment the slope angle was 5.5 degrees. The tray rested on the bottom at the shallow end, the depth at the deep end was 78 mm. The starting salinities were 7 PSS in the tank and 28 PSS in the tray. The datalogger was again used with all three micro-cells. Time-series of micro-cell data were taken with t=0 at 14:00. Salinity profiles from data taken at port #5 over t=40-59 (see figure F-23) and at port #4 over t=109-121 (figure F-24) show a typical mixed layer and the bottom slopeflow region with a rise in salinity of 0.2-0.4 PSS in the lowest 8 mm. As the salinity in both the mixed layer and the slope flow increases over time, the deep end of the tank becomes stably stratified. This can be seen in a profile at port #7 over t=87-100 (figure F-25). The shadowgraph image shows that after one hour the mixed layer extends about 3 cm down from the tray and no convective penetration is seen below this depth. Dye in the slope flow was seen to split: one part continues along the bottom, the other flows along the interface where it is entrained into the mixed layer by the velocity shear . Shadowgraph images of the onset of convection and the start up of the slopeflow were recorded on videotape. The video timer was started at 13:48 so t[videol=ttprt]- 12. The slope flow was seen to start up very close to the shallow end soon after the saltflux through the membrane became visible on the shadowgraph as a slowly descending curtain of lines. The descent was nearly even along the tank except slightly faster in the area where a 164 counter-rotating cell formed in previous experiments. No such cell was seen this time. A cloud of dye, injected in the stable layer near the deep end of the tank, slowly diffused below the sharp interface with the mixed layer. It was entrained above this and lifted into the return circulation. The slope flow velocity was determined from video footage of dye movement: Table F14. Flow velocity and saltflux - sloperun #7 dye moved 5 cm in : dt(video)= 2: 25 :55-2:26:37 =42s and : dt = 2: 26 :37-2:27:26 =49s slope flow max. v = 0.102-0.119 cm/s t i me 16:14 t[pr1 = 138 minutes after start S-tray fluid S2 = 26.552 PSS S-mixed layer SI = 16.871 PSS tank temp T-tnk = 24.179 °C tray density D2 = 17.2106 s i gma-1 tank density DI = 9.930 s igma-t pressure P = 23.569 g/cm/s2 volume flux Vw = 6.33e-5 cm/s membr.salt flux B = 1.710e-6 gr/cmJ/s 165 >2 MICRO-CELL TIMESERIES 9-5-86 SLOPERUN #1 d=0-78mm h=34 K=1892, 1795, 1817 30.0H Time (min) Figure F-23. SALINITY PROFILE SLOPERUN #7 K=1892, 1795, 1817 167 Figure F-24. SALINITY PROFILE SLOPERUN #7 K=1892, 1795, 1817 168 Figure F-25. SALINITY PROFILE SLOPERUN #7 K=1892,1795,1817 169 F.8 SLOPE FLOW EXPERIMENT #8 In experiment #8, the bottom slope angle was 5.1 degrees, and at the shallow end the depth under the tray was 12 mm. The HP-3497A Data Acquisition system was used for all thermistors and for the output from the individual conductivity circuits which powered the three micro-cells. The system was controlled with an HP-9825 computer which stored all data on tape, printed the calculated values from each sensor and plotted time-series data of calculated salinities. Simultaneous salinity profiles were obtained from data taken near the middle of the tank and at 20 cm to either side. The intakes of micro-cells C#l, C#2 and C#3 were lowered through ports #7, #5 and #3 respectively, and set to touch the sloped bottom. Simultaneous data were taken at successive depths after raising the intakes of the micro-cell together to the same height above the bottom (see figure F-26). Figure F-26. Arrangement of micro-cells 170 In the first series of profile data, taken over a period of 20 minutes, the intakes were lowered through the convectively mixed layer and the slope flow region to the bottom and raised again. Second order curves were fit through those sequences of data from each cell which in an expanded time-series (figure F-28) appeared to be part of the mixed layer: S(t) = A + Bt + Ct2 Micro data-file number coefficients of 2nd order fit: -cell from to and to F# F# F# F# A= B= C = #1 95-104 124-132 9.564049 0.02755713 -2.00482E-4 #2 96-104 119-132 9.619223 0.02237656 -1.101477-4 #3 101-104 121-132 9.793305 0.02583053 -2.490983-4 Simultaneous quasi-instantaneous profiles were obtained from: S(corr) = S(actual) - S(fit) + S(fit at start) and in the profiles so obtained, the mixed layer salinities of each individual station are the same at the start and end of the profile sequence (figures F-29,30).A second set of salinity profiles, from data taken about 85 minutes later, (figure F-31) shows that the salinity in the bottom current does not rise as much above that in the mixed layer as in the earlier set. The later profile from micro-cell #1 in port#7 near the deep end shows a nearly linear stratification from heavy fluid which collected in the bottom. Differences in the shape of profiles from micro-cells #2 and #3 did not change over that time. Tests done after this experiment show that a sudden shift in conduc tance may occur with a shift in relative position of the outlet tubes of those micro-cells which syphon into the same bottle. 171 ta ta ca to ta ca ca DATA 10-31-86 HP-DATALOGGER • i L 11 0 E L OJ-P QJ4-e <H I— 09 4- +r ca 0) CT) II 6 ^ •rt C -P CD o Figure F~27. Time-series slope flow exp#8 300 SEC/DIV i i t i t MICRO-CELL SALINITY TIME SERIES PLOT Fiqure F-Z9, SALINITY PROFILE 3 SLOPE RUN m 9. 55 40 E E o _u V > 0 _Q 0 ID 20 •rt a; 10 -0 Salinity (PSS) g> g5 I l l 10. 15 i / / / t=ll: 58-12: 06 ' quasi-instantaneous' profiles, using 2nd order fit. Cl : port#7 C2 i port#5 C3 t portl?3 174 FIGURE F-30. SALINITY PROFILE SLOPE RUN #8 9. 90 40 30 -E E E 0 -P 0 -0 > 0 J) 0 •rt X 10 " Salinity (PSS)10- 20 I I L_ C2 Cl 10. 50 _L I t - 12:06™12t 17 F#i 110-132 'quaoi-inetantaneoue' profilea ueing aeoond order fit through mixed layer data Cl C2 C3 port#7 port#5 port#3 h=13mm, AS=0.38-0.46 0 175 SALINITY PROFILE FIGURE F-31. SLOPE RUN #8 0 Salinity <PSS) ig> 3 1 I L_ 13. 6 1 quasi-inetantaneoue profilee (correoted for change in salinity in the mixed layer during profiling). Simultaneous points at equal height© above the elcping bottom*, spaced 20 cm: in port#7 (deep) cell#2 in port#5 (middle) oell#3 in port#3 (shallow) t=13:42-13t 56 (data F6-46) AS = 0.31-0.37 176 

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