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A laboratory study of slope flow induced by a surface salt flux 1987

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A LABORATORY STUDY OF SLOPE FLOW INDUCED BY A SURFACE SALT FLUX by Bon J . van Hardenberg B . Sc . , U n i v e r s i t y of B r i t i s h 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 t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 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 s a l t e x p u l s i o n c a u s e d by t h e f r e e z i n g o f s e a w a t e r and t h e d r a i n a g e o f b r i n e f r o m t h e i c e c r e a t e s a c o n v e c t i v e l y m i x e d l a y e r , w h i c h e x t e n d s t o t h e b o t t o m i n s h a l l o w c o a s t a l r e g i o n s . T h i s b u o y a n c y f l u x a t t h e s u r f a c e was s i m u l a t e d i n l a b o r a t o r y e x p e r i m e n t s by p e r c o l a t i n g s a l t w a t e r t h r o u g h a p o r o u s membrane i n t o a t a n k . S h a d o w g r a p h images show t h a t a d o w n - s l o p e f l o w i s i n d u c e d when t h e b o t t o m o f t h e t a n k i s s e t a t an a n g l e . V e l o c i t y maxima i n t h e s l o p e f l o w , m e a s u r e d f r o m t h e movement o f i n j e c t e d dye r a n g e d f r o m 0.09 t o 0.66 cm/s. F l u i d d e n s i t i e s were d e t e r m i n e d u s i n g t h e r m i s t o r s and s m a l l - v o l u m e c o n d u c t i v i t y m i c r o - c e l l s d e v e l o p e d f o r t h i s p u r p o s e . F o r b o t t o m s l o p e a n g l e s b e t w e e n 2.2° and 5.5°, and a t c o m p u t e d s a l t f l u x e s b e t w e e n 1 . 8 2 * 1 0 _ 5 a n d 1 . 6 3 * 1 0 _ & g/cm 2/s, t h e s a l i n i t y p r o f i l e s showed s l o p e f l o w d e p t h s b e t w e e n 7 and 17 mm w i t h a r i s e i n s a l i n i t y o f 0.24 t o 0.92 p p t above t h o s e i n t h e m i x e d l a y e r . E n t r a i n m e n t a t a d e n s i t y i n t e r f a c e w i t h o u t s h e a r , u s i n g t h i s e x p e r i m e n t a l a r r a n g e m e n t , a g r e e d c l o s e l y w i t h p r e d i c t e d r e s u l t s by Bo P e d e r s e n . U s i n g t h e e n t r a i n m e n t model f o r a t u r b u l e n t g r a v i t y c u r r e n t , e n t r a i n m e n t f a c t o r s c o m p u t e d f r o m t h e d a t a o f t h e s l o p e f l o w e x p e r i m e n t s were up t o two o r d e r s o f m a g n i t u d e l a r g e r t h a n t h o s e p r e d i c t e d f o r f l o w s i n a q u i e s c e n t e n v i r o n - ment. T h i s i s c o n t r a r y t o v i s u a l e v i d e n c e o f t h e e x p e r i m e n t s o r t o A r c t i c f i e l d d a t a , w h i c h i n d i c a t e l o w r a t e s o f e n t r a i n m e n t . T h i s s u g g e s t s t h a t a d i f f e r e n t model i s r e q u i r e d t o e x p l a i n t h e i n t e r a c t i o n b e t w e e n s u c h f l o w s a nd t h e t u r b u l e n t e n v i r o n m e n t . i i T A B L E O F C O N T E N T S A b s t r a c t i i Table of contents i i i L i s t of f i gure s v i L i s t of photos x L i s t of t a b l e s x i Acknowledgements x i i 1 - I N T R O D U C T I O N 1 1.1 A r c t i c subsurface i n t r u s i o n s and slope flow 1 1.2 Laboratory study 3 2 - E X P E R I M E N T A L M E T H O D S 5 2.1 Tank and t r a y arrangement 5 2.2 Flow v i s u a l i z a t i o n 7 2.3 Instrumentation f o r d e n s i t y d e t e r m i n a t i o n 9 2.3.1 Thermistors and m i c r o - c e l l s 9 2.3.2 C a l i b r a t i o n of c e l l c o nstants 12 2.3.3 Time response c h a r a c t e r i s t i c s 13 2.3.4 S p a t i a l r e s o l u t i o n 15 2.4 Data a c q u i s i t i o n 17 2.5 Experimental procedure 19 2.6 Determination of membrane s a l t f l u x 21 2.6.1 S a l t - and volume f l u x e s 21 2.6.2 S a l t f l u x c a l i b r a t i o n 22 2.6.3 Membrane s a l t f l u x d e t e r m i n a t i o n 24 2.6.4 S a l t f l u x and entrainment 28 2.6.5 A r c t i c s a l t f l u x and c o n v e c t i o n depth 37 i i i 3 - EXPERIMENTAL RESULTS AND INTERPRETATION 40 3.1 S l o p e a n g l e s , s t a r t i n g s a l i n i t i e s a n d s a l t f l u x 40 3.2 S h a d o w g r a p h o b s e r v a t i o n s 41 3.3 I n j e c t e d dye 44 3.4 S a l i n i t i e s a n d s a l i n i t y p r o f i l e s 50 3.5 S a l t f l u x e s and f l o w v e l o c i t i e s 57 3.6 I n t e r p r e t a t i o n 62 4 - SUMMARY AND CONCLUSIONS 67 BIBLIOGRAPHY 70 A p p e n d i x A - S A L I N I T Y AND DENSITY CALCULATION 73 A . l Sa U n i t y 74 A. 2 D e n s i t y 76 A p p e n d i x B - CONDUCTIVITY MICRO-CELLS 79 B. l C e l l c o n s t r u c t i o n 80 B.2 M i c r o - c e l l e l e c t r o n i c s 81 B.3 AM/CT D a t a l o g g e r c o n d u c t i v i t y e l e c t r o n i c s 82 B.4 D e t e r m i n a t t i o n o f c a l i b r a t i o n c o n s t a n t s 83 B.5 M i c r o - c e l l t i m e r e s p o n s e 91 B. 6 S p a t i a l r e s o l u t i o n o f t h e m i c r o - c e l l s 102 A p p e n d i x C - THERMISTORS 105 C l T h e r m i s t o r use 106 C. 2 L e a k s 107 C.3 R e - c a l i b r a t i o n f o r e x t e n d e d r a n g e 108 C.4 D a t a l o g g e r c a l i b r a t i o n c o r r e c t i o n 109 i v A p p e n d i x D - DATALOGGERS 114 D . l A p p l i e d M i c r o s y s t e m s d a t a l o g g e r 115 D. 2 HP-Da t a A c q u i s i t i o n S y s t e m 118 A p p e n d i x E - MEMBRANE FLUX CALIBRATION 119 E. l S a l t and volume f l u x a n d d r i v i n g p r e s s u r e 120 E. 2 F l u x c a l i b r a t i o n e x p e r i m e n t s 121 A p p e n d i x F - DESCRIPTION OF EXPERIMENTS 127 F. l S l o p e f l o w e x p e r i m e n t #1 129 F.2 S l o p e f l o w e x p e r i m e n t #2 137 F.3 S l o p e f l o w e x p e r i m e n t #3 144 F.4 S l o p e f l o w e x p e r i m e n t #4 149 F.5 S l o p e f l o w e x p e r i m e n t #5 154 F.6 S l o p e f l o w e x p e r i m e n t #6 159 F.7 S l o p e f l o w e x p e r i m e n t #7 164 F.8 S l o p e f l o w e x p e r i m e n t #8 170 v L I S T OF FIGURES Fig.1-1 T y p i c a l A r c t i c p r o f i l e s in winter 2 Fig.2-1 Apparatus f o r slope flow experiments 7 2-2 Diagram of arrangement f o r shadowgraphs 7 2-3 M i c r o - c e l l with t h e r m i s t o r s 10 2-4 M i c r o - c e l l s in experiments 11 2-5 Volume r e q u i r e d to f l u s h c e l l 14 2-6 M i c r o - c e l l s p a t i a l r e s o l u t i o n 16 2-8 Data a c q u i s i t i o n - manual input 17 2-9 Data a c q u i s i t i o n : AM/CT data l o g g e r 18 2-10 Data a c q u i s i t i o n : HP-3497A data system 19 2-11 Flux - d r i v i n g force ... 23 2-12 S a l i n i t y p r o f i l e in t a n k / t r a y edge 25 2-13 S a l i n i t y p r o f i l e in the t r a y 26 2-15 Membrane volume f l u x vs. pressure 27 2-16 Diagram of i n t e r f a c e entrainment d e f i n i t i o n s 29 2-17 Entrainment at i n t e r f a c e of 2 - layer system 31 2-18 Time s e r i e s p l o t of i n t e r f a c e depth and mixed l a y e r s a l i n i t y 34 2-19 I n t e r f a c e depth vs. mixed l a y e r s a l i n i t y , and i n i t i a l s t r a t i f i c a t i o n 35 2-20 Entrainment by p e n e t r a t i v e c o n v e c t i o n 36 2- 21 P r o f i l e s and ice t h i c k n e s s - f i e l d data 39 Fig.3-1 Sketch of t y p i c a l shadowgraph p a t t e r n 42 3- 2 Sketch of downhi11/ups1 ope flow c e l l s 43 3-3 Mixed l a y e r t i m e - s e r i e s and l i n e a r f i t 52 v i 3-4 A c t u a l and a d j u s t e d s a l i n i t y p r o f i l e s 53 3-5 M i c r o - c e l l t i m e - s e r i e s - slope flow exp#3 54 3-6 S a l i n i t y r a t e of change in mixed l a y e r and bottm flow 56 3-7 Slope flow v e l o c i t y vs. s a l t f l u x 60 3-8 Flow v e l o c i t y vs. slope angle 61 3-9 Slope flow diagram 62 Fig.A-1 C o n d u c t i v i t y r a t i o vs. s a l i n i t y 77 A-2 Density vs. s a l i n i t y 78 Fig.B-1 Diagram of m i c r o - c e l l assembly 81 B-2 M i c r o - c e l l c onstants vs. temperature 85 B-3 T i m e - s e r i e s of m i c r o - c e l l c a l i b r a t i o n c o n s t a n t s ... 89 B-4 C e l l c a l i b r a t i o n c onstants vs. s a l i n i t y 90 B-5 Time response - experimental arrangement 91 B-6 M i c r o - c e l l time response - C#l t i m e - s e r i e s 96 B-7 M i c r o - c e l l time response - C#2 t i m e - s e r i e s 97 B-8 M i c r o - c e l l time response - C#3 t i m e - s e r i e s 98 B-9 M i c r o - c e l l response curve - C#l 99 B-10 M i c r o - c e l l response curve - C#2 100 B - l l M i c r o - c e l l response curve - C#3 101 B-12 R e s o l u t i o n in 2-layer system - 5 PSS 103 B-13 R e s o l u t i o n in 2-layer system - 0.5 PSS 104 Fig.C-1 Thermistors at m i c r o - c e l l i n l e t and o u t l e t 107 C-2 Thermistor c a l i b r a t i o n curve 113 v i i Flg.E-1 Membrane f l u x c a l i b r a t i o n - t i m e - s e r i e s 124 E-2 Membrane volume f l u x c a l i b r a t i o n before and a f t e r f i r s t slope flow experiment .... 125 E-3 Membrane volume f l u x c a l i b r a t i o n curves 126 Fig.F-1 M i c r o - c e l l t i m e - s e r i e s p l o t - experiment #1 ..... 131 F-2 S a l i n i t y p r o f i l e s - slope flow exp #1 132 F-3 T i m e - s e r i e s p l o t of p r o f i l e p o i n t s 133 F-4 Adjusted p r o f i l e s - slope flow exp#l 134 F-5 S a l i n i t y d i s t r i b u t i o n along the c e n t e r l l n e 135 F-6 T i m e - s e r i e s p l o t of d i s t r i b u t i o n data 136 Flg.F-7 M i c r o - c e l l t i m e - s e r i e s p l o t - experiment #2 139 F-8 Tim e - s e r i e s p l o t and l i n e a r f i t 140 F-9 S a l i n i t y p r o f i l e s - slope flow exp#2 141 F-10 T i m e - s e r i e s p l o t and l i n e a r f i t 142 F - l l S a l i n i t y p r o f i l e s - slope flow exp #2 143 Fig.F-12 M i c r o - c e l l t i m e - s e r i e s p l o t - experiment #3 146 F-13 T i m e - s e r i e s p l o t and l i n e a r f i t 147 F-14 S a l i n i t y p r o f i l e s - slope flow exp #3 148 Fig.F-15 S a l i n i t y p r o f i l e s - slope flow exp#4 151 F-16 S a l i n i t y p r o f i l e s - slope flow exp#4 152 F-17 S a l i n i t y d i s t r i b u t i o n along bottom slope 153 v i i i Fig .F-18 M i c r o - c e l l t ime-series plot - experiment #5 156 F-19 S a l i n i t y p r o f i l e s - slope flow exp#5 157 F-20 S a l i n i t y p r o f i l e s - slope flow exp#5 158 Fig.F-21 M i c r o - c e l l t ime-series plot - experiment #6 163 Fig .F-22 M i c r o - c e l l t ime-series plot - experiment #7 166 F-23 S a l i n i t y p r o f i l e s - slope flow exp#7 167 F-24 S a l i n i t y p r o f i l e s - slope flow exp#7 168 F-25 S a l i n i t y p r o f i l e s - slope flow exp#7 169 Fig .F-26 Arrangement of micro-ce l l s - experiment #8 170 F-27 M i c r o - c e l l t ime-series plot - experiment #8 172 F-28 Expanded t ime-series and curve f i t 173 F-29 S a l i n i t y p r o f i l e s - slope flow exp#8 174 F-30 S a l i n i t y p r o f i l e s - slope flow exp#8 175 F-31 S a l i n i t y p r o f i l e s - slope flow exp#8 176 i x L I S T OF PHOTOS P h o t o 1. E x p e r i m e n t a l t a n k and t r a y 5 P h o t o 2. S h a d o w g r a p h image o f s l o p e f l o w 8 P h o t o 3. I n t e r f a c e e n t r a i n m e n t 28 P h o t o 4. Dye i n t h e m i x e d l a y e r a n d s l o p e f l o w ... 45 P h o t o 5. V e l o c i t y maxima i n dye 46 P h o t o 6. Dye a t s h a l l o w end o f t a n k 47 P h o t o 7. B i f u r c a t i o n i n s l o p e f l o w 48 P h o t o 8. Waves i n dye a t l o w e r e nd o f s l o p e 49 P h o t o 9. Dye i n s t a b l y s t r a t i f i e d r e g i o n 49 P h o t o 10. Dye and s h a d o w g r a p h 162 x L I S T OF TABLES T a b l e 2.0 M i c r o - c e l l c a l i b r a t i o n c o n s t a n t K 13 2.1 E n t r a i n m e n t i n 2 - l a y e r s y s t e m 32 2.2 E n t r a i n m e n t In l i n e a r s t r a t i f i c a t i o n . .. 33 2.3 E n t r a i n m e n t f r o m A r c t i c f i e l d d a t a 38 T a b l e 3.1 S t a r t i n g c o n d i t i o n s f o r s l o p e f l o w e x p e r i m e n t s .. 41 3.2 C o m p i l e d r e s u l t s f r o m s l o p e f l o w e x p e r i m e n t s .... 58 T a b l e B l . M i c r o - c e l l c a l i b r a t i o n c o n s t a n t s 87 T a b l e C l . T h e r m i s t o r c a l i b r a t i o n c o n s t a n t s 109 T a b l e D l . C l o c k b o a r d edge c o n n e c t o r p i n f u n c t i o n s 117 T a b l e D2. M u l t i p l e x e r i n p u t c h a n n e l c y c l i n g p a t t e r n 117 T a b l e F I . S a l t f l u x e s a n d f l o w v e l o c i t i e s - s l o p e r u n # l ... 130 F 2 . F l o w v e l o c i t i e s f r o m p h o t o s - s l o p e r u n # 2 137 F 3 . S a l i n i t y o f t r a y f l u i d - s l o p e r u n # 2 138 F 4 . S a l t f l u x e s and f l o w v e l o c i t i e s - s l o p e r u n # 2 .... 139 F 5 . F l o w v e l o c i t i e s f r o m p h o t o s - s l o p e r u n # 3 145 F 6 . S a l t f l u x e s a n d f l o w v e l o c i t i e s - s l o p e r u n # 3 ... 145 F 7 . S a l i n i t i e s i n t h e t r a y - s l o p e r u n # 4 149 F 8 . S a l t f l u x e s and f l o w v e l o c i t i e s - s l o p e r u n # 4 ... 150 F 9 . S a l i n i t i e s i n t h e t r a y d u r i n g s l o p e r u n # 5 154 F 1 0 . F l o w v e l o c i t i e s a n d s a l t f l u x e s - s l o p e r u n # 5 ... 156 F l l . S l o p e f l o w v e l o c i t i e s - s l o p e r u n # 6 160 F 1 2 . S a l i n i t i e s l n t r a y a n d t a n k - s l o p e r u n # 6 161 F 1 3 . F l o w v e l o c i t i e s and s a l t f l u x e s - s l o p e r u n # 6 ... 162 F14. F l o w v e l o c i t y a n d s a l t f l u x - s l o p e r u n # 7 165 x i ACKNOWLEDGEMENTS The a u t h o r i s g r a t e f u l t o D r . D. R. Topham o f t h e I n s t i t u t e o f Ocean S c i e n c e s i n S i d n e y , who s u g g e s t e d t h i s p r o b l e m and p r o v i d e d t h e r e q u i r e d e q u i p m e n t , a d v i c e a n d much o f t h e f u n d i n g f o r t h e e x p e r i m e n t a l w o r k , a nd t o Dr P.H. L e B l o n d o f U.B.C. who p r o v i d e d e n c o u r a g e m e n t , f u r t h e r f u n d i n g a n d t h e a c a d e m i c a d v i c e r e q u i r e d t o s u c c e s s f u l l y c o m p l e t e t h e p r o j e c t . The l a t e R.B. S u d a r p r o v i d e d i n v a l u a b l e g u i d a n c e i n t h e d e v e l o p m e n t o f t h e s a l i n i t y measurement s y s t e m . S p e c i a l t h a n k s a l s o g o e s t o t h e t e c h n i c a l s t a f f o f t h e F r o z e n S e a s g r o u p o f Ocean P h y s i c s a t t h e I n s t i t u t e o f Ocean S c i e n c e s i n S i d n e y , B.C. who h e l p e d t o g e t t h e e x p e r i m e n t a l s y s t e m o p e r a t i o n a l . T h i s work was p a r t i a l l y f u n d e d u n d e r G o v e r n m e n t o f Canada c o n t r a c t s n r . F P 9 4 1 - 4 - 1 9 1 9 a nd F P 9 4 1 - 5 - 1 2 9 0 . x i i 1 - INTRODUCTION 1.1 A r c t i c subsurface i n t r u s i o n s and slope flow T y p i c a l oceanographic p r o f i l e s taken d u r i n g winter of the s a l i n i t y and temperature under the ice in the Beaufort Sea (see f i g u r e 1-1) show a well-mixed s u r f a c e l a y e r extending to depths of up to 50 meters. This l a y e r i s i s o t h e r m a l , near the f r e e z i n g p o i n t , and i s o h a l i n e due to c o n v e c t i v e o v e r t u r n i n g caused by the e x p u l s i o n of s a l t at the ice/water i n t e r f a c e from the ice that forms as sea water f r e e z e s . The subsurface l a y e r below t h i s c o n t a i n s the p y c n o c l i n e where a la r g e increase in s a l i n i t y g e n e r a l l y i s accompanied by a small r i s e in temperature. Below the thermocllne there i s gradual mixing with water of A t l a n t i c o r i g i n to form the A r c t i c Deep Water. In many of the p r o f i l e s , i n t r u s i o n s i n to t h i s sub-surface l a y e r were found of up to 30 meters in t h i c k n e s s , c h a r a c t e r i z e d by temperature minima (see f e a t u r e 'a' in f i g u r e 1-1). T h i s c o l d e r water most l i k e l y was formed as a c o n v e c t i v e l y mixed su r f a c e l a y e r in some other l o c a t i o n where water at the s u r f a c e had a higher s a l i n i t y or where a f a s t e r f r e e z i n g r a t e caused a higher s a l t f l u x . The c o l d e r and s a l t i e r water moved to the depth of i n t r u s i o n where i t was found at the p r o f i l i n g s t a t i o n p o s s i b l y as a slope c u r r e n t or s h e l f drainage flow. Such slope flows c o u l d be the cause of c o l d water i n t r u s i o n s p e n e t r a t i n g out into the A r c t i c Ocean at depths up to 200 meters (see P e r k i n and Lewis (1979), M e l l i n g and Lewis (1982)). 1 -Q TJ -2 0 2 0 -\ 4 0 6 0 8 0 U J f v ID to 1 0 0 u cr CL 120 14 0 - 160 T E M P . ° C . 1 32.7 temperatures STATION: 0 9 T S 29-11-79 30 31 32 — r ~ 33 34 35 S A L I N I T Y F i g u r e 1-1. T y p i c a l A r c t i c p r o f i l e s in winter (Frozen Seas Research Group, IOS) As sea water f r e e z e s , some of the s a l t i s e x p e l l e d immedia- t e l y from the ice which forms. Subsequently, more s a l t d r a i n s as b r i n e from a system of d e n d r i t i c channels that develops in the i c e . The i n f l u x of s a l t causes a d e n s i t y increase at the ice/seawater i n t e r f a c e and r e s u l t s in c o n v e c t i v e o v e r t u r n i n g of the water column below the i c e . Laboratory s t u d i e s by F o s t e r (1969) and by E l l i o t t (1972) looked at h a l i n e c o n v e c t i o n under sea i c e . The r e j e c t e d s a l t was seen to form a p a t t e r n of plumes or streamers with downward v e l o c i t i e s ranging from 0.09 to 0.23 cm/s f o r ice growth r a t e s from 0.3 to 7.8 cm/day. A 2 f i e l d study of s a l t r e j e c t i o n by sea ice du r i n g growth i s d e s c r i b e d by Lake and Lewis (1970). In shallow seas, such as p a r t s of the Beaufort Sea in the Canadian A r c t i c , the c o n v e c t i - vely mixed l a y e r which i s d r i v e n by f r e e z i n g may extend to the bottom. The d e n s i t y in t h i s l a y e r w i l l vary with the amount of s a l t f l o w i n g into i t and with the depth into which i t i s mixed. An uneven s a l t f l u x or a bottom slope w i l l c r e a t e h o r i z o n t a l g r a d i e n t s in the d e n s i t y which in turn can cause a downslope c u r r e n t along the bottom and i n t r u s i o n s at l e v e l s below that of normal mixing from s u r f a c e e f f e c t s ; compensating c u r r e n t s w i l l occur at higher l e v e l s . 1.2 L a b o r a t o r y s t u d y A s e r i e s of l a b o r a t o r y experiments was conducted under the aus p i c e s of the Ocean P h y s i c s Group at the I n s t i t u t e of Ocean Sciences in Sidney, B r i t i s h Columbia, to examine under c o n t r o l - l e d c o n d i t i o n s and on a small s c a l e , slope flows induced by a surf a c e s a l t f l u x over a s l o p i n g bottom. Slope flows were observed in each of the experiments, which were conducted in a p l e x i g l a s s tank with the bottom set at some small slope angle. The su r f a c e s a l t f l u x was simulated by slow p e r c o l a t i o n of s a l t water through a membrane into the tank, and a simple f o r m u l a t i o n was developed to o b t a i n estimates of the magnitude of the s a l t f l u x e s which generated and maintained the observed slope flows. Shadowgraph images and dye were used to v i s u a l i z e f l u i d motions in the c o n v e c t i v e l y mixed l a y e r and to determine v e l o c i t i e s in the slope flow. A s e r i e s of m i c r o - c e l l s 3 were d e v e l o p e d t o o b t a i n t h e e l e c t r i c a l c o n d u c t i v i t y o f f l u i d w i t h d r a w n f r o m p o i n t s i n t h e t a n k . The t e m p e r a t u r e s o f f l u i d i n t h e m i c r o - c e l l a nd i n t h e e x p e r i m e n t a l t a n k , d e t e r m i n e d w i t h m i c r o - b e a d t h e r m i s t o r s , were c o m b i n e d w i t h t h e c o n d u c t i v i t y t o compute t h e s a l i n i t y a n d d e n s i t y o f t h e f l u i d ( a p p e n d i x A ) . P a t t e r n s o f m o t i o n s i n s h a d o w g r a p h s show t h e s l o p e f l o w and a w e a k e r o p p o s i t e f l o w i n t h e m i x e d l a y e r . Movement o f i n j e c t e d dye shows a v e l o c i t y d i s t r i b u t i o n i n t h e s l o p e f l o w w i t h a peak o f 0.09 t o 0.66 cm/s a t a b o u t 0.5 cm above t h e b o t t o m . S a l i n i t y p r o f i l e s i n d i c a t e s l o p e f l o w d e p t h s o f 7 t o 17 mm i n w h i c h t h e s a l i n i t y r i s e s 0.24 t o 0.92 p p t a b o v e t h a t i n t h e c o n v e c t i v e l y m i x e d l a y e r . E s t i m a t e s o f s a l t f l u x e s i n t h e s e e x p e r i m e n t s r a n g e d f r o m 1.82e-5 t o 1.63e-6 g/cm'/s. The n o t a t i o n (e+n) i s u s e d i n t h e f o l l o w i n g s e c t i o n s t o d e n o t e ( 1 0 t o t h e p o w e r t n ) . The c o m p u t e d s a l t f l u x e s t i m a t e s were s e v e r a l o r d e r s o f m a g n i t u d e l a r g e r t h a n t h o s e f o u n d i n A r c t i c f i e l d d a t a , b u t m i x i n g d e p t h s were s e v e r a l o r d e r s s m a l l e r . The b u o y a n c y v e l o c i t y s c a l e W*, w h i c h c a n be u s e d t o c h a r a c t e r i z e c o n v e c t i o n , was t h e r e f o r e n e a r l y t h e same i n b o t h c a s e s . When t h e s l o p e f l o w was c o n s i d e r e d a s a t u r b u l e n t g r a v i t y c u r r e n t , e n t r a i n m e n t f a c t o r s c a l c u l a t e d by i n s e r t i n g d a t a f r o m t h i s s e r i e s o f s l o p e f l o w e x p e r i m e n t s were up t o two o r d e r s o f m a g n i t u d e l a r g e r t h a n t h o s e p r e d i c t e d f o r a q u i e s c e n t e n v i r o n - ment. T h i s i s a l s o c o n t r a r y t o e v i d e n c e f r o m t h e e x p e r i m e n t s a n d t o A r c t i c f i e l d d a t a w h i c h show t h a t s u c h f l o w s m a i n t a i n t h e i r c h a r a c t e r i s t i c s o v e r g r e a t d i s t a n c e s f r o m t h e s o u r c e . 4 2 - EXPERIMENTAL METHODS 2.1 Tank a n d t r a y a r r a n g e m e n t A s e r i e s of l a b o r a t o r y e x p e r i m e n t s was c o n d u c t e d i n a t ank made of 12 mm t h i c k p l e x i g l a s s . The i n s i d e d i m e n s i o n s were 8 7 . 5 cm l o n g , 23cm wide and 25cm deep (see photo 1 and f i g u r e 2 - 1 ) . The tank was r a i s e d a t one end to c r e a t e a s l o p i n g bot tom and was p a r t l y f i l l e d w i t h a m i x t u r e of f r e s h and sea w a t e r . Photo 1. E x p e r i m e n t a l tank and t r a y A t r a y was suspended l e v e l w i t h the s u r f a c e of the f l u i d i n the t a n k , and the e x p u l s i o n of s a l t from sea i ce was s i m u l a t e d by a s low seepage of h i g h e r s a l i n i t y water t h r o u g h the bot tom of t h i s t r a y . The t r a y bot tom c o n s i s t e d of a porous membrane (a M l l l l p o r e f i l t e r membrane, 0 .8 m i c r o m e t e r pore s i z e ) mounted between two l a y e r s of f i b e r g l a s s c i r c u i t b o a r d s , w i t h a l i g n e d p e r f o r a t i o n s . The t r a y was f i l l e d w i t h sea water to s e v e r a l 5 m i l l i m e t e r s above t h e h e i g h t t o w h i c h l e v e l l i n g s l o t s i n t h e s i d e s were t a p e d s h u t . I n some o f t h e e x p e r i m e n t s p u r e s e a s a l t was a d d e d t o i n c r e a s e t h e s a l t f l u x . When t h e h i g h s a l i n i t y f l u i d p e r c o l a t e s t h r o u g h t h e membrane i n t o t h e t a n k t h i s c a u s e s an e q u a l r e t u r n f l o w o f t h e l i g h t e r f l u i d t o t h e t r a y . A s m a l l pump was u s e d t o s t i r t h e f l u i d i n t h e t r a y , a n d e x c h a n g e i t w i t h t h a t i n a b a c k - u p r e s e r v o i r t o h e l p m a i n t a i n t h e h i g h e r s a l i n i t y i n t h e t r a y . The v o l u m e s o f f l u i d i n t a n k , t r a y a n d r e s e r v o i r were k e p t c o n s t a n t d u r i n g e a c h r u n and t h e s y s t e m i s s e l f - l e v e l l i n g . A s e r i e s o f 6 cm l o n g c o p p e r t u b e s o f 1.6 mm i n s i d e d i a m e t e r were mounted t h r o u g h t h e membrane i n t h e b o t t o m o f the t r a y , a t 10 cm i n t e r v a l s a l o n g t h e c e n t r e l i n e , s t a r t i n g 7.5 cm f r o m t h e s h a l l o w e n d o f t h e t a n k . These a c c e s s t u b e s o r p o r t s #1 t o #8, numbered f r o m t h e s h a l l o w end o f t h e t a n k , were u s e d t o i n j e c t dye o r t o w i t h d r a w f l u i d f r o m v a r i o u s l o c a t i o n s and d e p t h s i n t h e t a n k t h r o u g h c o n d u c t i v i t y m i c r o - c e l l s t o d e t e r m i n e s a l i n i t y a n d d e n s i t y. F i g u r e 2-1 shows a d i a g r a m o f t h e a r r a n g e m e n t o f t h e t a n k , t h e t r a y w i t h t h e s a m p l i n g t u b e s and l e v e l l i n g s l o t s , t h e added r e s e r v o i r , and t h e c i r c u l a t i o n pump u s e d t o mix t r a y f l u i d and e x c h a n g e i t w i t h t h a t i n t h e r e s e r v o i r . The m i c r o - c e l l s a r e shown w i t h o u t t h e s m a l l pumps w h i c h r e t u r n t h e s y p h o n e d f l u i d t o t a n k a n d t r a y t o m a i n t a i n c o n s t a n t l e v e l s . 6 reservoir F i g u r e 2-1. A p p a r a t u s f o r s l o p e f l o w e x p e r i m e n t s . 2.2 F l o w v i s u a l i z a t i o n L i g h t f r o m a s o u r c e p l a c e d a t a d i s t a n c e b e h i n d t h e t a n k was f o c u s e d by c y l i n d r i c a l l e n s e s i n t o a n e a r l y p a r a l l e l beam ( s e e f i g u r e 2 - 2 ) . T h i s beam was p r o j e c t e d t h r o u g h t h e s i d e o f t h e t a n k o n t o a t r a n s l u c e n t m y l a r f i l m on t h e o p p o s i t e s i d e t o f o r m s h a d o w g r a p h Images. c a m e r a C a p p r o x i m a t e l y 7 m e t e r s t a n k c r o s s - s e c t i on i i i a r ID] a d p r o j e c t o r s l o t c y 1 i n d r l e n s e s t r a n s p . f i l m F i g u r e 2-2. D i a g r a m o f a r r a n g e m e n t f o r s h a d o w g r a p h s 7 D u r i n g the e x p e r i m e n t s , v a r i a t i o n s i n the r e f r a c t i v e index due c o n v e c t i v e o v e r t u r n i n g formed p a t t e r n s of w r i n k l e d l i n e s i n the shadowgraph image. The mean c i r c u l a t i o n p a t t e r n c r e a t e d by the bot tom s l o p e f l o w and the c o m p e n s a t i n g f l o w i n the mixed l a y e r were v i s i b l e as d e f l e c t i o n s i n the l i n e p a t t e r n s (see photo 2). The image r e p r e s e n t s the m o t i o n s of s m a l l s t r e a m e r s or p a r c e l s of f l u i d , i n t e g r a t e d o v e r the w i d t h of the tank and t h e r e f o r e can not show any c r o s s - s e c t i o n a l c i r c u l a t i o n p a t t e r n s . Photo 2. Shadowgraph image of s l o p e f l o w The s l o p e f l o w was a l s o v i s u a l i z e d by i n j e c t i n g d y e , w h i c h was d i l u t e d w i t h f l u i d from the mixed l a y e r i n an a t t e m p t to match the s l o p e f l o w d e n s i t y . The dye was i n j e c t e d t h r o u g h one of the s a m p l i n g tubes a l o n g the c e n t e r l i n e of the t r a y . W h i l e some of the dye was e n t r a i n e d i n the c o n v e c t i v e m o t i o n s as i t sank t h r o u g h the mixed l a y e r , most of i t was c a r r i e d a l o n g as S dye s t r e a k s i n t h e s l o p e f l o w . The f l o w v e l o c i t i e s a t d i f f e r e n t s l o p e a n g l e s o v e r a r a n g e o f s a l t f l u x e s were d e t e r m i n e d f r o m t h e d i s t a n c e t h a t t h e dye moved i n a known t i m e i n t e r v a l i n p h o t o and s l i d e s e q u e n c e s o r on v i d e o t a p e f o o t a g e . 2.3 Instrumentation f o r d e n s i t y d e t e r m i n a t i o n S e v e r a l s m a l l - v o l u m e c o n d u c t i v i t y c e l l s were d e v e l o p e d f o r s a l i n i t y d e t e r m i n a t i o n and u s e d i n c o m b i n a t i o n w i t h t h e r m i s t o r s t o o b t a i n a q u a n t i t a t i v e d e s c r i p t i o n o f f l u i d d e n s i t i e s i n the s l o p e f l o w s a nd i n t h e c o n v e c t i v e l y m i x e d l a y e r . The d a t a were t a k e n m a n u a l l y o r w i t h a d a t a l o g g e r and p r o c e s s e d u s i n g a d e s k - t o p c o m p u t e r . 2.3.1 T h e r m i s t o r s and m i c r o - c e l l s To d e t e r m i n e t h e e l e c t r i c a l c o n d u c t i v i t y o f f l u i d t a k e n f r o m d i f f e r e n t p o i n t s i n t h e e x p e r i m e n t a l t a n k , c o n d u c t i v i t y m i c r o - c e l l s were d e v e l o p e d w i t h a s m a l l i n t e r n a l volume o f a b o u t 0.15 ml ( f i g u r e 2 - 3 ) . F l u i d was s a m p l e d by s y p h o n i n g i t f r o m a p o i n t i n t h e t a n k o r t r a y t h r o u g h one o f t h e m i c r o - c e l l s . The m i c r o - c e l l s c o n s i s t e d o f f o u r p l a t i n u m f o i l e l e c t r o d e r i n g s ( o f 3 mm d i a m e t e r by 5 mm l o n g ) s e p a r a t e d by s e g m e n t s o f g l a s s t u b i n g ( o f 1.8 mm i n s i d e a nd 3.0 mm o u t s i d e d i a m e t e r ) . M i c r o - b e a d t h e r m i s t o r s were i n s e r t e d i n t h e f l o w a t t h e i n l e t a n d o u t l e t o f e a c h m i c r o - c e l l . The a v e r a g e o f t h e tempe- r a t u r e s d e t e r m i n e d f r o m t h e i r r e s i s t a n c e s was c o m b i n e d w i t h t h e c o n d u c t i v i t y r a t i o t o c a l c u l a t e t h e s a l i n i t y u s i n g t h e p o l y n o - m i a l s o f t h e P r a c t i c a l S a l i n i t y s c a l e ( s e e a p p e n d i x A l ) . 9 The d e n s i t y o f t h e f l u i d a t t h e i n t a k e p o i n t i n t h e t a n k was c o m p u t e d by c o m b i n i n g t h i s s a l i n i t y w i t h t h e t e m p e r a t u r e f r o m a n o t h e r t h e r m i s t o r l o c a t e d i n t h e t a n k u s i n g t h e p o l y n o m i a l s o f t h e U n e s c o e q u a t i o n o f S t a t e f o r s e a w a t e r ( a p p e n d i x A 2 ) . S t a b l e a n d r e p e a t a b l e r e a d i n g s were o b t a i n e d w i t h c o n t i n u o u s s l o w s y p h o n i n g o f f l u i d t h r o u g h t h e m i c r o - c e l l s . The low r a t e o f w i t h d r a w a l f r o m a p o i n t l n t h e t a n k d i d n o t p e r c e p t i b l y i n f l u e n c e t h e g e n e r a l f l o w p a t t e r n s . D i m e n s i o n s a nd a s s e m b l y d e t a i l s o f t h e c e l l s a r e d e s c r i b e d i n a p p e n d i x B. NEEDLE F i g u r e 2-3. M i c r o - c e l l w i t h t h e r m i s t o r s One c e l l was mounted on a v e r t i c a l t r a v e l l e r w h i c h was moved a l o n g a t r a c k o v e r t h e t a n k t o one o f t h e s a m p l i n g t u b e s s p a c e d a l o n g t h e c e n t e r l l n e i n t h e t r a y . D a t a p o i n t s f o r s a l i n i t y 10 p r o f i l e s of f l u i d in the tank were obtained by lowering the t i p of the intake tube to successive depths. A second c e l l was used for simultaneous readings at a f ixed depth in the convect ive ly mixed layer to determine the change ln background s a l i n i t y and the t h i r d c e l l was used to monitor the slow change in tray s a l i n i t y . F l u i d was syphoned through the c e l l s at a f ixed rate of 0.05-0.15 ml/s (1 to 3 drops / sec ) . A small pump with two pump-heads was used to return f l u i d from the out le t s of d i f f e - rent c e l l s to the tray and to the tank to maintain the f ixed f l u i d l eve l s and volumes used to ca lcu la te the sa l t f luxes , as shown ln figure 2-4. t— Figure 2-4. M i c r o - c e l l s in experiments 1 1 2.3.2 Ca l i b r a t i o n of c e l l constants The e l e c t r i c a l c o n d u c t i v i t y in the m i c r o - c e l l s changes with the s a l i n i t y of the f l u i d . An e l e c t r o n i c c i r c u i t was designed so the output voltage (VC) was a l i n e a r f u n c t i o n of the micro- c e l l conductance (1/R) f o r f l u i d of a gi v e n temperature and s a l i n i t y . A c e l l constant (K) was expressed in ohms r e s i s t a n c e of the c e l l at S = 35 PSS and T=15 °C. The c o n d u c t i v i t y r a t i o (RR) i s then computed from the m i c r o - c e l l output voltage as the product of conductance and c e l l c o n s t a n t : (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 l e a s t squares l i n e a r f i t through output v o l t a g e s f o r . a s e r i e s of high accuracy standard res i s t o r s . In a number of the experiments an A p p l i e d Microsystems C/T da t a l o g g e r was used to take m i c r o - c e l l and t h e r m i s t o r readings (see s e c t i o n 2.4)-. It was found that the d i f f e r e n t c u r r e n t s and v o l t a g e s used by the i n t e r n a l c o n d u c t i v i t y c i r c u i t to d r i v e the m i c r o - c e l l s r e q u i r e d d i f f e r e n t values f o r the constants A and B and f o r the c e l l constant K to c a l c u l a t e the c o n d u c t i v i t y r a t i o from the dat a l o g g e r numbers (NC): (2.3) RR = K ' . ( R ' t B ' . N C ) A'= 5.53084e-5 B'= 1.3290e-7 The c e l l c o n s t a n t s were chosen as those i n t e g e r values f o r which the s a l i n i t y of a f l u i d sample, c a l c u l a t e d from the m i c r o - c e l l c o n d u c t i v i t y r a t i o and temperature, was c l o s e s t to 12 the value determined with a G u i l d l i n e A u t o s a l . This c a l i b r a t i o n was f r e q u e n t l y repeated to ensure that no s h i f t s had occurred due to aging or e l e c t r o d e f o u l i n g . The average values of the c a l i b r a t i o n constant f o r each of the m i c r o - c e l l s are l i s t e d in t a b l e 2.0 below (see appendix B t a b l e B . l f o r d e t a i l s ) . Table 2.0 M i c r o - c e l l c a l i b r a t i o n constant K C a l i b r a t i o n constant K for: Cel1#1 Cel1#2 Cel 1#3 f o r the AM/CT d a t a l o g g e r : ( s t d . dev. f o r 18 samples) f o r separate c o n d . c i r c u i t : (std.dev. f o r 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 c h a r a c t e r i s t i c s As the s a l i n i t y changes at the intake to a m i c r o - c e l l , an amount of f l u i d must pass through the intake tubing and the c e l l to f l u s h i t , before a r e a d i n g i s taken. The time response to a sudden change in s a l i n i t y at the intake p o i n t was d e t e r m i - ned f o r each of the c e l l s , at flow r a t e s ranging from about 1 to 3 drops per second (or 0.05 to 0.15 ml/s) and f o r s a l i n i t y steps between 0.5 to 5 PSS. To o b t a i n t y p i c a l response curves f o r the m i c r o - c e l l s the r e s u l t s were normalized by p l o t t i n g the change in the s a l i n i t y as a f r a c t i o n of the t o t a l s a l i n i t y step a g a i n s t the volume r e q u i r e d , which is the product of flow r a t e and time. For these syphon flow r a t e s , the volume to f l u s h the intake t ubing and the m i c r o - c e l l was found to be about 4 ml. The r e s u l t s are shown in f i g u r e 2-5. 13 MICRO-CELL TIME RESPONSE Fiqure 2~5. Volume required to flush the c e l l 2.3.4 S p a t i a l r e s o l u t i o n The f l u i d syphoned from the i n t a k e p o i n t to the m i c r o - c e l l can be c o n s i d e r e d as a p o i n t s i n k i n a f l o w , and the c a l c u l a t e d s a l i n i t y i s an average of f l u i d drawn from a s m a l l r e g i o n . Some measure of the s p a t i a l r e s o l u t i o n i s then the e x t e n t to which a sharp i n t e r f a c e appears b l u r r e d i n a s a l i n i t y p r o f i l e . A t w o - l a y e r f l u i d system w i t h a sharp d e n s i t y i n t e r f a c e was o b t a i n e d by p a r t l y f i l l i n g a c o n t a i n e r w i t h d i l u t e d sea water, then s l o w l y p i p i n g water of a h i g h e r s a l i n i t y to the bottom and s h a r p e n i n g the i n t e r f a c e by syphoning f l u i d from a p o i n t j u s t below i t . The i n t e r f a c e was v i s i b l e as a b r i g h t l i n e i n a shadowgraph. F l u i d was then syphoned t h r o u g h the m i c r o - c e l l a t a f i x e d f l o w r a t e of about 2 drops per second and r e a d i n g s were t a k e n a f t e r 30 seconds a t s u c c e s s i v e c l o s e l y spaced d e p t h s . For such t w o - l a y e r systems w i t h a s t e p i n s a l i n i t y between 0.5 and 5 p p t , s a l i n i t y p r o f i l e s p l o t t e d from d a t a t a k e n a c r o s s the i n t e r f a c e show a s e t of d i s t i n c t s t e p s over a few m i l l i - meters of depth ( f i g u r e 2-6). A d e t a i l e d d e s c r i p t i o n of the d i m e n s i o n s and assembly of the m i c r o - c e l l s , c a l i b r a t i o n of the c e l l c o n s t a n t s and e l e c t r o n i c s , the time response c h a r a c t e r i s t i c s and the s p a t i a l r e s o l u t i o n i s g i v e n i n 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 c e l l : abt. 3 dr/aec R e s o l u t i o n of i n t e r f a c e i n 2 ~ l a y e r s y s t jystem 1— riqure 2-6. M i c r o - c e l l spa-tial r e s o l u t i o n 16 2.4 Data a c q u i s i t i o n I n t h e i n i t i a l t e s t s , a s m a l l c o n d u c t i v i t y c i r c u i t was u s e d w i t h a s w i t c h t o power e a c h m i c r o - c e l l In t u r n . The o u t p u t v o l - t a g e f r o m t h i s c i r c u i t and t h e r e s i s t a n c e s o f t h e t h e r m i s t o r s were r e a d f r o m a s e t o f d i g i t a l v o l t m e t e r s ( D V M 's). The numbers were e n t e r e d v i a t h e k e y b o a r d i n t o an HP-9825 d e s k t o p c o m p u t e r , w h i c h was p r o g r a m e d t o a p p l y t h e c a l i b r a t i o n r e l a t i o n s f o r t h e t h e r m i s t o r s a n d m i c r o - c e l l s t o t h e d a t a , p r i n t t h e raw d a t a a n d co m p u t e d v a l u e s , p l o t s e l e c t e d p a r a m e t e r s a n d s t o r e t h e d a t a on m a g n e t i c t a p e ( s e e f i g u r e 2 - 8 ) . SWITCH MICRO-CELL ELECTRONICS EXPERIMENTAL TANK 1 VC" DVM RT" D V M TAPP HP-7225 PLOTTER HP-9825 COMPUTER L I N E PRINTER F i g u r e 2-8. D a t a a c q u i s i t i o n - manual i n p u t I n most o f t h e e x p e r i m e n t s , t h e m i c r o - c e l l s a n d t h e r m i s t o r s were i n t e r f a c e d v i a an A p p l i e d M i c r o s y s t e m s (AM/CT) d a t a l o g g e r t o t h e HP-9825. The d a t a l o g g e r i n t e r n a l c o n d u c t a n c e c i r c u i t was m o d i f i e d f o r use w i t h t h e m i c r o - c e l l s . The d i f f e r e n t d r i v i n g v o l t a g e and s e n s i n g c u r r e n t u s e d by t h i s c i r c u i t r e q u i r e d s e p a r a t e m i c r o - c e l l c a l i b r a t i o n c o n s t a n t s ( s e e s e c t i o n 2 . 3 . 2 ) . The AM/CT d a t a l o g g e r c o u l d be t r i g g e r e d m a n u a l l y o r a t a s e t c l o c k i n t e r v a l t o c y c l e t h r o u g h a l l s e n s o r s a n d t h e n t r a n s m i t 17 t h e d a t a v i a a s e r i a l c o n v e r t e r a n d an RS-232 i n t e r f a c e module t o t h e HP-9825 c o m p u t e r ( s e e f i g u r e 2 - 9 ) . The s a l i n i t y r a n g e o f t h e AM/CT d a t a l o g g e r was l i m i t e d a n d when t h e c o n d u c t i v i t y o f t h e t r a y f l u i d was o u t o f r a n g e , t h e s e p a r a t e s m a l l c i r c u i t was u s e d w i t h t h e DVM's. T-TNK y EXPERIMENTAL TANK AM/CT DATA LOGGER S E R I A L CONVERTER RS-232 TAPE HP-9825 COMPUTER HP-7225 PLOTTER 1 HP-LINE PRINTER F i g u r e 2-9. D a t a a c q u i s i t i o n : AM/CT d a t a l o g g e r I n t h e l a s t s e v e r a l e x p e r i m e n t s an HP-3497A D a t a A c q u i s i t i o n S y s t e m was u s e d , c o m b i n e d w i t h a s e p a r a t e c o n d u c t i v i t y c i r c u i t f o r e a c h m i c r o - c e l l . T h i s a l l o w e d a more r a p i d s a m p l i n g r a t e , a u t o m a t i c a v e r a g e s o f m u l t i p l e r e a d i n g s f o r e a c h s e n s o r c i r c u i t (5 r a p i d r e a d i n g s were t a k e n o f e a c h s e n s o r ) , and a l s o showed l e s s v a r i a b i l i t y b e c a u s e t h e c e l l s were c o n t i n u o u s l y p o w e r e d . Some s m a l l s h i f t s were f o u n d i n d a t a s e q u e n c e s f r o m e x p e r i m e n t s and l a t e r t e s t i n g r e v e a l e d t h a t any s h i f t l n r e l a t i v e p o s i t i o n o f t h e m i c r o - c e l l o u t l e t t u b e s c o u l d c a u s e a c h a n g e i n a p p a r e n t c o n d u c t i v i t y . D a t a o b t a i n e d w i t h t h i s a r r a n g e m e n t ( f i g u r e 2-10) p r o v i d e d t h e most d e t a i l e d p r o f i l e s o f d e n s i t y d i s t r i b u t i o n i n th e s l o p e f l o w . 18 CIRCUIT "A" CIRCUIT "B" CIRCUIT "C" C#l t : C#2 C#3 Z Z f c J T-TNK J EXPERIMENTAL TANK CONDUCTIVITY ELECTRONICS HP-7225 PLOTTER HP-3497A DATA ACQUISITION SYSTEM TAPE HP-9825 COMPUTER L I N E PRINTER F i g u r e 2-10. D a t a a c q u i s i t i o n : HP-3497A S y s t e m The raw d a t a f r o m e a c h s e n s o r c i r c u i t a n d t h e c o m p u t e d v a l u e s o f t e m p e r a t u r e s , c o n d u c t i v i t y r a t i o , s a l i n i t y and d e n s i t y f o r e a c h o f t h e c e l l s were p r i n t e d on a l i n e - p r i n t e r and s a v e d on m a g n e t i c t a p e . D e p t h s o f t h e m i c r o - c e l l i n t a k e d u r i n g p r o f i l i n g were m a n u a l l y s e t and n o t e d on t h e p r i n t - o u t . The s a l i n i t y t i m e s e r i e s p o i n t s were p l o t t e d d u r i n g e a c h e x p e r i m e n t . P r o f i l e s o f s a l i n i t y i n t h e t a n k were l a t e r p l o t t e d f r o m t h e s e d a t a , a s i s d e s c r i b e d w i t h t h e e x p e r i m e n t a l r e s u l t s ( I n s e c t i o n 3 ) . 2.5 E x p e r i m e n t a l p r o c e d u r e S e a w a t e r was m i x e d w i t h t a p w a t e r i n one t a n k t o c r e a t e low s a l i n i t y f l u i d f o r t h e e x p e r i m e n t a l t a n k , a nd s a l t was a d d e d t o s e a w a t e r i n a n o t h e r t a n k f o r t h e h i g h s a l i n i t y f l u i d u s e d i n t r a y a n d r e s e r v o i r i n some r u n s . The f l u i d s were pumped t o t h e e x p e r i m e n t a l t a n k o r t o r e s e r v o i r and t r a y - f i l l i n g p a i l t h r o u g h a 0.8 m i c r o n f i l t e r t o remove most o r g a n i c m a t t e r and were l e f t 19 f o r a t l e a s t one day t o s t a b i l i z e a t a m b i e n t room t e m p e r a t u r e , a n d t o d e - g a s t o a v o i d t h e f o r m a t i o n o f b u b b l e s on t h e s e n s o r s u r f a c e s w h i c h w o u l d a d v e r s e l y a f f e c t r e a d i n g s d u r i n g t h e e x p e - r i m e n t . F o r t h e i n i t i a l w e t t i n g o f t h e membrane, t h e t a n k was f i l l e d t o t h e t o p w i t h low s a l i n i t y f l u i d . The t r a y was l o w e r e d s i d e w a y s i n t o t h e t a n k and g e n t l y t a p p e d t o remove t h e a i r b u b b l e s t r a p p e d i n t h e p e r f o r a t e d b o a r d s . The t r a y was t h e n l o w e r e d h o r i z o n t a l l y t o t h e d e s i r e d d e p t h a nd t h e t a n k d r a i n e d u n t i l t h e f l u i d was l e v e l w i t h t h e b o t t o m o f t h e t r a y . A t t h e b e g i n n i n g o f an e x p e r i m e n t a l r u n , t h e t r a y was f i l l e d w i t h h i g h s a l i n i t y f l u i d w h i l e low s a l i n i t y f l u i d was a d d e d i n t h e edge b e t w e e n t a n k a nd t r a y t o k e e p t h e f l u i d l e v e l s a t t h e same h e i g h t . T h i s was done t o p r e v e n t a r a p i d i n i t i a l f l u x due t o p r e s s u r e c a u s e d by a d i f f e r e n c e i n f l u i d l e v e l s In e x c e s s o f t h a t due t o t h e d i f f e r e n c e i n d e n s i t y b e t w e e n t h e two f l u i d s . The s t a r t o f c o n v e c t i o n was s e e n i n t h e s h a d o w g r a p h image a s a s l o w l y and n e a r l y e v e n l y d e s c e n d i n g c u r t a i n o f s m a l l p l u m e s . C o n v e c t i v e o v e r t u r n i n g p r o d u c e d a m i x e d l a y e r w h i c h e x t e n d e d t o t h e b o t t o m o f t h e t a n k . A d o w n - s l o p e b o t t o m f l o w was s e e n t o e s t a b l i s h i t s e l f s h o r t l y a f t e r t h e s t a r t o f e a c h e x p e r i m e n t a nd was m a i n t a i n e d by t h e s a l t f l u x t h r o u g h o u t e a c h e x p e r i m e n t . O b s e r v a t i o n s were u s u a l l y t a k e n o v e r a p e r i o d o f 3 t o 5 h o u r s , b u t i n one c a s e t h e s l o p e f l o w was s t i l l s e e n a b o u t 15 h o u r s l a t e r . The s h a d o w g r a p h images a nd t h e movement o f i n j e c t e d dye were r e c o r d e d i n p h o t o a nd s l i d e s e q u e n c e s o r on v i d e o t a p e t o s t u d y t h e f l o w p a t t e r n s and t o d e t e r m i n e s l o p e f l o w v e l o c i t i e s . The e x p e r i m e n t a l r e s u l t s a r e d e s c r i b e d i n s e c t i o n 3. 20 2.6 Determination of membrane s a l t f l u x The s a l t f l u x t h r o u g h t h e p o r o u s membrane I s a f u n c t i o n o f t h e h e i g h t o f f l u i d i n t h e t r a y , t h e d e n s i t y d i f f e r e n c e b e t w e e n th e f l u i d i n t a n k a n d t h a t i n t h e t r a y a n d t h e membrane c h a r a c - t e r i s t i c s . The m a g n i t u d e o f t h i s b u o y a n c y f l u x d e t e r m i n e s t h e t u r b u l e n c e i n t h e c o n v e c t i v e l y m i x e d l a y e r . 2.6.1 S a l t - and volume f l u x e s I n i t i a l e s t i m a t e s o f t h e n e t s a l t f l u x were o b t a i n e d f r o m t h e s a l i n i t y t i m e - s e r i e s o f f l u i d i n t h e t r a y and t h e known v o l u m e s o f f l u i d i n t r a y a n d r e s e r v o i r . The n e t s a l t f l u x i s t h e r a t e o f ch a n g e i n t h e t o t a l amount o f s a l t i n t h e c o m b i n e d t r a y a n d r e s e r v o i r volume t a k e n p e r u n i t o f t r a y a r e a : ( 2 . 4 ) Bn= d ( S 2 * D 2 ) * ( V 2 + V r ) Bn = n e t s a l t f l u x ( g r / c m 2 / s ) d t 1000 A S2 = s a l i n i t y ( g r / k g o r p p t ) D2 = d e n s i t y ( g r / c m 3 ) V2 = t r a y f l u i d volume (cm 3) Vr = r e s e r v o i r volume (cm 3) A = membrane a r e a (cm 2) S u f f i x 2 I s u s e d f o r p r o p e r t i e s l n t h e t r a y a n d 1 f o r t h o s e In t h e t a n k . The n e t s a l t f l u x I s t h e r a t e a t w h i c h s a l t f l o w s I n t o t h e t a n k t h r o u g h t h e membrane i n t h e t r a y b o t t o m , r e d u c e d by t h a t In t h e r e t u r n f l o w t h r o u g h t h e l e v e l l i n g s l o t s l n t h e t r a y , t a k e n p e r u n i t s u r f a c e a r e a ( s e e f i g u r e 2 - 1 1 ) . The r e t u r n f l o w f o r m s a t h i n l a y e r a t t h e t o p o f t h e t r a y w h i c h i s o n l y p a r t l y m i x e d i n t o i t by t h e pump w h i c h e x c h a n g e s t r a y and r e s e r v o i r f l u i d . E q u a t i o n 2.4 w i l l t h e r e f o r e o n l y y i e l d a r o u g h 21 i n i t i a l e s t i m a t e o f t h e n e t f l u x due t o t h e i n c o m p l e t e m i x i n g i n t r a y and t h e s l o w e x c h a n g e o f t r a y and r e s e r v o i r f l u i d . The amount o f f l u i d e n t e r i n g t h e t a n k t h r o u g h t h e membrane must e q u a l t h e r e t u r n f l o w f r o m t h e t a n k t o t h e t r a y , and t h e volume f l u x F c a n be e x p r e s s e d i n t e r m s o f t h e n e t s a l t f l u x : ( 2 . 5 ) B n = F * ( D 2 * S 2 - D l * S l ) F= volume f l u x ( c m 3 / c m 2 / s ) 1000 The membrane s a l t f l u x B i s t h e n t h e p r o d u c t o f volume f l u x a nd t h e amount o f s a l t p e r u n i t volume o f f l u i d f r o m t h e t r a y : ( 2 . 6 ) B = F * ( D2*S2 ) B= s a l t f l u x ( g r / c m 2 / s ) 1000 The c o n v e c t i o n i s d r i v e n by t h i s membrane s a l t f l u x . 2.6.2 S a l t f l u x c a l i b r a t i o n To c a l i b r a t e t h e membrane s a l t and volume f l u x e s , a s e r i e s o f e x p e r i m e n t s was done i n w h i c h t h e b o t t o m o f t h e t a n k was k e p t h o r i z o n t a l . I n t h e s e e x p e r i m e n t s t h e p a t t e r n s o f l i n e s i n s h a d o w g r a p h images i n d i c a t e d a n e a r l y u n i f o r m d i s t r i b u t i o n o f c o n v e c t i v e m o t i o n s , w i t h end e f f e c t s o f d i m i n i s h e d a c t i v i t y n e a r t h e end w a l l s o f t h e t a n k . The r a t e o f c h a n g e i n s a l i n i t y o f f l u i d f r o m a p o i n t n e a r t h e c e n t e r o f t h e t a n k was t h e n t a k e n t o r e p r e s e n t t h e a v e r a g e c h a n g e f o r t h e w h o l e t a n k f l u i d v o l u m e . E s t i m a t e s o f t h e n e t s a l t f l u x were o b t a i n e d f r o m t h e r a t e o f c h a n g e i n s a l i n i t y and d e n s i t y i n t h e t a n k : ( 2 . 7 ) Bn=_d ( S 1 * D 1 ) * V 1 d t 1000 A 22 W i t h t h e f l u i d In t a n k a n d t r a y a t the same l e v e l , t h e s a l t f l u x t h r o u g h t h e membrane i s d r i v e n by t h e p r e s s u r e due t o t h e d e n s i t y d i f f e r e n c e o f f l u i d c o l u m n s o f e q u a l h e i g h t i n t h e t r a y and i n t h e edge s p a c e b e t w e e n t a n k and t r a y : ( 2 . 8 ) P = ( D 2 - D l ) * g * h w i t h : P = p r e s s u r e ( g r / c m / s 2 ) D = d e n s i t y ( g r / c m 3 ) h = t r a y f l u i d h e i g h t (cm) g = g r a v i t y = 981 ( c m / s 2 ) Ay LEVELLING SLOT me mbrane TANK S i , Dl F i g u r e 2-11. F l u x - d r i v i n g f o r c e S a l i n i t y p r o f i l e s o f f l u i d i n t h e edge s p a c e b e t w e e n t a n k and t r a y ( f i g u r e 2-12) d i d show a s t a b l e s t r a t i f i c a t i o n c a u s e d by the I n c r e a s i n g s a l i n i t y o f f l u i d r i s i n g f r o m t h e m i x e d l a y e r t o r e t u r n t h r o u g h t h e l e v e l l i n g s l o t s t o t h e t r a y , and p r o f i l e s o f s a l i n i t y In t h e t r a y ( f i g u r e 2-13) show t h a t t h i s r e t u r n f l o w f o r m e d a l i g h t l a y e r a t t h e t o p i n t h e t r a y . To c a l c u l a t e t h e d r i v i n g p r e s s u r e , a c o r r e c t i o n was made by a p p r o x i m a t i n g t h e s e s t a b l e s t r a t i f i c a t i o n s w i t h s i m p l e 2 - l a y e r s y s t e m s and r e d u c i n g t h e h e i g h t of t h e f l u i d c o l u m n s by t h e 2-3 mm o f common u p p e r l a y e r s a l l n 1 t y . 23 The d r i v i n g p r e s s u r e s a n d c o r r e s p o n d i n g volume f l u x e s were c a l c u l a t e d f r o m t i m e s e r i e s d a t a f o r f l u i d i n t h e t r a y and i n t h e t a n k , u s i n g e q u a t i o n s 2.6 t o 2.8 and t h e s e a p p r o x i m a t i o n s . A c a l i b r a t i o n c u r v e was f i t t e d t h r o u g h s e t s o f membrane f l u x d a t a o b t a i n e d b e f o r e a n d a f t e r t h e f i r s t s l o p e f l o w e x p e r i m e n t ( f i g u r e 2 - 1 5 ) . 2.6.3 Membrane s a l t f l u x d e t e r m i n a t i o n To e s t i m a t e t h e membrane s a l t f l u x a t t h e t i m e t h a t a s l o p e f l o w v e l o c i t y was m e a s u r e d d u r i n g an e x p e r i m e n t , t h e s a l i n i t i e s o f f l u i d i n t h e t r a y a n d i n t h e m i x e d l a y e r a t t h a t t i m e were o b t a i n e d by l i n e a r i n t e r p o l a t i o n , when n e a r b y d a t a p o i n t s were a v a i l a b l e f r o m the t i m e - s e r i e s . S a l i n i t i e s were e s t i m a t e d from a l e a s t s q u a r e s c u r v e f i t when o n l y a few t r a y d a t a p o i n t s were t a k e n , o r when no n e a r b y m i x e d l a y e r d a t a were a v a i l a b l e . The d r i v i n g p r e s s u r e was t h e n c a l c u l a t e d f r o m t h e c o r r e s p o n d i n g d e n s i t i e s , c o m p u t e d f r o m t h o s e s a l i n i t i e s a n d t h e t e m p e r a t u r e i n t h e t a n k , u s i n g t h e U n e s c o E q u a t i o n o f S t a t e ( a p p e n d i x A ) . The c o r r e s p o n d i n g volume f l u x was o b t a i n e d f r o m t h e c a l i b r a - t i o n g r a p h o f membrane f l o w ( f i g u r e 2-15) and t h e membrane s a l t f l u x was c a l c u l a t e d f r o m e q u a t i o n 2.6. S e v e r a l s e r i e s o f f l u x c a l i b r a t i o n e x p e r i m e n t s were done t o d e v e l o p t h e d a t a a c q u i s i t i o n m e t h o d s . The r a t e o f ch a n g e i n t h e t a n k and t r a y d e n s i t i e s was a l w a y s v e r y s i m i l a r , b u t i n d i v i d u a l n u m e r i c r e s u l t s f o r t h e volume f l u x v a r i e d , i n p a r t due t o some c l o g g i n g o f t h e membrane i n s u c c e s s i v e e x p e r i m e n t s o r t o p o o r r e a d i n g s o f f l u i d d e p t h s i n t a n k o r t r a y . 24 25 2 2 . 0 S a l i n i t y (PSS) 2A, 5 0 4 E E 10 J Q- (U a 20 J 30 J 40 J 50 J 60 J L i t J I I I L P r o f i l e i n the "tray a t the cent re bottom o f t r a y i 1 1 1 1 1 1 r 27. 0 Figure 2-13. Sa l in i ty pro f i l e in the tray. 26 Figure 2-15. MEMBRANE VOLUME-FLUX vs PRESSURE ca l ibrat ion data for sloperuns 2.6.4 S a l t f l u x a n d e n t r a i n m e n t S e v e r a l s e p a r a t e e x p e r i m e n t s were c o n d u c t e d w i t h o u t a b o t t o m s l o p e , o v e r a r a n g e o f s a l t f l u x e s s i m i l a r t o t h o s e u s e d In t h e s l o p e f l o w e x p e r i m e n t s , t o measure i n t e r f a c e e n t r a i n m e n t c a u s e d by c o n v e c t i v e t u r b u l e n c e In t h e a b s e n c e o f s h e a r . The s a l t f l u x i n t o e i t h e r a 2 - l a y e r s y s t e m o r i n t o a l i n e a r s t r a t i f i c a t i o n c r e a t e d an u p p e r w e l l - m i x e d l a y e r w h i c h s l o w l y i n c r e a s e d i n d e n s i t y due t o t h e s a l t f l u x a n d I n d e p t h due t o e n t r a i n m e n t . The i n t e r f a c e was v i s i b l e i n t h e s h a d o w g r a p h a s a b r i g h t l i n e s e p a r a t i n g t h e l i n e p a t t e r n s i n t h e u p p e r l a y e r o f c o n v e c t i v e t u r b u l e n c e f r o m t h e c l e a r q u i e s c e n t r e g i o n b e l o w ( p h o t o 3 ) . T h i s l i n e s l o w l y moved downward due t o e n t r a i n m e n t . I n t h e 2 - l a y e r s y s t e m , t h e l i n e f a d e d a s t h e s t e p i n d e n s i t y a c r o s s t h e i n t e r f a c e became s m a l l and t h e i n d i v i d u a l c o n v e c t i v e e l e m e n t s p e n e t r a t e d t h r o u g h i t . P h o t o 3 . I n t e r f a c e e n t r a i n m e n t 28 The e n t r a i n m e n t v e l o c i t y m i x e d l a y e r w i t h t i m e : i s m e a s u r e d as t h e d e e p e n i n g o f t h e Ve = d Y / d t ( 2 . 9 ) The f o l l o w i n g d i a g r a m d e f i n e s t h e d i m e n s i o n s , v e l o c i t i e s and d e n s i t i e s u s e d t o f o r m u l a t e i n t e r f a c e e n t r a i n m e n t : Tank and t r a y 2 - l a y e r s y s t e m D Dw I DL l i n e a r s t r a t i f i c a t i o n Y = = m i x e d l a y e r d e p t h Ve = = e n t r a i n m e n t v e l o c i t y H = = d e p t h o f f l u i d l n t a n k Vw = = membrane volume f l u x L = = b o t t o m o f l i n e a r s t r a t l f . Dw = = t r a y f l u i d d e n s i t y AW = = t r a y membrane a r e a D = - m i x e d l a y e r d e n s i t y Ae = = t a n k I n t e r f a c e a r e a De = = d e n s i t y a t I n t e r f a c e DL = = d e n s i t y a t d e p t h L F i g u r e 2-16. D i a g r a m o f I n t e r f a c e e n t r a i n m e n t d e f i n i t i o n s The i n t e n s i t y o f t h e c o n v e c t i v e o v e r t u r n i n g c a n be e x p r e s s e d a s a v e r t i c a l v e l o c i t y s c a l e W* d e r i v e d f r o m t h e m i x e d l a y e r d e p t h Y and b u o y a n c y f l u x Q u s i n g s i m p l e d i m e n s i o n a l a n a l y s i s : W* = ( Y . Q ) 1 ^ = [ Y . V w . g . ( D w - D ) \ ^ ( 2 . 1 0 ) L D r e f ' D r e f = 1 gr/cm^ g = g r a v i t y a c c e l e r a t i o n 29 The r a t i o o f t h e i n e r t i a l f o r c e t o t h e b u o y a n c y f o r c e a t t h e i n t e r f a c e d e s c r i b e s t h e r e l a t i v e I m p o r t a n c e o f p e n e t r a t i v e c o n v e c t i o n v e r s u s a s t a b i l i z i n g d e n s i t y s t r a t i f i c a t i o n a n d h a s b e e n e x p r e s s e d e i t h e r a s a non-d1 m e n s l o n a l o v e r a l l R i c h a r d s o n number R i by K a n t h a ( 1 9 7 8 ) o r a s an i n t e r n a l F r o u d e number F r by Bo P e d e r s e n ( 1980) : F r 2 = 1/Ri = W*2 ( 2 . 1 1 ) g . Y . ( D - D e ) / D r e f The e n t r a i n m e n t h y p o t h e s i s d e r i v e d by Bo P e d e r s e n p r e d i c t s t h a t t h e r a t i o o f f l u x t o e n t r a i n m e n t , w r i t t e n as a b u l k f l u x R i c h a r d s o n number R f T , i s n e a r l y c o n s t a n t : R f T = Ve.(De-D) * 0.20 ( 2 . 1 2 ) (Dw-D).Vw I n t h e s e e x p e r i m e n t s , c o n s e r v a t i o n of mass r e q u i r e s t h a t t h e r a t e a t w h i c h t h e s a l t f l u x a d d s mass t o t h e volume i n t h e t a n k e q u a l s t h e sum o f c h a n g e s In m i x e d l a y e r a nd l o w e r l a y e r : I n t h e 2 - l a y e r s y s t e m , t h e l o w e r l a y e r d e n s i t y I s c o n s t a n t . The mass i n t h e t a n k i s : M '= Ae.tY.D + ( H - Y ) . D e l ( 2 . 1 3 ) a n d c o n s e r v a t i o n o f mass i s d e s c r i b e d f o r t h e 2 - l a y e r s y s t e m by: (Vw.Aw)(Dw-D) = A e . _ d f Y . D + D e . ( H - Y ) ] d t L J o r Vw = Ae . f V e . ( D - D e ) + Y.dD1 ( 2 . 1 4 ) Aw.(Dw-D) L d t J The e n t r a i n m e n t v e l o c i t y was o b t a i n e d f r o m v i d e o o b s e r v a t i o n s o f i n t e r f a c e d e p t h ( f i g u r e 2 - 1 7 ) . T a b l e 2,1 l i s t s t h e c o m p u t e d v a l u e s f o r t h e s c a l e v e l o c i t y a nd non-d1 mens 1 o n a l p a r a m e t e r s . 30 Figure 2-17. Entrainment at i n t e r f a c e of 2-layer system. 31 The a n a l y s i s was done u s i n g t h e d a t a o f t h e 5-23-86 e x p e r i m e n t . The r a t i o o f t r a y t o t a n k a r e a was Aw/Ae=0.824, t h e l o w e r l a y e r d e n s i t y D e = l . 0 0 9 2 6 (g/cm 3) a nd t h e r a t e o f c h a n g e i n t h e m i x e d l a y e r d e n s i t y was n e a r l y c o n s t a n t dD/dt=6.076e-4 g/cm 3/s. T a b l e 2.1 E n t r a i n m e n t i n 2 - l a y e r s y s t e m t Ve .e-4 Vw.e-4 W* Rf T Ve/W* F r 2 R i m i n ) < 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 I n t h e c a s e o f a s t r a t i f i c a t i o n w h i c h I s l i n e a r t o a d e p t h L t h e mass u n d e r t h e t r a y t o t h a t d e p t h i s : M = Ae.^Y.D + ( L - Y ) . ( D L + D e ) j ( 2 . 1 5 ) and c o n s e r v a t i o n o f mass f o r t h e l i n e a r l y s t r a t i f i e d c a s e i s : (Vw.AwXDw-D) = Ae. d [ Y . D+ (De +DL) . (H-Y ) 1 d t L 2 J The t i m e - s e r i e s p l o t s f o r i n t e r f a c e d e p t h a n d s a l i n i t y i n t h e m i x e d l a y e r ( f i g u r e 2-18) were c o m b i n e d t o show t h e I n t e r f a c e d e p t h s a t t h e c o r r e s p o n d i n g m i x e d l a y e r s a l i n i t y ( f i g u r e 2 - 1 9 ) . A p r o f i l e o f t h e i n i t i a l s t r a t i f i c a t i o n , p l o t t e d i n t h i s same g r a p h , shows t h a t t h e s t e p i n s a l i n i t y a c r o s s t h e i n t e r f a c e i s c o n s t a n t , o r : De-D= c o n s t so _d.(De)= d ( D ) d t d t 32 o r Vw = Ae .[Ve.(2D-De-DL) + ( Y + L ) . d D l (2.16) Aw(Dw-D) L 2 2 d t i A l i n e a r l e a s t - s q u a r e s f i t t o t h e i n t e r f a c e d e p t h s f r o m v i d e o f o o t a g e , f o r p o i n t s In t h e n e a r l y l i n e a r p a r t o f t h e p r o f i l e , y l e l d e d : Y = 5.30 + ( t - 2 4 ) * 6 0 * l . 1 2 8 e - 3 (Y i n cm, t i n min) and t h u s a c o n s t a n t e n t r a i n m e n t v e l o c i t y : Ve = 1.128e-3 (cm/s) V a l u e s f o r f l u x , s c a l e v e l o c i t y a n d n o n - d i m e n s i o n a l p a r a m e t e r s were c o m p u t e d u s i n g t h e above d e r i v a t i o n s . The r e s u l t s f o r d a t a f r o m t h e l i n e a r s t r a t i f i c a t i o n e x p e r i m e n t a r e l i s t e d i n t a b l e 2.2 be 1ow. T a b l e 2.2 E n t r a i n m e n t i n l i n e a r s t r a t i f i c a t i o n t Vw.e-4 W*.e-2 R f T Ve/W* F r 2 R i ( m i n ) ( c m / s ) ( c m / 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 c o m p u t e d r e s u l t s o f t h e s e e x p e r i m e n t s show good a g r e e m e n t w i t h t h e h y p o t h e s i s f o r e n t r a i n m e n t due t o f r e e p e n e t r a t i v e c o n v e c t i o n by Bo P e d e r s e n ( 1 9 8 0 ) and a g r e e w i t h d a t a f r o m o t h e r s o u r c e s when p l o t t e d i n g r a p h s o f c o m p i l e d f i e l d a n d l a b o r a t o r y r e s u l t s by Bo P e d e r s e n and J u r g e n s e n ( 1 9 8 4 ) and by K a n t h a ( 1 9 7 6 ) , a s shown i n f i g u r e 2-20. 33 E n t n a i n m e n t by c o n v e c t i o n L i n e a r - s t r a t i f i c a t i o n 5 - 3 0 - 8 6 and mixed layer s a l i n i 34 Figure 2-19. Interface depth vs. mixed layer sa l in i ty , and i n i t i a l s t ra t i f i ca t ion . 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 , c o n v e c t ior l i n e a r s t r 1 i n t o - ~ a t i f . / * - , c o n v e c t i o i 2 ~ l a y e r e ,1 1 l l L1I l n i n t o yetem 1_i—i i i 111 r 2 V\ Fr = Yg AD - /D r ef - 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 f i e l d data by: ^ Bo Pedersen and JUrgensen (1984)- laboratory *PP Heidt (1975)- laboratory experiments s i , s i W i l l i s and Deardorff (1974)- laboratory A Farmer (1975)- so lar heating under lake ice + BvanH (1986) - laboratory salt flux 36 2.6.5 A r c t i c s a l t f l u x a nd c o n v e c t i o n d e p t h To compare l a b o r a t o r y c o n d i t i o n s w i t h t h o s e e n c o u n t e r e d i n t h e f i e l d , d a t a f r o m C a m b r i d g e Bay i n t h e C a n a d i a n A r c t i c (Gade e t a l , 1974) were u s e d t o d e r i v e v a l u e s f o r t h e b u o y a n c y f l u x , e n t r a i n m e n t and F r o u d e number f o l l o w i n g t h e above n o t a t i o n . The d a t a i n c l u d e d i c e t h i c k n e s s H, m i x e d l a y e r s a l i n i t y Sm and o b s e r v e d d e p t h o f c o n v e c t i o n Y b e t w e e n O c t o b e r 1971 and A p r i l 1972. The i c e s a l i n i t y S i was e s t i m a t e d a s 3.0 p p t and i c e d e n s i t y D i as 0.9 g/cm 3. The i c e g r o w t h was o b t a i n e d by l i n e a r i n t e r p o l a t i o n o v e r t h e t i m e b e t w e e n o b s e r v a t i o n s . The s a l t f l u x i n t o t h e i c e i s t h e p r o d u c t o f g r o w t h , d e n s i t y a n d s a l i n i t y i n t h e i c e . U s i n g a s i m p l i f i e d m o d e l , t h e amount o f s a l t e x p e l l e d i n t o t h e m i x e d l a y e r c a n t h e n be e x p r e s s e d a s a s a l t f l u x F : F = ( d H / d t ) . D i . t S m - S i l ( 2 . 1 7 ) The f o l l o w i n g t a b l e shows t h e f i e l d d a t a a n d t h e d e r i v e d v a l u e s f o r e n t r a i n m e n t v e l o c i t y Ve= d Y / d t , i c e g r o w t h ( d H / d t ) , s a l t f l u x F and b u o y a n c y f l u x Q= F.g ( g = g r a v i t y ) , c o n v e c t i v e s c a l e v e l o c i t y W*= CY.Q] 1' 3 and c o r r e s p o n d i n g F r o u d e number F r . The s a l t f l u x f r o m f r e e z i n g e s t i m a t e d f r o m t h e s e f i e l d d a t a Is s e v e r a l o r d e r s o f m a g n i t u d e s m a l l e r t h a n t h o s e u s e d i n t h e l a b o r a t o r y , h o w e v e r , t h e l a r g e d e p t h s o f t h e m i x e d l a y e r i n t h e f i e l d b r i n g t h e v a l u e s f o r t h e s c a l e v e l o c i t y W* c l o s e t o t h o s e i n t h e e x p e r i m e n t s . 37 T a b l e 2.3 E n t r a i n n e n t f r o m A r c t i c f i e l d d a t a M i x e d l a y e r I c e Da t e D e p t h I n c r Ve S a l i n Dens Thk I n c r G r o w t h d a y s (m) (m) (cm/s ( p p t ) ( s i g m a ) (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 V a l u e s i n b r a c k e t s a r e l i n e a r i n t e r p o l a t i o n s b e t w e e n t h o s e f r o m t h e d a t e s o f o b s e r v a t i o n . Days S a l t B u o y a n c y F l u x ( g / c m 2 / s ) .e-7 F l u x ( g / c m / s 3 .e-4 W* ) (cm/s) Ve /W* F r 2 R f T 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 c o m p u t e d v a l u e s f o r e n t r a i n m e n t e f f l c i e n c y a g r e e w i t h t h e 0.20 p r e d i c t e d by Bo P e d e r s e n b u t t h e r e were few o b s e r v a t i o n s , s p a c e d o v e r a p e r i o d o f s i x months ( f i g u r e 2 - 2 1 ) , and t h e v a l u e s f o r e n t r a i n m e n t d e r i v e d f r o m t h e s e f i e l d d a t a n e g l e c t a n y a d v e c t i o n o f s a l t by t i d a l f l o w s o r by t h e t y p e o f r e v e r s e e s t u a r i n e f l o w s u g g e s t e d by t h e s l o p e f l o w e x p e r i m e n t s , o r any e n t r a i n m e n t c a u s e d by I n t e r n a l w a v es. 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 S A L . (%o) -I +1 +3 T E M P . ( °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. P r o f i l e s and ice thickness - f i e l d data 39 3 - EXPERIMENTAL RESULTS AND INTERPRETATION S l o p e f l o w s were I n d u c e d i n a s e r i e s o f e x p e r i m e n t s c o n d u c t e d w i t h d i f f e r e n t b o t t o m s l o p e a n g l e s , s e t b e t w e e n 2.2° and 5.5°. S a l t f l u x e s t i m a t e s c o m p u t e d f r o m m i c r o - c e l l d a t a t a k e n d u r i n g t h e e x p e r i m e n t s r a n g e d f r o m 1.82e-5 t o 1.63e-6 g r / c m 2 / s . A s l o p e f l o w was o b s e r v e d In e a c h o f t h e e x p e r i m e n t s . 3 .1 S l o p e a n g l e s , s t a r t i n g s a l i n i t i e s a n d s a l t f l u x e s The b o t t o m s l o p e a n g l e o f t h e t a n k was f i x e d b e f o r e t h e s t a r t o f e a c h e x p e r i m e n t . The s a l t f l u x r a n g e t h r o u g h t h e membrane d u r i n g t h e e x p e r i m e n t i s d e t e r m i n e d by t h e h e i g h t o f f l u i d i n t h e t r a y a nd by t h e d i f f e r e n c e i n t h e i n i t i a l s a l i n i t i e s o f t h e f l u i d s i n t a n k and t r a y . S e a w a t e r was u s e d i n t h e t r a y and r e s e r v o i r f o r t h e l o w e r s a l t f l u x e s , where c o n d u c t i v i t i e s were w i t h i n r a n g e o-f t h e AM/CT D a t a l o g g e r c i r c u i t . F o r t h e h i g h e r s a l t f l u x e s , p u r e s e a s a l t was m i x e d i n t o t h e s e a w a t e r f o r t r a y and r e s e r v o i r t o o b t a i n s a l i n i t y d i f f e r e n c e s o f 40-60 p p t b e t w e e n t h e f l u i d s i n t a n k and t r a y . I n t h e s e c a s e s t h e t r a y s a l i n i t i e s were m o n i t o r e d w i t h a s e p a r a t e c o n d u c t i v i t y c i r c u i t a n d a d i g i t a l v o l t m e t e r . T a b l e 3.1 l i s t s t h e b o t t o m s l o p e a n g l e , t h e d e p t h s o f f l u i d s i n and u n d e r t h e t r a y , t h e s t a r t i n g s a l i n i t i e s f o r e a c h o f t h e s l o p e f l o w e x p e r i m e n t s , and t h e r a n g e o f c o m p u t e d membrane s a l t f l u x e s . 40 T a b l e 3.1 S t a r t i n g C o n d i t i o n s f o r S l o p e F l o w E x p e r i m e n t s Exp A n g l e T r a y - h T a n k - d e p t h S a 1 i n i t y ( p p t ) S a l t f l u x e s # ( d e g r ) (mm) Max(mm)Min T r a y Tank ( g / c m 2 / 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 W i t h t h e end o f t h e t r a y r e s t i n g on t h e b o t t o m a t t h e s h a l l o w e n d o f t h e t a n k , t h e amount o f f l u i d and t h e d e p t h s i n t h e w e d g e - s h a p e d volume b e l o w t h e t r a y became v e r y s m a l l a t s m a l l s l o p e a n g l e s . I n i n i t i a l t e s t s , n e i t h e r t h e s h a d o w g r a p h n o r i n j e c t e d dye d i d show any d i s t i n c t c o n t r i b u t i o n t o t h e s l o p e f l o w n e a r t h e s h a l l o w e n d . T h e r e f o r e , t h e t r a y was r a i s e d so t h e f l u i d d e p t h a t t h e s h a l l o w end o f t h e t a n k was 7 mm im t h e f i r s t and s e c o n d s l o p e f l o w e x p e r i m e n t s and 20 mm i n n e a r l y a l l s u b s e q u e n t e x p e r i m e n t s . 3.2 S h a d o w g r a p h o b s e r v a t i o n s When t h e t r a y was n e a r l y f i l l e d w i t h t h e d e n s e r f l u i d t o t h e s e l e c t e d h e i g h t , and t h e f l u i d s i n t h e t r a y a nd i n t h e edge s p a c e b e t w e e n t a n k a n d t r a y r e a c h e d a l m o s t t h e same l e v e l , s a l t b e g an t o p e r c o l a t e t h r o u g h t h e membrane i n t h e t r a y b o t t o m and c o n v e c t i o n s t a r t e d a s a f i e l d o f s m a l l p l u m e s o r s t r e a m e r s . I t 41 became v i s i b l e i n t h e s h a d o w g r a p h image a s a c u r t a i n o f s m a l l w r i n k l e d l i n e s e g m e n t s , s l o w l y a n d f a i r l y e v e n l y d e s c e n d i n g a t a s p e e d e s t i m a t e d a t l e s s t h a n one c m / s e c , d e p e n d i n g on t h e m a g n i t u d e o f t h e s a l t f l u x . A d o w n s l o p e f l o w was s e e n t o s t a r t up s h o r t l y a f t e r p a r t o f t h i s c u r t a i n r e a c h e d t h e b o t t o m a t t h e s h a l l o w e nd o f t h e t a n k : t h e m o s t l y v e r t i c a l o r i e n t a t i o n o f t h e l i n e s e g m e n t s i n t h e s h a d o w g r a p h image b e g a n t o d i s p l a y a bend t o w a r d s t h e s h a l l o w end o f t h e t a n k i n t h e m i x e d r e g i o n , and n e a r t h e b o t t o m became p a r a l l e l w i t h i t . The t y p i c a l s h a d o w g r a p h images s e e n d u r i n g t h e e x p e r i m e n t s ( s e e n i n p h o t o 2, page 8) show a d e f l e c t i o n o f t h e v e r t i c a l l i n e p a t t e r n s f r o m c o n v e c t i v e o v e r t u r n i n g by t h e g e n e r a l f l o w p a t t e r n i m p o s e d by t h e s l o p e f l o w a n d a s s o c i a t e d r e t u r n f l o w i n t h e m i x e d r e g i o n ( s e e f i g u r e 3-1 b e l o w ) . F i g u r e 3-1. S k e t c h o f t y p i c a l s h a d o w g r a p h p a t t e r n The s l o p e f l o w u s u a l l y was s e e n t o s t a r t up v e r y c l o s e t o t h e s h a l l o w end s o o n a f t e r t h e s a l t f l u x t h r o u g h t h e membrane became v i s i b l e , b u t i n s e v e r a l o f t h e e x p e r i m e n t s i t was s e e n t o s t a r t i n i t i a l l y a t 20 t o 30 cm f r o m t h e s h a l l o w end o f t h e 42 t a n k and t o f o r m a c o u n t e r - r o t a t i n g c e l l u p h i l l f r o m t h e r e ( s e e f i g u r e 3 - 2 ) . I n t h e s e c a s e s , t h e d o w n s l o p e / u p h 1 1 1 f l o w c e l l s d i d r e - e s t a b l i s h t h e m s e l v e s a g a i n a f t e r s t i r r i n g t h e f l u i d u n d e r t h e t r a y t o remove f l o w p a t t e r n s w h i c h m i g h t have been i n t r o d u c e d by une v e n c o n d i t i o n s w h i l e f i l l i n g t h e t r a y . I n some o f t h e e x p e r i m e n t s , t h e i n i t i a l d e s c e n t o f t h e c u r t a i n o f l i n e s i n t h e s h a d o w g r a p h was s l i g h t l y f a s t e r i n t h e a r e a o f t h e t r a y where t h e s l o p e f l o w was s e e n t o s t a r t . The s t a r t i n g p o i n t o f t h e s l o p e f l o w g r a d u a l l y moved t o w a r d t h e s h a l l o w e n d , w h i l e t h e u p h i l l f l o w c e l l s h o r t e n e d a n d o f t e n d i s a p p e a r e d o v e r 8 t o 20 m i n u t e s . I n e x p e r i m e n t #6, w h i c h had t h e l o w e s t s l o p e a n g l e ( 2 . 3 d e g r e e s ) , t h e u p h i l l f l o w c e l l d e c r e a s e d i n l e n g t h t o t h e l a s t 10 cm a t t h e t o p o f t h e s l o p e , b u t p e r s i s t e d t h r o u g h o u t t h e e xpe r i ment. F i g u r e 3-2. S k e t c h o f downs 1 o p e / u p h i 1 1 f l o w c e l l s The s l o p e f l o w a p p e a r e d t o a c c e l e r a t e f r o m t h e s t a r t i n g p o i n t b u t t h e n t o s l o w n down and r e a c h some e q u i l i b r i u m w i t h i n a b o u t 43 20 t o 30 cm down t h e s l o p e , b e y o n d w h i c h i t was n o t p o s s i b l e t o a c c u r a t e l y measure any i n c r e a s e o r d e c r e a s e i n t h e f l o w s p e e d . As t h e e x p e r i m e n t s p r o g r e s s e d a n d t h e h e a v i e r f l u i d c o l l e c t e d a t t h e deep end o f t h e t a n k , t h e l i n e p a t t e r n s a s s o c i a t e d w i t h c o n v e c t i v e t u r b u l e n c e d i d n o t p e n e t r a t e i n t o t h e d e e p e r p a r t o f th e t a n k . The s l o p e f l o w was s e e n t o s e p a r a t e f r o m t h e b o t t o m a t an i n c r e a s i n g d i s t a n c e f r o m t h e end o f t h e s l o p e a n d move a l o n g t h e i n t e r f a c e w i t h t h e s t a b l y s t r a t i f i e d f l u i d a t t h e deep e n d . On s e v e r a l o c c a s i o n s , p i n h o l e l e a k s were s e e n i n t h e shadow- g r a p h Images a t some o f the p o i n t s where s a m p l i n g t u b e s c u t t h r o u g h t h e membrane i n t h e t r a y . The l e a k s showed a s s m a l l s t r e a m e r s o f d e n s e r f l u i d d e s c e n d i n g s l i g h t l y f a s t e r t h r o u g h t h e m i x e d l a y e r t h a n t h e o t h e r m o t i o n s o b s e r v e d and p e n e t r a t i n g i n t o t h e s t a b l y s t r a t i f i e d l a y e r w h i c h f o r m s i n t h e d e e p e r p a r t o f t h e t a n k . W h i l e t h e s e c o n t r i b u t e d t o t h e s a l t f l u x , t h e y a r e b e l i e v e d t o be m i n o r . Some v a r i a b i l i t y i n t h e s a l i n i t y p r o f i l e p o i n t s may have b e e n c a u s e d when a s t r e a m e r f r o m a s m a l l l e a k i n t e r m i t t e n t l y was s y p h o n e d i n t o a m i c r o - c e l l d u r i n g p r o f i l i n g , a s was s e e n t o o c c u r i n one i n s t a n c e on v i d e o f o o t a g e . 3.3 I n j e c t e d dye S m a l l amounts o f f o o d dye were i n j e c t e d t h r o u g h one o f t h e s a m p l i n g t u b e s s e t a l o n g t h e c e n t e r l i n e o f t h e t r a y . The dye was m i x e d w i t h some s a l t w a t e r t o a d e n s i t y s l i g h t l y above t h a t o f t h e f l u i d l n t h e t a n k . D u r i n g i n j e c t i o n , a l i n e o f dye was s e e n t o s i n k t h r o u g h t h e c o n v e c t i v e l y m i x e d l a y e r , i n w h i c h i t 44 was d e f l e c t e d toward the s h a l l o w end of the tank by the o v e r a l l f l o w p a t t e r n , s i m i l a r to the l i n e s seen i n the shadowgraph . When the dye was more d i l u t e d and I t s d e n s i t y was c l o s e to t h a t i n the mixed l a y e r , the s t r e a k s made d u r i n g d e s c e n t t h r o u g h the mixed l a y e r were d i s t o r t e d by the c o n v e c t i v e m o t i o n s and moved toward the s h a l l o w end of the tank ( p h o t o 4). Photo 4. Dye i n the mixed l a y e r and s l o p e f l o w Where the dye l i n e sank t h r o u g h the bot tom f l o w , vee- shaped f e a t u r e s f o r m e d , s h o w i n g a v e l o c i t y maximum a t about 3 to 6 mm above the b o t t o m . These f e a t u r e s were c a r r i e d a l o n g much of the l e n g t h of the tank bot tom w i t h o u t n o t i c e a b l e d i s p e r s i o n from m i x i n g , w h i c h i n d i c a t e s l i m i t e d l e v e l s of t u r b u l e n c e i n the s l o p e f l o w . The vee- shaped f e a t u r e s sugges t a s h e a r f l o w w i t h a d e p t h w h i c h would be t w i c e t h a t of the h e i g h t of maximum v e l o - c i t y i f the f r i c t i o n a t the i n t e r f a c e was e q u a l to t h a t a t the b o t t o m . The v e l o c i t y s h e a r and the p e n e t r a t i o n of c o n v e c t i v e 45 t u r b u l e n c e a t the upper edge of the s l o p e f l o w e n t r a i n e d some of the dye from t h i s edge w h i l e bottom f r i c t i o n s t r e t c h e s the lower p a r t of the tongue of dye. (see photo 5 ) . Photo 5. V e l o c i t y maxima i n dye The maximum f l o w v e l o c i t y was e s t i m a t e d a t v a r i o u s times i n each experiment from the d i s t a n c e t h a t these dye tongues moved i n timed photo or s l i d e sequences, or i n v i d e o tape f o o t a g e . V e l o c i t i e s were g e n e r a l l y d e t e r m i n e d from o b s e r v a t i o n s made between about 30 to 60 cm from the top of the s l o p e , s i n c e the f l o w i n t h i s r e g i o n appeared steady and not much a f f e c t e d by the c o n d i t i o n s at the ends of the tank. The measured f l o w v e l o c i t i e s ranged from 0.09 to 0.52 cm/s and d e c r e a s e d w i t h time d u r i n g each experiment as the s a l t f l u x d i m i n i s h e d . In s e v e r a l of the e x p e r i m e n t s , dye which was i n j e c t e d In the 46 edge between tank and t r a y was slowly r a i s e d and c a r r i e d to the s l o t s into the tr a y by the r e t u r n flow from the tank. This flow causes s t a b l e s t r a t i f i c a t i o n in the edge space. Dye i n j e c t e d under the tr a y at the shallow end was seen to be mixed into the l a s t 4 to 6 cm of the tank by the c o n v e c t i o n but d i d not flow down-slope f o r the slope angles and s a l t f l u x e s 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 l i f t e d and e n t r a i n e d into the mixed l a y e r . When the slope flow v e l o c i t i e s slowed down in the l a t e r part of an experiment, c o n v e c t i v e motions near the deep end of the tank d i d appear to penetrate c l o s e r to the bottom in the shadowgraph 47 e d g e b e t w e e n t a n k a n d t r a y w a s s l o w l y r a i s e d a n d c a r r i e d t o t h e s l o t s i n t o t h e t r a y b y t h e r e t u r n f l o w f r o m t h e t a n k . T h i s f l o w c a u s e s s t a b l e s t r a t i f i c a t i o n i n t h e e d g e s p a c e . D y e i n j e c t e d u n d e r t h e t r a y a t t h e s h a l l o w e n d w a s s e e n t o b e m i x e d i n t o t h e l a s t 4 t o 6 c m o f t h e t a n k b y t h e c o n v e c t i o n b u t d i d n o t f l o w d o w n - s l o p e f o r t h e s l o p e a n g l e s a n d s a l t f l u x e s u s e d i n t h e s e e x p e r i m e n t s ( s e e p h o t o 6 ) . P h o t o 6 . D y e a t s h a l l o w e n d o f t a n k A t t h e d e e p e n d o f t h e t a n k t h e d y e f r o m t h e s l o p e f l o w w a s s l o w l y l i f t e d a n d e n t r a i n e d i n t o t h e m i x e d l a y e r . W h e n t h e s l o p e f l o w v e l o c i t i e s s l o w e d d o w n i n t h e l a t e r p a r t o f a n e x p e r i m e n t , c o n v e c t i v e m o t i o n s n e a r t h e d e e p e n d o f t h e t a n k d i d a p p e a r t o p e n e t r a t e c l o s e r t o t h e b o t t o m i n t h e s h a d o w g r a p h 47 Image. In the course of an e x p e r i m e n t , the h e a v i e r f l u i d from the s l o p e flow accumulated at the deep end of the tank, where i t formed a s t a b l y s t r a t i f i e d r e g i o n i n which no c o n v e c t i v e p e n e t r a t i o n was seen, below a mixed l a y e r of n e a r l y u n i f o r m depth. In s e v e r a l of the e x p e r i m e n t s , the dye i n the s l o p e f l o w was seen to b i f u r c a t e where i t reached t h i s s t a b l e f l u i d (see arrows i n photo 7 ) . Photo 7. B i f u r c a t i o n of s l o p e f l o w The s l o p e f l o w l i f t e d o f f the bottom on r e a c h i n g the s t a b l y s t r a t i f i e d lower p a r t of the tank. Dye t r a v e l l i n g a l o n g the i n t e r f a c e was o f t e n seen to c l i m b up and over s t e e p waves which were not v i s i b l e i n the shadowgraph (see photo 8). A c l o u d of dye, I n j e c t e d i n the c e n t r e of the s t r a t i f i e d r e g i o n , d i d not move but s l o w l y d i f f u s e d below the sharp i n t e r f a c e w i t h the mixed l a y e r (see photo 9). 48  A l o n g t h e p a r t o f t h e s l o p e a b o u t 30 cm away f r o m t h e e n d s o f t h e t a n k , t h e r e were no p e r c e p t i b l e c h a n g e s In the d e p t h o f t h e s l o p e f l o w o r In t h e f l o w v e l o c i t y , a s s e e n l n t h e dye o r s h a d o w g r a p h i m a g e s . S i n c e t h e volume o f f l u i d l n t h e t a n k i s c o n s t a n t , t h e r e must be a r e t u r n f l o w a b o v e t h e b o t t o m s l o p e f l o w f o r c o n t i n u i t y . T h i s was a l r e a d y s e e n t o e x i s t f r o m t h e d e f l e c t i o n o f t h e l i n e s i n t h e s h a d o w g r a p h image. A f t e r dye i n t h e s l o p e f l o w r e a c h e d t h e d e e p end o f t h e t a n k , i t was s e e n t o r i s e and be c a r r i e d i n the o p p o s i t e d i r e c t i o n a t much s l o w e r v e l o c i t i e s a n d i n a much l e s s o r g a n i z e d manner, w h i l e b e i n g d i f f u s e d by c o n v e c t i v e eddy m o t i o n s . The f l o w v e l o c i t y i n t h e m i x e d l a y e r i n c r e a s e s as t h e d e p t h i n t h i s l a y e r d e c r e a s e s t o w a r d t h e t o p o f t h e s l o p e . 3 .4 S a l i n i t i e s a n d s a l i n i t y p r o f i l e s D u r i n g t h e e x p e r i m e n t s , d a t a were t a k e n f r o m t h e r m i s t o r s a n d m i c r o - c e l l s t o d e t e r m i n e t e m p e r a t u r e s , s a l i n i t i e s and d e n s i t i e s o f f l u i d i n t h e t r a y and a t v a r i o u s l o c a t i o n s and d e p t h s i n t h e m i x e d l a y e r and i n t h e s l o p e f l o w ( a s d e s c r i b e d i n s e c t i o n 2 ) . F l u i d was s y p h o n e d t h r o u g h t h e c e l l s a t a c o n s t a n t r a t e o f a b o u t 1 m l / s (2 d r o p s p e r s e c o n d ) , a n d t h e c a l i b r a t i o n c o n s t a n t s f o r t h e m i c r o - c e l l s were u s u a l l y c h e c k e d b e f o r e an e x p e r i m e n t . Due t o t h e s a l t f l u x , t h e s a l i n i t y i n t h e m i x e d l a y e r s l o w l y i n c r e a s e d i n t h e t i m e n e e d e d t o t a k e a s e r i e s o f d a t a p o i n t s . ' Q u a s 1 - i n s t a n t a n e o u s ' s a l i n i t y p r o f i l e s were o b t a i n e d by s u b - t r a c t i n g t h e c h a n g e i n s a l i n i t y a t a f i x e d p o i n t i n t h e m i x e d l a y e r f r o m a c t u a l p r o f i l e d a t a : 50 S ( p r o f i l e ) = S ( a c t u a l ) - S ( m i x e d ) + S ( t l ) ( 3 . 1 ) i n w h i c h S ( a c t u a l ) i s t h e s a l i n i t y c a l c u l a t e d f r o m t he d a t a a t t h e p r o f i l e d e p t h , S ( m i x e d ) and S ( t l ) a r e t h e s a l i n i t i e s i n t h e m i x e d l a y e r a t t h e same t i m e t h a t t h e p r o f i l e d a t a were t a k e n and a t t h e t i m e ( t l ) t h a t t h e f i r s t p r o f i l e p o i n t was t a k e n . The a d j u s t m e n t was made e i t h e r by p o i n t w i s e s u b t r a c t i n g t h e cha n g e i n t h e c o m p u t e d m i x e d l a y e r s a l i n i t y , o r by s u b t r a c t i n g a ' s m o o t h e d ' v a l u e f o r t h i s c h a n g e u s i n g t h e s l o p e o f a l e a s t s q u a r e s l i n e a r f i t t h r o u g h t h e m i x e d l a y e r s a l i n i t i e s f o r s h o r t p e r i o d s o f t i m e ( f i g u r e 3 - 3 ) . A l i n e t h r o u g h t h e t i m e - a d j u s t e d p r o f i l e p o i n t s i n t h e m i x e d l a y e r t h e n became v e r t i c a l ( f i g u r e 3-4) w h i c h i n d i c a t e s t h a t t h e l a y e r was w e l l m i x e d ( e x c e p t f o r p o i n t s n e a r t h e u n d e r s i d e o f t h e t r a y where t h e s a l t e n t e r s t h e t a n k ) . T i m e - s e r i e s p l o t s o f s a l i n i t y d a t a t a k e n i n t h e m i x e d l a y e r i n d i c a t e t h a t f o r l o n g e r o b s e r v a t i o n t i m e s a s e c o n d o r d e r c u r v e g i v e s a b e t t e r a p p r o x i m a t i o n f o r t h e cha n g e i n t h e m i x e d l a y e r s a l i n i t y d u r i n g an e x p e r i m e n t ( f i g u r e 3 - 5 ) . The s l o p e f l o w was s e e n i n t h e p r o f i l e s a s a 7 t o 17 mm t h i c k l a y e r where t h e s a l i n i t y r o s e by 0.24 t o 0.92 PSS above t h e v a l u e i n t h e m i x e d l a y e r . A p p e n d i x F g i v e s a b r i e f d e s c r i p t i o n o f e a c h s l o p e f l o w e x p e r i m e n t w i t h c o m p u t e d r e s u l t s , t i m e - s e r i e s p l o t s and p r o f i 1 e s . E x c e s s i v e n o i s e i n some o f t h e d a t a was c a u s e d by f a u l t y m i c r o - b e a d t h e r m i s t o r s a t t h e m i c r o - c e l l s , and i n some c a s e s s a l i n i t i e s were r e - c a l c u l a t e d u s i n g t h e t e m p e r a t u r e f r o m t h e go o d t h e r m i s t o r , o f f s e t by h a l f t h e a v e r a g e d d i f f e r e n c e . 51 X ime (min) Figure 3~3. Time-series and linear f i t Figure 3-4. Actual and adjusted sal inity profiles 53 Figure 3~5. MICRO-CELL TIME-SERIES SLOPE FLOW EXP#3 I n a separate s l o p e f l o w e x p e r i m e n t , s u c c e s s i v e p r o f i l e d a t a were t a k e n by r a i s i n g t h e I n t a k e s o f a l l t h r e e m i c r o - c e l l s t o th e same h e i g h t above t h e b o t t o m , b u t l o c a t e d n e a r t h e m i d d l e o f t h e t a n k and 20 cm t o e i t h e r s i d e ( f i g u r e F - 2 6 ) . The use o f t h e HP-3497A D a t a l o g g e r S y s t e m a l l o w e d more f r e q u e n t s a m p l i n g , a n d i a v e r a g i n g o f r a p i d m u l t i p l e r e a d i n g s f o r e a c h s e n s o r . Time s e r i e s d a t a f r o m t h i s ( f i g u r e 3-6) and e x p e r i m e n t #8 ( f i g u r e F- 27) i n d i c a t e t h a t t h e r a t e o f ch a n g e o f s a l i n i t y w i t h t i m e was t h e same a t d i f f e r e n t l o c a t i o n s a l o n g t h e s l o p e In b o t h m i x e d l a y e r a n d s l o p e f l o w . A c u r v e f i t t h r o u g h t i m e - s e r i e s d a t a f r o m t h e m i x e d l a y e r c a n t h u s be u s e d t o c o r r e c t f o r t h e c h a n g e i n s a l i n i t y d u r i n g t h e t i m e r e q u i r e d t o c o l l e c t p r o f i l e d a t a . When many p o i n t s were t a k e n , a s e c o n d o r d e r c u r v e was u s e d ( f i g u r e F-28) t o o b t a i n ' q u a s 1 - 1 n s t a n t a n e o u s ' p r o f i l e s ( f i g u r e s F-30 and F-31) f o r w h i c h t h e m i x e d l a y e r s a l i n i t i e s a t t h e end w o u l d m atch t h o s e a t t h e s t a r t . A s m a l l b u t p e r s i s t e n t w e a k e n i n g i n t h e s a l i n i t y g r a d i e n t was s e e n n e a r b o t t o m i n s a l i n i t y p r o f i l e s f r o m l o c a t i o n s s p a c e d 20 cm a p a r t down t h e s l o p e . As h e a v y f l u i d f r o m t h e s l o p e f l o w c o l l e c t e d i n t h e b o t t o m , a wedge o f f l u i d f o r m e d a t t h e deep end i n w h i c h few c o n v e c t i v e m o t i o n s were s e e n t o p e n e t r a t e i n t h e s h a d o w g r a p h i m a g e s . A p r o f i l e t a k e n a t p o r t #7 i n e x p e r i m e n t #7, when t h i s wedge was a b o u t 3 cm t h i c k ( f i g u r e F - 2 5 ) , shows t h e s t a b l e s t r a t i f i c a t i o n o f f l u i d a t t h e deep e n d o f t h e t a n k . S a l i n i t y p r o f i l e s f r o m d a t a t a k e n i n t h e edge b e t w e e n t a n k a nd t r a y ( f i g u r e 2-12) a l s o was s t a b l y s t r a t i f i e d : t h e r e t u r n f l o w , r i s i n g f r o m t h e t a n k , b r o u g h t up f l u i d o f i n c r e a s i n g s a l i n i t y f r o m t h e m i x e d l a y e r . 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 l i s C3; / • J r? :Cl i f : " 4mm above bottor F i qure 3-6. TIME: 300SEC/DIV S a l i n i t y ra te of change i n mixed l a y e r and bottom f l o w . A s e q u e n c e o f m i c r o - c e l l d a t a t a k e n d u r i n g e x p e r i m e n t #1 n e a r t h e b o t t o m and 6 mm b e l o w t h e t r a y i n s u c c e s s i v e s a m p l i n g p o r t s d i d n o t show enough d e t a i l t o see a d i s t i n c t d i s t r i b u t i o n i n t h e s a l i n i t y a l o n g t h e s l o p e o r u n d e r t h e t r a y ( f i g u r e F - 5 ) , b u t d a t a t a k e n d u r i n g e x p e r i m e n t #4 show a h i g h e r s a l i n i t y o v e r t h e u p p e r p a r t o f t h e s l o p e , a nd a t t h e d e e p end ( f i g u r e F - 1 7 ) . 3.5 S a l t f l u x e s a n d f l o w v e l o c i t i e s The t i m e a f t e r s t a r t , t h e raw d a t a f r o m t h e r m i s t o r s and m i c r o - c e l l s and t h e c a l c u l a t e d v a l u e s o f t e m p e r a t u r e s , c o n d u c t i v i t y r a t i o s , s a l i n i t i e s and d e n s i t i e s ( s i g m a - t ) f o r e a c h s e t o f o b s e r v a t i o n s were l i s t e d on t h e l i n e p r i n t e r . These s a l i n i t i e s were p l o t t e d as a t i m e - s e r i e s d u r i n g e a c h e x p e r i m e n t t o m o n i t o r t h e o v e r a l l b e h a v i o u r o f t h e s y s t e m . The s a l t f l u x s l o w l y d e c r e a s e d d u r i n g e a c h e x p e r i m e n t as t h e i n f l u x o f s a l t i n t o t h e t a n k r e d u c e d t h e d i f f e r e n c e i n s a l i n i t y b e t w e e n t a n k and t r a y f l u i d s . F o r t h e t i m e s i n an e x p e r i m e n t a t w h i c h s l o p e f l o w v e l o c i t i e s were d e t e r m i n e d , t h e s a l t f l u x was c a l c u l a t e d f r o m t h e t i m e - s e r i e s d a t a o f s a l i n i t y i n t h e t r a y a n d i n t h e m i x e d l a y e r i n t h e t a n k , a s o u t l i n e d i n s e c t i o n 2.6. The c a l c u l a t e d r e s u l t s were t a b u l a t e d f o r e a c h e x p e r i m e n t a nd i n c l u d e d w i t h t h e t i m e - s e r i e s p l o t s and s a l i n i t y p r o f i l e s i n t h e d e s c r i p t i o n o f t h e i n d i v i d u a l e x p e r i m e n t s i n a p p e n d i x F. T a b l e 3.2 b e l o w l i s t s t h e c o m p i l e d v a l u e s f r o m t h e s l o p e f l o w e x p e r i m e n t s o f s l o p e a n g l e 6, t i m e t a f t e r s t a r t i n g t h e e x p e r i - ment, s l o p e f l o w v e l o c i t y maxima Vmax m e a s u r e d f r o m p h o t o o r s l i d e s e q u e n c e s o r f r o m v i d e o f o o t a g e o f i n j e c t e d d y e , c o m p u t e d 57 s a l t f l u x e s f o r t i m e s a t w h i c h t h e v e l o c i t y was d e t e r m i n e d , s l o p e f l o w d e p t h h and r i s e i n s a l i n i t y dS above t h a t i n t h e m i x e d l a y e r ( f r o m p r o f i l e s ) , a n d co m p u t e d e n t r a i n m e n t w i t h o u t ( E l ) a n d w i t h ( E 2 ) b o t t o m d r a g Cd ( s e e s e c t i o n 3.6) w h e r e : Cd= 4.2e-2/(h.Vmax) E l = h . g ' s i n G / V 2 and E2 = E l - Cd T a b l e 3.2 C o m p i l e d r e s u l t s o f s l o p e f l o w e x p e r i m e n t s s l o p e t Vmax s a l t f l x f l o w S a l i n i t y dS d r a g E n t r a i n m e n t # 6 ( m i n ) ( g r / c m 2 / s d e p t h ( P S S ) Cd E l 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 t a b u l a t e d v e l o c i t i e s have b e e n p l o t t e d a g a i n s t b o t h t h e c o r r e s p o n d i n g a n g l e s and s a l t f l u x e s t o c h e c k t h e d e p e n d e n c e o f t h e s l o p e f l o w v e l o c i t i e s on t h e m a g n i t u d e o f t h e s a l t f l u x e s ( f i g u r e 3-7) and on t h e b o t t o m s l o p e a n g l e s ( f i g u r e 3 - 8 ) . V e r - t i c a l b a r s were u s e d i n t h e p l o t s t o i n d i c a t e t h e r a n g e i n t h e m e a s u r e d v e l o c i t i e s . The r e l a t i o n b e t w e e n v e l o c i t y a nd s l o p e a n g l e i s n o t d i s t i n c t f o r t h e r a n g e o f a n g l e s u s e d i n t h e e x p e - r i m e n t s , b u t t h e r e l a t i o n d e s c r i b i n g t h e v i s i b l e r i s e i n s l o p e f l o w v e l o c i t y a t i n c r e a s i n g s a l t f l u x e s i s f u r t h e r e x p l o r e d i n t h e n e x t s e c t i o n . The s l o p e f l o w d e p t h s , e s t i m a t e d f r o m t h e s a l i n i t y p r o f i l e s , r a n g e d f r o m 7 t o 17 mm. T h e r e was no s h a r p i n t e r f a c e b e t w e e n t h e f l o w and t h e c o n v e c t i v e l y m i x e d l a y e r : i n t h e most d e t a i l e d p r o f i l e s t he u p p e r p a r t o f t h e b o t t o m f l o w , where s h e a r and p e n e t r a t i v e c o n v e c t i o n d o m i n a t e , shows a weak d e n s i t y g r a d i e n t . The l o w e r p a r t o f t h e s l o p e f l o w i s s t r o n g l y s t r a t i f i e d and dye ' t o n g u e s ' a s s o c i a t e d w i t h v e l o c i t y maxima a r e c a r r i e d a l o n g w i t h l i t t l e d i s p e r s i o n . The l e v e l o f t u r b u l e n c e h e r e i s g r e a t l y r e d u c e d f r o m t h a t i n t h e u p p e r p a r t o f t h e s l o p e f l o w and i n t h e m i x e d r e g i o n , where dye i s more r a p i d l y d i f f u s e d . 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 OJ 1- 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 a r e s a l t f l u x e s (*e~5) b a r s i n d i c a t e r a n g e i n v e l o c i t i e s 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 v e l o c i vs. 4 6 Slope angle (degrees) s l o p e a n g l e 3.6 I n t e r p r e t a t i o n D e n s i t y c u r r e n t s and p e n e t r a t i v e c o n v e c t i o n have b e e n s t u d i e d s e p a r a t e l y i n g e o p h y s i c a l f l u i d f l o w s a n d i n t h e l a b o r a t o r y by many r e s e a r c h e r s . I n t h i s s e r i e s o f l a b o r a t o r y e x p e r i m e n t s t h e two mechanisms a r e s i m u l t a n e o u s l y i n v o l v e d : t h e s u r f a c e s a l t f l u x i n d u c e s a s l o p e f l o w , w h i c h i s d r i v e n by t h e component o f ( r e d u c e d ) g r a v i t y a l o n g t h e s l o p e . The f l o w i s s l o w e d down by f r i c t i o n a t t h e b o t t o m a nd by s h e a r a t t h e i n t e r f a c e w h i c h i s m o d i f i e d by c o n v e c t i v e t u r b u l e n c e i n t h e o v e r l y i n g e n v i r o n m e n t . The f l o w r e a c h e s a s t e a d y s t a t e when t h e g r a v i t a t i o n a l f o r c e i s b a l a n c e d by t h e f r i c t i o n a t t h e b o t t o m a nd a t t h e i n t e r f a c e : h . g ' s i n G = ( t i +tw) Ds K. V 3 i n w h i c h g' i s t h e r e d u c e d g r a v i t y : g'= g.Ds-Do Dre f ( 3 . 1 ) ( 3 . 2 ) h = d e p t h o f t h e f l o w Ds= d e n s i t y i n s l o p e f l o w Do= d e n s i t y o f e n v i r o n m e n t g = g r a v i t y a c c e l e r a t i o n 9 = s l o p e a n g l e t i = f r i c t i o n a t i n t e r f a c e tw= f r i c t i o n a t b o t t o m K = d r a g f a c t o r V = a v e r a g e d f l o w s p e e d Ve= e n t r a i n m e n t v e l o c i t y 7 ->v V e \ h w " / vmax ' n - e F i g u r e 3-9. S l o p e f l o w d i a g r a m 62 C o n v e n t i o n a l t u r b u l e n t d e n s i t y p l u m e s have b e e n c h a r a c t e r i z e d by an o v e r a l l R i c h a r d s o n number R i ( K a n t h a , 1975) w h i c h i s t h e i n v e r s e o f t h e s q u a r e o f t h e d e n s i m e t r i c F r o u d e number F r (Bo P e d e r s e n , 1980) : R i = 1 = h . q ' c o s G ( 3 . 3 ) F r 2 V 2 S u c h g r a v i t y c u r r e n t s grow i n d e p t h w i t h d i s t a n c e d o w n s t r e a m as f l u i d f r o m a q u i e s c e n t e n v i r o n m e n t i s ' e n t r a i n e d * i n t o t h e t u r b u l e n t f l o w . T h i s i n f l o w i s c h a r a c t e r i z e d by a n e n t r a i n m e n t v e l o c i t y Ve. The l i n e a r s p r e a d w i t h d i s t a n c e o f f r e e p l u m e s l e d t o t h e a s s u m p t i o n by M o r t o n , T a y l o r a n d T u r n e r ( 1 9 5 6 ) t h a t Ve i s p r o p o r t i o n a l t o t h e mean f l o w v e l o c i t y V. The r a t i o ( V e / V ) i s t h e e n t r a i n m e n t f a c t o r E. G r a v i t y c u r r e n t s a t t a i n a c o n s t a n t mean v e l o c i t y V and s p r e a d l i n e a r l y w i t h d i s t a n c e a l o n g t h e s l o p e . E l l i s o n and T u r n e r ( 1 9 5 9 ) m o d i f i e d t h e a s s u m p t i o n f o r g r a v i t y c u r r e n t s t o i n c l u d e a R i c h a r d s o n d e p e n d e n c e o f t h e e n - t r a i n m e n t f a c t o r , a n d d e s c r i b e d g r a v i t y d r i v e n t u r b u l e n t s l o p e c u r r e n t s i n t e r m s o f v a r i a b l e s i n t e g r a t e d o v e r t h e d e p t h o f t h e f l o w , s p e c i f i e d by f l o w d e p t h h and mean v e l o c i t y V w h i c h a r e o n l y d e p e n d e n t on d o w n s l o p e d i s t a n c e x and by t h e b u o y a n c y f l u x A= h.V.g'. No a s s u m p t i o n s were made a b o u t t h e d i s t r i b u t i o n o f p r o p e r t i e s i n a c r o s s s e c t i o n o f the f l o w . The c o n s e r v a t i o n e q u a t i o n s c o u l d t h e n be r e d u c e d t o : mass _ d ( h . V ) = E.V ( 3 . 4 ) dx momentum _ d ( h . V 2 ) = h . g ' s i n G - Cd.V 2 ( 3 . 5 ) dx b u o y a n c y _ d ( h . V . g ' ) = - h . V . N 2 ( x ) ( 3 . 6 ) dx 63 i n w h i c h Cd i s t h e c o e f f i c i e n t o f b o t t o m f r i c t i o n ( d r a g ) , N = (-_g_. d@) 1 / 2 i s t h e l o c a l b u o y a n c y f r e q u e n c y and @o dz @o i s t h e r e f e r e n c e d e n s i t y . I n t h e s e d e r i v a t i o n s i t was assumed t h a t t h e R e y n o l d s numbers were h i g h e n o u g h t h a t any m o l e c u l a r e f f e c t s c o u l d be i g n o r e d . The d e n s i t y d i f f e r e n c e s were c o n s i d e r e d s m a l l enough t o n e g l e c t i n e r t i a t e r m s i n t h e e q u a t i o n s o f m o t i o n ( B o u s s i n e s q a p p r o x i m a - t i o n ) , i n w h i c h c a s e t h e e n t r a i n m e n t f a c t o r ( E ) o n l y d e p e n d s on t h e R i c h a r d s o n number. A l g e b r a i c m a n i p u l a t i o n o f e q u a t i o n 3.5 and s u b s t i t u t i o n o f e q a t i o n s 3.4 and 3.3 y i e l d s : _ d ( h . V 2 ) = V . _ d ( h . V ) + h.V.dV = E.V 2 = h . g ' s i n G - Cd.V 2 dx dx dx o r : E = h.g's i n 9 - Cd = R i . t a n G - Cd ( 3 . 7 ) V 2 F o r s l o p e c u r r e n t s d o m i n a t e d by t u r b u l e n t e n t r a i n m e n t a t t h e i n t e r f a c e , t h e b o t t o m f r i c t i o n c a n be i g n o r e d and e q u a t i o n 3.7 i s r e d u c e d t o a s i m p l e r e l a t i o n : E ( R i ) = R i . t a n G ( 3 . 8 ) I n t h e p r e s e n t e x p e r i m e n t s w i t h low l e v e l s o f t u r b u l e n c e i n t h e l o w e r p a r t o f t h e o b s e r v e d f l o w s , t h e b o t t o m f r i c t i o n was e s t i m a t e d f r o m : Tw = j i . d U = Cd.@.U2 ( 3 . 9 ) dy i n w h i c h y/& = *? i s t h e k i n e m a t i c v i s c o s i t y , a b o u t 1.4e-2 cm 2/s and a f i r s t o r d e r a p p r o x i m a t i o n f o r dU/dy i s t h e r a t i o o f Vmax t o h e i g h t y o f t h e maximum v e l o c i t y above t h e b o t t o m ( a b o u t 1/3 o f t h e f l o w d e p t h , b a s e d on s h a d o w g r a p h and dye o b s e r v a t i o n s ) , a n d t h u s : Cd = v. 1 = 4. 2e-2 ( 3 . 1 0 ) y.V h.V 64 The d e p t h a v e r a g e d v e l o c i t y V, u s e d i n t h e c o m p u t a t i o n o f t h e e n t r a i n m e n t f a c t o r s , was e s t i m a t e d f r o m v e l o c i t y p r o f i l e s f o r s l o p e f l o w s shown by L O f q u i s t ( I 9 6 0 ) : V = Vmax/1.12 ( 3 . 1 1 ) F i e l d and l a b o r a t o r y d a t a c o m p i l e d by Bo P e d e r s e n ( 1 9 8 0 ) f r o m t h e l i t e r a t u r e and f r o m h i s own work i n d i c a t e t h a t t h e e n t r a i n - ment f a c t o r f o r s u b - c r i t i c a l f l o w s c a n be a p p r o x i m a t e d b y : E = Ve/V = 0.072 s i n 9 ( 3 . 1 2 ) The p r e d i c t e d v a l u e s f o r e n t r a i n m e n t i n a q u i e s c e n t e n v i r o n m e n t f r o m e q u a t i o n 3.12 w o u l d r a n g e f r o m 2.76e-3 t o 6.9e-3 f o r s l o p e a n g l e s b e t w e e n 2.2° and 5.5° u s e d i n t h e p r e s e n t e x p e r i m e n t s . The e n t r a i n m e n t f a c t o r s c a l c u l a t e d f r o m d a t a o f t h e s l o p e f l o w e x p e r i m e n t s u s i n g e q u a t i o n s 3.7 and 3.10 above ( t a b l e 3.2) were 0.08 t o 1.84 w i t h o u t b o t t o m f r i c t i o n ( E l ) . W h i l e i n c l u d i n g t h e b o t t o m f r i c t i o n ( C d ) r e d u c e d t h e s e v a l u e s ( E 2 ) , i n n e a r l y e v e r y c a s e t h e c o m p u t e d e n t r a i n m e n t f a c t o r e x c e e d e d t h a t p r e d i c t e d f o r t h e q u i e s c e n t e n v i r o n m e n t by up t o two o r d e r s o f m a g n i t u d e . The f o r m u l a t i o n w h i c h d e s c r i b e s g r a v i t y f l o w s was u s e d h e r e t o compare e n t r a i n m e n t f a c t o r s b e t w e e n f l o w s i n t u r b u l e n t and i n q u i e s c e n t e n v i r o n m e n t s . The l a r g e v a l u e s f o r c a l c u l a t e d e n t r a i n m e n t w o u l d i n d i c a t e t h a t t h e b o t t o m f l o w s w o u l d r a p i d l y l o o s e t h e i r d e n s i t y d i f f e r e n c e . T h i s c o n t r a d i c t s t h e p r e s e n t e x p e r i m e n t a l f i n d i n g s a s w e l l a s A r c t i c f i e l d d a t a w h i c h show t h a t s u c h s l o p e f l o w s m a i n t a i n t h e i r c h a r a c t e r i s t i c s o v e r g r e a t d i s t a n c e s , and s u g g e s t s t h a t a d i f f e r e n t model i s r e q u i r e d t o a c c o u n t f o r t h e i n t e r a c t i o n b e t w e e n t h e t u r b u l e n c e and s h e a r . 65 The i n t e n s i t y o f t u r b u l e n t m o t i o n s s e e n i n t h e s h a d o w g r a p h image a p p e a r s much h i g h e r In t h e m i x e d l a y e r t h a n i n t h e b o t t o m s l o p e , w h i c h c o u l d l e a d t o n e t e n t r a i n m e n t o f mass a n d momentum upward o u t o f t h e f l o w . The R i c h a r d s o n numbers c a l c u l a t e d f r o m d a t a i n t a b l e 3.2 u s i n g e q u a t i o n 3.3 r a n g e f r o m 2.10 t o 19.5 an d w o u l d c a u s e c o n s i d e r a b l e d a m p i n g o f t h e t u r b u l e n c e a t t h e i n t e r f a c e . I n a t w o - l a y e r s y s t e m , t h e v e l o c i t y a n d d e n s i t y p r o f i l e s a r e i d e a l i z e d by a d i s c r e t e s t e p a t t h e I n t e r f a c e b e t w e e n t h e s l o p e f l o w a n d t h e e n v i r o n m e n t . I n p r o f i l e s f r o m e x p e r i m e n t a l d a t a t h e d e n s i t y c h a n g e d s l o w l y w i t h t h e d e p t h i n t h e s l o p e f l o w and t h e v e l o c i t y p r o f i l e e x t e n d e d u p w a r d I n t o t h e m i x e d l a y e r f l u i d s i n c e some o f I t i s s t r a i n e d a l o n g by t h e f r i c t i o n . W i t h t h e I n s t r u m e n t a t i o n d e v e l o p e d f o r t h e s e e x p e r i m e n t s more d e t a i l s o f t h e g r o w t h o r d e c a y o f s u c h s l o p e c u r r e n t s m i g h t be o b t a i n e d i f a l o n g e r s l o p e was u s e d . The c h a n g e i n t h e sha p e o f s a l i n i t y p r o f i l e s t a k e n a t d i f f e r e n t l o c a t i o n s a l o n g t h e s l o p e shows t h e d i s t r i b u t i o n o f mass w i t h i n t h e s l o p e f l o w , and c a n be u s e d t o a s s e s s t h e d o w n - s l o p e c h a n g e i n mass when I n t e g r a t e d o v e r t h e d e p t h . 66 4 - SUMMARY AND CONCLUSIONS I n a s e r i e s o f l a b o r a t o r y e x p e r i m e n t s , t h e s a l t f l u x due t o t h e f r e e z i n g o f s e a w a t e r was s i m u l a t e d by a p e r c o l a t i o n o f s e a w a t e r t h r o u g h a p o r o u s membrane i n t o a p l e x i g l a s s t a n k b e l o w . A t w o - d i m e n s i o n a l b o t t o m s l o p e f l o w was I n d u c e d by t h e c o n v e c t i o n when t h e b o t t o m o f t h e t a n k was s e t a t a s m a l l a n g l e . Low v a l u e s o f s a l t f l u x e s , c o n t r o l l e d by s e l e c t e d s t a r t i n g c o n d i t i o n s , were c a l i b r a t e d f r o m d e n s i t y d i f f e r e n c e s a c r o s s t h e membrane. I n s e v e r a l i n t e r f a c e e n t r a i n m e n t e x p e r i m e n t s w i t h t w o - l a y e r a n d l i n e a r s t r a t i f i c a t i o n s , t h i s s y s t e m c o n f i r m e d t h a t t h e c o n s t a n t e n t r a i n m e n t e f f i c i e n c y f o r f r e e p e n e t r a t i v e c o n v e c t i o n a s p r e d i c t e d by Bo P e d e r s e n c o u l d be e x t e n d e d f o r t h e s e low s a l t f l u x e s . The i n t e r f a c e e n t r a i n m e n t a s s u m p t i o n s were a p p l i e d t o a s e t o f A r c t i c f i e l d d a t a . The s m a l l v a l u e s o f c o m p u t e d e n t r a i n m e n t d i d n o t a g r e e c l o s e l y w i t h t h e p r e d i c t e d v a l u e s , w h i c h may be due i n p a r t t o s a l t a d v e c t e d i n t o t h e bay by t h e r e v e r s e e s t u a - r i n e c i r c u l a t i o n c a u s e d by s l o p e f l o w i n t h e p e r i m e t e r r e g i o n s . S h a d o w g r a p h images o f t h e f l u i d i n t h e e x p e r i m e n t a l t a n k d i d show p a t t e r n s o f c o n v e c t i v e m o t i o n s i n t h e m i x e d l a y e r , w h i c h were c a r r i e d a l o n g a n d s m o o t h e d o u t by a b o t t o m s l o p e f l o w . A w e a k e r f l o w i n t h e o p p o s i t e d i r e c t i o n was s e e n s u p e r i m p o s e d on t h e c o n v e c t i v e p a t t e r n . V e l o c i t y maxima i n t h e s l o p e f l o w o f 0.09 t o 0.66 cm/s were m e a s u r e d f r o m t h e p r o g r e s s o f t o n g u e 67 f e a t u r e s i n i n j e c t e d d y e , r e c o r d e d i n s e q u e n c e s o f c o l o r s l i d e s a n d p h o t o g r a p h s a n d on v i d e o t a p e f o o t a g e . S a l i n i t y p r o f i l e s o f f l u i d i n t h e m i x e d l a y e r and i n t h e s l o p e f l o w were p l o t t e d f r o m d a t a o b t a i n e d f r o m t h e r m i s t o r s a n d f r o m c o n d u c t i v i t y m i c r o - c e l l s d e v e l o p e d f o r t h i s p u r p o s e . These m i c r o - c e l l s have a r e s o l u t i o n i n c a l c u l a t e d s a l i n i t y o f b e t t e r t h a n 0.05 p p t , r e q u i r e a b o u t 4 ml t o f l u s h and m a i n t a i n e d s t a b l e r e a d i n g s o v e r e x t e n d e d p e r i o d s o f u s e . The s a l i n i t y p r o f i l e s show a r e g i o n w e l l m i x e d by c o n v e c t i v e t u r b u l e n c e , a n d a r i s e i n s a l i n i t y i n t h e s l o p e f l o w o f 0.24 t o 0.92 p p t a b o v e t h e m i x e d l a y e r v a l u e , f o r f l o w d e p t h s o f 7 t o 17 mm a n d c a l c u l a t e d s a l t f l u x e s b e t w e e n 1.82e-5 an d 1.63e-6 g/cm 2/s. The s p a t i a l r e s o l u t i o n a c h i e v e d w i t h t h e m i c r o - c e l l s a l l o w s a more d e t a i l e d l o o k a t t h e d e n s i t y d i s t r i b u t i o n w i t h i n a s l o p e f l o w , and w i t h a l o n g e r s l o p e i t may be p o s s i b l e t o model t h e d o w n - s l o p e b e h a v i o u r o f t h e s e b o t t o m c u r r e n t s . The d e p t h o f t h e s l o p e f l o w , t h e d e n s i t y d i f f e r e n c e b e t w e e n t h e f l o w and t h e m i x e d l a y e r d e t e r m i n e d f r o m t h e p r o f i l e s , and t h e v e l o c i t y maxima m e a s u r e d i n t h e f l o w , were a p p l i e d t o t h e model f o r p r e d i c t i n g e n t r a i n m e n t o f f l u i d f r o m a q u i e s c e n t e n v i r o n m e n t by a t u r b u l e n t g r a v i t y c u r r e n t . E n t r a i n m e n t f a c t o r s c o m p u t e d by i n s e r t i n g d a t a f r o m t h e s l o p e f l o w e x p e r i m e n t s were s e v e r a l o r d e r s o f m a g n i t u d e l a r g e r t h a n t h e p r e d i c t e d v a l u e s f o r t h e q u i e s c e n t e n v i r o n m e n t . 68 The c o n c l u s i o n s f r o m t h e s e e x p e r i m e n t s a r e : - Low c a l i b r a t e d s a l t f l u x e s t o s i m u l a t e s a l t e x p u l s i o n due t o f r e e z i n g were a c h i e v e d by p e r c o l a t i n g s e a w a t e r t h r o u g h a p o r o u s membrane. The m a g n i t u d e was c o n t r o l l e d by s e l e c - t i n g s t a r t i n g d e p t h s and d e n s i t y d i f f e r e n c e s . - E n t r a i n m e n t e x p e r i m e n t s a c r o s s a d e n s i t y i n t e r f a c e w i t h o u t s h e a r c o n f i r m e d t h a t t h e c o n s t a n t e n t r a i n m e n t e f f i c i e n c y p r e d i c t e d by Bo P e d e r s e n a p p l i e d t o t h e s e l o w s a l t f l u x e s . - A s u r f a c e s a l t f l u x o v e r a s l o p i n g b o t t o m a l w a y s p r o d u c e d a s l o p e f l o w . - Maxima i n t h e s l o p e f l o w v e l o c i t y show an i n c r e a s e f o r h i g h e r s a l t f l u x e s ( f i g u r e 3 - 5 ) , b u t f o r b o t t o m s l o p e s o f 2.2° t o 5.5° i n t h e e x p e r i m e n t s , t h e r e was no d i s t i n c t r e - l a t i o n b e t w e e n f l o w v e l o c i t y a n d s l o p e a n g l e ( f i g u r e 3 - 6 ) . - H i g h r e s o l u t i o n s a l i n i t y p r o f i l e s were o b t a i n e d f r o m d a t a f r o m s m a l l - v o l u m e c o n d u c t i v i t y m i c r o - c e l l s , d e v e l o p e d f o r t h e s e e x p e r i m e n t s a n d u s e d w i t h m i c r o - b e a d t h e r m i s t o r s . - E n t r a i n m e n t f a c t o r s c a l c u l a t e d by i n s e r t i n g d a t a f r o m t h e s l o p e f l o w e x p e r i m e n t s i n t o a model f o r t u r b u l e n t g r a v i t y f l o w s were s e v e r a l o r d e r s o f m a g n i t u d e l a r g e r t h a n t h o s e p r e d i c t e d f o r a q u i e s c e n t e n v i r o n m e n t , c o n t r a r y t o v i s u a l e v i d e n c e f r o m t h e e x p e r i m e n t s o r f r o m A r c t i c f i e l d d a t a , w h i c h show t h a t s u c h f l o w s u n d e r a t u r b u l e n t e n v i r o n m e n t m a i n t a i n t h e i r c h a r a c t e r i s t i c s o v e r g r e a t d i s t a n c e s . T h i s s u g g e s t s t h a t a d i f f e r e n t model i s r e q u i r e d t o d e s c r i b e t h e i n t e r a c t i o n b e t w e e n t h e s l o p e f l o w and t h e t u r b u l e n t env i r o n m e n t . 69 BIBLIOGRAPHY B e n j a m i n , T.B. 1968. G r a v i t y c u r r e n t s and r e l a t e d phenomena. J . F l u i d Mech. 3 1 , 209-248 Bo P e d e r s e n , F. 1980. A monograph on t u r b u l e n t e n t r a i n m e n t and f r i c t i o n i n t w o - l a y e r s t r a t i f i e d f l o w . P a p e r 25, I n s t . o f H y d r o d y n . , T e c h n . U n i v . o f Denmark, 397 pp. Bo P e d e r s e n , F. and C. J u r g e n s e n , 1984. L a b o r a t o r y e x p e r i m e n t s on e n t r a i n m e n t due t o f r e e c o n v e c t i o n . P r o g . R e p . 6 1 I n s t . o f H y d r o d y n . , T e c h n . U n i v . o f Denmark, pp.47-54 D e a r d o r f f J.W., G.E. W i l l i s and D.K. L i l l y , 1969. L a b o r a t o r y i n v e s t i g a t i o n o f n o n - s t e a d y p e n e t r a t i v e c o n v e c t i o n J . F l u i d Mech. 3 5 , 7-31 D e a r d o r f f J.W. 1980. P r o g r e s s i n u n d e r s t a n d i n g e n t r a i n m e n t a t t h e t o p o f a m i x e d l a y e r . A m . M e t e o r o l . S o c . 1978 Workshop on t h e P l a n e t a r y B o u n d a r y L a y e r , pp.33-66 D e a r d o r f f J.W,, G.E. W i l l i s a n d B.H. S t o c k t o n 1980. L a b o r a t o r y s t u d i e s o f t h e e n t r a i n m e n t zone o f a c o n v e c t i v e l y m i x e d l a y e r . J . F l u i d Mech. 100, 41-64 E l l i o t t , J.A. 1972. C o n v e c t i v e m o t i o n s u n d e r s e a i c e . F r o z e n S e a s R e s e a r c h G r o u p , I n s t . o f O cean S c i . S i d n e y , B.C. U n p u b l i s h e d , 17 pp. E l l i s o n , T.H. and T u r n e r , J . S . 1959. T u r b u l e n t e n t r a i n m e n t l n s t r a t i f i e d f l o w s . J . F l u i d Mech. 6, 423-448 F o f o n o f f , N.P. and R.C. M i l l a r d J r . , 1983. A l g o r i t h m s f o r com- p u t a t i o n o f f u n d a m e n t a l p r o p e r t i e s o f s e a w a t e r . U n e s c o T e c h n . P a p e r s i n M a r i n e S c i . 44, 53 pp. F o s t e r , T.D. 1969. E x p e r i m e n t s on h a l i n e c o n v e c t i o n i n d u c e d by t h e f r e e z i n g o f s e a w a t e r . J . G e o p . R e s . 74,6967-6974 Gade, H.G., R.A. L a k e , E.L. L e w i s and E.R. W a l k e r , 1974 O c e a n o g r a p h y o f an A r c t i c B ay. Deep-Sea R e s . 2 1 , 547-571 70 H e i d t , F.D. 1977. The g r o w t h o f t h e m i x e d l a y e r i n a s t r a t i f i e d f l u i d due t o p e n e t r a t i v e c o n v e c t i o n . B d y . L a y e r Met. 12, 439-461 K a t o , H. and O.M. P h i l l i p s , 1969. On t h e p e n e t r a t i o n o f a t u r b u l e n t l a y e r i n t o a s t r a t i f i e d f l u i d . J . F l u i d Mech. 37, 643-655 K a n t h a L.H. 1975. T u r b u l e n t e n t r a i n m e n t a t t h e d e n s i t y i n t e r f a c e o f a t w o - l a y e r s t a b l y s t r a t i f i e d f l u i d s y s t e m . T e c h n . R e p o r t 7 5 - 1 , J o h n s H o p k i n s U n i v . 162pp. K u l l e n b e r g , G. 1977. E n t r a i n m e n t v e l o c i t y In n a t u r a l s t r a t i f i e d s h e a r f l o w . E s t u . & C o a s t . M a r . S c i . 5, 329-338 L a k e , R.A. and E.L. L e w i s 1970. S a l t r e j e c t i o n by s e a i c e d u r i n g g r o w t h . J . G e o p h y s . R e s . 7 5 , 583-597 L i n d e n , P.F. 1975. The d e e p e n i n g o f a m i x e d l a y e r i n a s t r a t i f i e d f l u i d . J . F l u i d Mech. 7 1 , 385-405 L O f q u i s t , K. 1960. F l o w and s t r e s s n e a r an i n t e r f a c e b e t w e e n s t r a t i f i e d l i q u i d s . P h y s . o f F l u i d s 3, 158-175 L o n g , R.R. 1975. The i n f l u e n c e o f s h e a r on m i x i n g a c r o s s d e n s i t y i n t e r f a c e s . J . F l u i d Mech. 7 0 , 305-329 M e a g h e r , T.B. A.M. P e d e r s o n and M.C. G r e g g , 1982. A l o w - n o i s e c o n d u c t i v i t y m i c r o - s t r u c t u r e I n s t r u m e n t . I EEE J . o f O c e a n . E n g , p p . 2 8 3 - 2 9 0 M e l l i n g , H. and. E.L. L e w i s 1982. S h e l f d r a i n a g e f l o w s i n t h e B e a u f o r t S e a and t h e i r e f f e c t on t h e A r c t i c O cean p y c n o c l i n e . Deep-Sea R e s . 29, 967-985 M i l l e r o , F . J . , C.T. Chen, A. B r a d s h a w and K . S c h l e i c h e r , 1980. A new h i g h - p r e s s u r e e q u a t i o n o f s t a t e f o r s e a w a t e r , Deep-Sea R e s . 27A, 255-264 M o o r e , M.J. and R.R. L o n g 1971. An e x p e r i m e n t a l I n v e s t i g a t i o n o f t u r b u l e n t s t r a t i f i e d s h e a r i n g f l o w . J . F l u i d Mech. 49, 635-655 71 Mowbray, D.E, 1967, The use o f s c h l l e r e n a n d s h a d o w g r a p h t e c h - n i q u e s l n t h e s t u d y o f f l o w p a t t e r n s i n d e n s i t y s t r a t i f i e d f l u i d s . J . F l u i d Mech. 27, 595-608 P e r k i n , R.G. and E.L. L e w i s 1978. M i x i n g i n an A r c t i c F j o r d , J . P h y s . O c e a n . 8 , 873-880 P e r k i n , R.G. and E.L. L e w i s 1978. S a l i n i t y : I t s d e f i n i t i o n a n d c a l c u l a t i o n . J . G e o p . R e s . 8 3 , 466-478 P e r k i n , R.G. and E.L. L e w i s 1980. The P r a c t i c a l S a l i n i t y S c a l e 1 9 7 8 : F i t t i n g t h e D a t a . IEEE J . o f O c e a n i c Eng. OE-5, 9-16 P h i l l i p s , O.M. 1972. T':>o e n t r a i n m e n t i n t e r f a c e J . F l u i d Mech. 5 1 , 97- 1 18 T h o r p e , S.A. 1973. T u r b u l e n c e . In s t r a t i f i e d f l u i d s : a r e v i e w o f l a b o r a t o r y e x p e r i m e n t s . B d y . L a y e r Met. 4 , 95-119 T u r n e r , J . S . 1968. The i n f l u e n c e o f m o l e c u l a r d i f f u s i v i t y on t u r b u l e n t e n t r a i n m e n t a c r o s s a d e n s i t y i n t e r f a c e . J . F l u i d Mech. 3 3 , 639-656 T u r n e r , J . S . 1973. " B u o y a n c y e f f e c t s i n f l u i d s " C a m b r i d g e U n i v e r s i t y P r e s s , 367 pp. T u r n e r , J . S . 1980. " S m a l l s c a l e m i x i n g . I n " E v o l u t i o n o f P h y s i c a l O c e a n o g r a p h y " , e d i t e d by B.A. W a r r e n & C. Wunsch, MIT P r e s s , C a m b r i d g e , pp.236-262 W a l i n , G. 1971. C o n t a i n e d non-homogeneous f l o w u n d e r g r a v i t y o r how t o s t r a t i f y a f l u i d i n t h e l a b . J . F l u i d Mech. 4 8 , 647-672 W y a t t , L.R. 1978. The e n t r a i n m e n t i n t e r f a c e i n a s t r a t i f i e d f l u i d . J . F l u i d Mech. 8 6 , 293-311 72 SALINITY AND DENSITY COMPUTATION APPKNDIX A 73 APPENDIX A S A L I N I T Y AND DENSITY C A L C U L A T I O N A . l S a l i n i t y The s a l i n i t y o f f l u i d s u s e d i n t h e c o n v e c t i o n e x p e r i m e n t s i s c a l c u l a t e d f r o m e l e c t r i c a l c o n d u c t i v i t y , p r e s s u r e and t e m p e r a - t u r e u s i n g a s t a n d a r d s e t o f p o l y n o m i a l s known a s t h e P r a c t i c a l S a l i n i t y S c a l e ( L e w i s a n d P e r k i n , 1 9 8 0 ) . I f R i s t h e c o n d u c t i v i t y r a t i o o f t h e f l u i d ( i . e . t h e r a t i o o f t h e c o n d u c t a n c e a t t e m p e r a t u r e T and p r e s s u r e P t o t h a t a t a t m o s p h e r i c p r e s s u r e and 15 °C) t h e n t h e s a l i n i t y S i n u n i t s o f t h e P r a c t i c a l S a l i n i t y S c a l e i s c a l c u l a t e d f r o m : Q = 1+ P ( A 1 + P ( A 2 + P * A 3 ) ) / ( 1 + T ( B 1 + T * B 2 ) + R ( B 3 + T * B 4 ) ) U = C0+T(C1+T(C2+T(C3+T*C4))) W = R/(Q*U) Y =W"2 F = ( T - 1 5 ) / ( 1 + . 0 1 6 2 ( T - 1 5 ) ) S = E 0 + F * F 0 + Y ( E 1 + F * F 1 + Y ( E 2 + F * F 2 + Y ( E 3 + F * F 3 + Y ( E 4 + F * F 4 + Y ( E 5 + F * F 5 ) ) ) ) ) i n w h i c h P i s t h e p r e s s u r e i n b a r s , T t h e t e m p e r a t u r e i n °C, S i s t h e s a l i n i t y i n PSS ( u n i t s a r e c l o s e t o t h e f o r m e r l y u s e d g r a m s / k i 1 o g r a m o r p a r t s - p e r - t h o u s a n d ) , Q, U, W, Y, F a r e i n t e r - m e d i a t e r e s u l t s , a n d A i t h r o u g h F i a r e c o n s t a n t s w i t h v a l u e s : A l = 2 . 0 7 0 e - 5 C0=0.6766097 E0=0.0080 F0=0.0005 A2=0.637e-9 C1=0.0200564 E l = - 0 . 1 6 9 2 F l = - 0 . 0 0 5 6 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 F o r l a b o r a t o r y e x p e r i m e n t s t h e s e c a l c u l a t i o n s a r e s i m p l i f i e d s i n c e P=0 a t a t m o s p h e r i c p r e s s u r e . T hese p o l y n o m i a l s a r e d e f i n e d f o r a r a n g e o f s a l i n i t i e s f r o m 2 t o 42 p a r t s - p e r - t h o u s a n d . A l t h o u g h PSS u n i t s a r e n o t d e f i n e d o u t s i d e t h i s r a n g e , a g r a p h o f t h e c o n d u c t i v i t y r a t i o o v e r an e x t e n d e d r a n g e o f s a l i n i t y a n d f o r l a b o r a t o r y t e m p e r a t u r e s f r o m 17 t o 25 °C shows t h a t t h e s e p o l y n o m i a l s s m o o t h l y e x t e n d t o h i g h e r v a l u e s o f S ( s e e f i g u r e A - 1 ) . To c r e a t e h i g h e r s a l t f l u x e s , p u r e s e a s a l t was a d d e d t o s e a w a t e r . S a l i n i t y v a l u e s o f t h i s f l u i d , o b t a i n e d w i t h an o p t i c a l r e f r a c t o m e t e r , from t h e G u i l d l i n e A u t o s a l a f t e r a 2 - t o - l volume d i l u t i o n and d o u b l i n g t h e r e s u l t , and f r o m t h e o u t p u t o f t h e c a l i b r a t e d m i c r o - c e l l were f o u n d t o a g r e e w i t h i n s e v e r a l p p t , i n d i c a t i n g t h a t v a l u e s c o m p u t e d f r o m t h e a b o v e f o r m u l a s f o r t h e P r a c t i c a l S a l i n i t y S c a l e may be u s e d w i t h c a u t i o n a s r e a s o n a b l e e s t i m a t e s . 75 A.2 Density The U n e s c o E q u a t i o n o f S t a t e f o r s e a w a t e r ( M i l l e r o , 1980) i s u s e d t o c a l c u l a t e f l u i d d e n s i t i e s D i n g/cm 3 o r i n u n i t s o f s i g m a - t = ( D-1)*1000 f r o m s a l i n i t y S ( P S S ) , t e m p e r a t u r e T (°C) and p r e s s u r e P ( b a r s ) f r o m t h e f o l l o w i n g s e t o f p o l y n o m i a l s : 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 2 8 8 e - 5 ) ) ) E= A + S ( - 9 . 9 3 4 8 e - 7 + T ( 2 . 0 8 1 6 e - 8 + T * 9 . 1 6 9 7 e - 1 0 ) ) F= B + S ( 2 . 2 8 3 8 e - 3 + T ( - l . 0 9 8 1 e - 5 - T * l . 6078e-6 ) ) +S 3 / 2* 1 .9 1075e-4 G= C + S ( 5 4 . 6 7 4 6 + T ( - 0 . 6 0 3 4 5 9 + T ( 0 . 0 1 0 9 9 8 7 - T * 6 . 1 6 7 e - 5 ) ) ) H= G + S 3 , 2 ( 0 . 0 7 9 44 + T ( 0 . 0 1 6 4 8 3 - T * 5 . 3009e-4) ) +P(F+P*E) J=999.8 42594+T(0.0679 395 2 + T ( - 9 . 0 9 * 2 9 e - 3 + T * 1 . 0 0 1 6 8 5 e - 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 4 6 7 e - 7 + T * 5 . 3 8 7 5 e - 9 ) ) ) M=-5.7 2 466e-3+T(1.02 2 7 e - 4 - T * l . 6 5 46e-6) N= J+S*K+S :" 2*M+S 2*4.8314e-4 D= N/1000/(1-P/H) = d e n s i t y i n g r / c m 3 S i m i l a r t o t h e p o l y n o m i a l s o f t h e P r a c t i c a l S a l i n i t y S c a l e , t h e s e a r e v a l i d f o r s a l i n i t i e s r a n g i n g f r o m 0 t o 42 PSS. They a l s o s i m p l i f y s i n c e P=0 f o r l a b o r a t o r y ( a t m o s p h e r i c p r e s s u r e ) . The r e l a t i o n b e t w e e n s a l i n i t y a n d d e n s i t y , p l o t t e d f r o m t h e above p o l y n o m i a l s , i s n e a r l y l i n e a r o v e r t h e e x t e n d e d r a n g e o f s a l i n i t i e s f o r t h e t e m p e r a t u r e s u s e d i n l a b o r a t o r y e x p e r i m e n t s ( s e e f i g u r e A - 2 ) . D e n s i t i e s so d e t e r m i n e d were u s e d t o compute e s t i m a t e s o f t h e membrane s a l t f l u x d u r i n g t h e e x p e r i m e n t s . 76 F i g u r e A - l . CONDUCTIVITY RATIO vs SALINITY f o r l a b o r a t o r y t e m p e r a t u r e s T-25 22 21 20 S a l i n i ty 0 15 30 45 E0 75 S a l i n i ty CONDUCTIVITY MICRO-CELLS A P P E N D I X B 79 APPENDIX B MICRO-CELLS A s e t o f s m a l l volume f o u r - e l e c t r o d e c o n d u c t i v i t y c e l l s was d e v e l o p e d t o d e t e r m i n e t h e s a l i n i t y o f f l u i d In an e x p e r i m e n t a l t a n k . As f l u i d i s s y p h o n e d t h r o u g h one o f t h e s e m i c r o - c e l l s , a t a f l o w r a t e o f a b o u t 2 d r o p s / s e c ( 0 . 1 5 m l / s ) , t h e e l e c t r i c a l c o n d u c t a n c e i n s i d e t h e c e l l c h a n g e s w i t h t h e s a l i n i t y o f t h e f l u i d . A s m a l l e l e c t r o n i c c i r c u i t c o n v e r t s t h i s c o n d u c t a n c e i n t o an o u t p u t v o l t a g e , w h i c h was c a l i b r a t e d t o y i e l d t h e c o n d u c t i v i t y r a t i o o f t h e f l u i d . T h e r m i s t o r s were a d d e d a t t h e i n l e t a n d o u t l e t o f t h e m i c r o - c e l l , a n d t h e s a l i n i t y o f f l u i d i n t h e m i c r o - c e l l i s c a l c u l a t e d f r o m t h e c o n d u c t i v i t y r a t i o a n d t h e a v e r a g e t e m p e r a t u r e o f t h e t h e r m i s t o r s , u s i n g t h e p o l y n o m i a l s o f t h e P r a c t i c a l S a l i n i t y S c a l e ( s e e a p p e n d i x A . l ) . The f l u i d d e n s i t y a t t h e i n t a k e p o i n t i n t h e t a n k i s c o m p u t e d f r o m t h i s s a l i n i t y a n d t h e t e m p e r a t u r e f r o m a n o t h e r t h e r m i s t o r l o c a t e d i n t h e t a n k , u s i n g t h e U n e s c o E q u a t i o n o f S t a t e f o r S e a W a t e r ( a p p e n d i x A . 2 ) . B . l C e l l c o n s t r u c t i o n The m i c r o - c e l l s , c o n s t r u c t e d by t e c h n i c a l s u p p o r t s t a f f a t t h e I n s t i t u t e o f Ocean S c i e n c e s , c o n s i s t o f f o u r r i n g - s h a p e d e l e c t r o d e s made o f 0.002" t h i c k p l a t i n u m f o i l a n d s e p a r a t e d by s e g m e n t s o f 1.8 mm l . D . g l a s s t u b i n g o f 0.6 mm w a l l t h i c k n e s s . F i g u r e B-1 shows a d i a g r a m o f t h e c e l l w i t h t h e p r i n c i p a l d i mens 1ons. 80 GLASS TUBING SECTIONS 1 .8mm I.D. - 3mm O.D, COLOR CODED LEADS FROM ELECTRODES 0.002" PLATINUM F O I L ELECTRODES, EACH 5mm WIDE PVC TUBING COVER F i g u r e B - l . D i a g r a m o f m i c r o - c e l l a s s e m b l y The e l e c t r o d e s a n d g l a s s s p a c e r s were h e l d i n p l a c e by s e c t i o n s o f h e a t s h r i n k t u b i n g , and c o l o r c o d e d e l e c t r i c a l l e a d s were s o l d e r e d t o t h e e l e c t r o d e s . The c o m p l e t e d a s s e m b l y was s e a l e d w i t h e p o x y i n a p r o t e c t i v e PVC s l e e v e . T h r e e s u c h m i c r o - c e l l s were made, u s i n g t h e same m a t e r i a l s a n d p h y s i c a l d i m e n s i o n s . B.2 M i c r o - c e l l e l e c t r o n i c s The f o u r e l e c t r o d e s o f t h e m i c r o - c e l l were c o n n e c t e d t o an e l e c t r o n i c c i r c u i t w h i c h c o n v e r t s t h e c o n d u c t a n c e ( 1 / R ) o f t h e m i c r o c e l l i n t o a l i n e a r f u n c t i o n o f t h e o u t p u t v o l t a g e ( V C ) . F l u i d s a m p l e s o f a known s a l i n i t y , d e t e r m i n e d w i t h a G u i l d - l i n e A u t o s a l b e n c h s a l i n o m e t e r , were u s e d t o o b t a i n v a l u e s f o r m i c r o - c e l l s c a l i b r a t i o n c o n s t a n t s K , e x p r e s s e d i n ohms o f c e l l r e s i s t a n c e a t a s a l i n i t y o f 35 p p t and a t e m p e r a t u r e o f 15 °C. 8 1 The c o n d u c t i v i t y r a t i o (RR) o b t a i n e d f r o m t h e m i c r o - c e l l i s t h e p r o d u c t o f c o n d u c t a n c e and c e l l c o n s t a n t : 1/R = = A + B.VC 1/R = = c e l l c o n d u c t a n c e VC = = o u t p u t v o l t a g e RR = = K.(A + B.VC) RR = = c o n d u c t i v i t y r a t i o K = c e l l c o n s t a n t and coe f f l c i e n t s : A = -2.6008e-8 B = -4.5954e-4 The c o e f f i c i e n t s A and B were d e t e r m i n e d w i t h a h i g h p r e c i s i o n d e c a d e r e s i s t o r b o x , and c h e c k e d a f t e r a b o u t 6 months o f u s e . Th e r e was no d r i f t o r t e m p e r a t u r e d e p e n d e n c e f o u n d i n t h e o u t p u t v o l t a g e o f t h e c i r c u i t . A l e a s t s q u a r e s l i n e a r f i t t o th e d a t a was u s e d t o c a l c u l a t e A a n d B. The s t a n d a r d d e v i a t i o n was 2.2065e-4 w i t h a c o r r e l a t i o n f a c t o r b e t t e r t h a n 0.9999 . B.3 AM/CT Datalogger c o n d u c t i v i t y e l e c t r o n i c s The AM/CT D a t a l o g g e r had a s l i g h t l y d i f f e r e n t c o n d u c t i v i t y c i r c u i t . I t was o r i g i n a l l y d e s i g n e d f o r c e l l s w i t h a c o n s t a n t o f a b o u t 100 ohms b u t was m o d i f i e d f o r use w i t h t h e m i c r o - c e l l s w h i c h have a much h i g h e r c e l l c o n s t a n t o f a b o u t 1800 ohms. The r e l a t i o n b e t w e e n N-number a nd c o n d u c t i v i t y r a t i o i s g i v e n b y : RR = K'.(A + B.NC) w i t h NC = AM/CT d a t a l o g g e r o u t p u t K'= c e l l c o n s t a n t and c o e f f i c i e n t s : A = 5.53084e-5 B = 1 .3290e-7 82 A number o f t r i a l r u n s were done t o d e t e r m i n e t h e s t a b i l i t y a n d v a r i a b i l i t y o f m e a s u r e m e n t s a t s e v e r a l c o n s t a n t s a l i n i t i e s . I n s e v e r a l o f t h e t e s t s , t h e v a r i a b i l i t y o f t h e raw t e m p e r a t u r e d a t a was l e s s t h a n + 2 i n t h e l a s t d i g i t (+0.007 °C>, and f o r raw c o n d u c t i v i t y a b o u t + 3 u n i t s ( c o r r e s p o n d i n g t o +0.025 P S S ) . As a l a r g e r r a n g e o f c o n d u c t i v i t i e s was u s e d w i t h t h e t h r e e m i c r o - c e l l s , t h e v a r i a b i l i t y i n t h e o u t p u t o f t h e d a t a l o g g e r c o n d u c t i v i t y c i r c u i t I n c r e a s e d . S e v e r a l s e r i e s o f o b s e r v a t i o n s were t a k e n o v e r l o n g e r p e r i o d s o f t i m e , u s i n g t h r e e m i c r o - c e l l s s i m u l t a n e o u s l y . D e v i a t i o n s i n t h e o b s e r v a t i o n s c o u l d be c a u s e d by s u d d e n v a r i a t i o n s i n t h e f l o w r a t e c a u s e d by s m a l l p a r t i c l e s o b s t r u c t i n g t h e f l o w . F i l t e r i n g a l l f l u i d s d i d n o t e l i m i n a t e t h e p r o b l e m . S m a l l b u b b l e s a d h e r i n g t o a m i c r o - c e l l e l e c t r o d e c o u l d c h a n g e t h e c o n d u c t a n c e i n t h e c e l l . The t e s t s d i d show t h a t any a b r u p t c h a n g e In t h e f l o w c a u s e s an i m m e d i a t e c h a n g e i n t h e c o m p u t e d s a l i n i t y w h i c h i n a b o u t 5 t o 20 s e c o n d s r e t u r n s t o t h e p r e v i o u s l e v e l . The c o m p u t e d v a l u e o f s a l i n i t y and t h e v a r i a b i l i t y d i d n o t d e p e n d on t h e m a g n i t u d e o f t h e f l o w t h r o u g h t h e m i c r o - c e l l s . The use o f a p e r i s t a l t i c pump t o draw t h e f l u i d t h r o u g h t h e c e l l s more t h a n d o u b l e s t h e v a r i a b i l i t y , p o s s i b l y due t o s h o c k s w h i c h c a u s e s m a l l p a r t i c l e s o r b u b b l e s t o d i s r u p t t h e p o t e n t i a l o r t h e c u r r e n t p a t t e r n i n s i d e t h e c e 1 1 . B.4 Determination of c a l i b r a t i o n constants The m i c r o - c e l l s were c a l i b r a t e d by u s i n g f l u i d s a m p l e s o f known s a l i n i t y . C e l l c o n s t a n t s were t h e n c h o s e n w h i c h y i e l d a c a l c u l a t e d s a l i n i t y e q u a l t o t h a t d e t e r m i n e d w i t h a G u i l d l i n e 83 A u t o s a l b e n c h s a l i n o m e t e r . The f l u i d was s y p h o n e d t h r o u g h e a c h m i c r o - c e l l a t s e v e r a l d i f f e r e n t s t e a d y f l o w r a t e s c o u n t e d t o be b e t w e e n 1 and 4 d r o p s p e r s e c o n d ( a b o u t 0.05 t o 0.20 m l / s ) . An I n t e g e r v a l u e was c h o s e n f o r K t o make t h e c a l c u l a t e d 3 a g r e e w i t h t h e v a l u e d e t e r m i n e d u s i n g t h e A u t o s a l . These c a l i b r a t i o n s were r e p e a t e d a t s e v e r a l t e m p e r a t u r e s a nd s a l i n i t i e s . The v a l u e s o f K were p l o t t e d a g a i n s t ^ t e m p e r a t u r e a t w h i c h t h e y were c a l c u l a t e d t o c h e c k f o r t e m p e r a t u r e d e p e n d e n c e ( f i g u r e B - 2 ) . S h i f t s In c o n d u c t i v i t y were f o u n d t o o c c u r when t h e c e l l o u t l e t t u b i n g made e l e c t r i c a l c o n t a c t w i t h t h e f l u i d w h i c h was pumped b a c k t o t h e t a n k i n s t e a d o f d r i p p i n g t o b r e a k t h e f l o w . An e x t e r n a l c u r r e n t l o o p f o r m e d v i a t h e pump o r one of t h e o t h e r c e l l s a n d c a u s e d a ch a n g e i n a p p a r e n t c o n d u c t i v i t y a n d t h u s i n t h e c e l l c o n s t a n t . F o r c e l l #2, t h e d a t a w i t h o u t an e x t e r n a l l o o p had an a v e r a g e v a l u e f o r K o f 1765 w i t h a s t a n - d a r d d e v i a t i o n o f 1.89 , w h i c h c h a n g e s t h e c a l c u l a t e d s a l i n i t y by 0.024 a t a s a l i n i t y o f 20 PSS and a t e m p e r a t u r e o f 20 °C. I n i t i a l l y , t h e c u r r e n t e l e c t r o d e s were t h o s e c l o s e s t t o t h e c e n t r e o f t h e c e l l , b u t e x c h a n g i n g t h e l e a d s o f p o t e n t i a l a n d c u r r e n t e l e c t r o d e s r e d u c e d t h e v a r i a b i l i t y i n t h e c a l c u l a t e d s a l i n i t y f r o m t h e D a t a l o g g e r t o n e a r l y h a l f t h e i n i t i a l v a l u e . T h i s e x c h a n g e o f e l e c t r o d e s c h a n g e d t h e e f f e c t i v e p o t e n t i a l p a t h i n s i d e t h e c e l l a n d c a u s e d a s m a l l c h a n g e i n t h e v a l u e s o f c e l l c o n s t a n t s . 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 X X X x * x x x< o e l l o u t l e t drip©, no e x t e r n a l l o o p 1750 J 1730 J 1710 x X X o e l l o u t l e t immereed, e x t e r n a l e l e o . l o o p x x 1590 iqure B-2. Micro-cell constants vs. temp. 85 C e l l s have been r e p o r t e d t© 'age' In s u c c e s s i v e c y c l e s o f w e t t i n g and d r y i n g . T h i s may a l t e r t h e s u r f a c e c h a r a c t e r i s t i c s o f t h e e l e c t r o d e s o f t h e new c e l l s , a n d c a u s e some s h i f t i n K. No s i g n i f i c a n t c h a n g e was f o u n d i n t h e c o n s t a n t o f t h e f i r s t c e l l i n more t h a n a y e a r . The c o n d u c t a n c e i n t h e c e l l i s s t r o n g l y a f f e c t e d by m i n u t e p a r t i c l e s o r b u b b l e s due t o t h e s m a l l s i z e o f t h e c e l l . I n some i n s t a n c e s , u s i n g a w e l l m i x e d f l u i d o f c o n s t a n t s a l i n i t y , t h e t i m e - s e r i e s p l o t o f c a l c u l a t e d v a l u e s o f S fr o m t h e D a t a l o g g e r o u t p u t d i d show a d r i f t down i n s a l i n i t y , f o l l o w e d by a jump ba c k t o t h e f o r m e r c o n s t a n t v a l u e . T h i s a p p a r e n t d r o p i n s a l i n i t y c o u l d be c a u s e d by a d e c r e a s i n g c o n t a c t s u r f a c e a t an e l e c t r o d e due t o t r a p p e d a n d c o a l e s c i n g b u b b l e s . O c c a s i o n a l l i g h t t a p p i n g on t h e c e l l may d i s l o d g e a ny p a r t i c l e o r b u b b l e t r a p p e d i n t h e c e l l and r e s t o r e t h e c o r r e c t c a l i b r a t i o n v a l u e . The AM/CT d a t a l o g g e r c o n d u c t i v i t y c i r c u i t u s e d d i f f e r e n t c u r r e n t a n d v o l t a g e v a l u e s f o r t h e c e l l e l e c t r o d e s , r e s u l t i n g i n v a l u e s f o r t h e c e l l c o n s t a n t s K w h i c h d i f f e r s i g n i f i c a n t l y f r o m t h o s e o b t a i n e d w i t h t h e s m a l l e l e c t r o n i c c i r c u i t s a s was e x p l a i n e d p r e v i o u s l y . C a l i b r a t i o n c h e c k s were f r e q u e n t l y done f o r b o t h s y s t e m s t o t r a c k t h e l o n g t e r m b e h a v i o u r o f t h e m i c r o - c e l l s . P r i n t - o u t s o f e a c h d a t e a r e I n c l u d e d In t h i s a p p e n d i x a n d t h e a v e r a g e d v a l u e o f c a l i b r a t i o n c o n s t a n t s f o r e a c h c e l l a r e shown i n t a b l e B . l b e l o w . E a c h c a l i b r a t i o n c o n s t a n t l i s t e d b e l o w i s an a v e r a g e o f 4 t o 8 o b s e r v a t i o n s . 86 T a b l e B . l M i c r o - c e l l c a l i b r a t i o n c o n s t a n t s Day Date S a l Temp. d a t a l o q q e r s m a l l ' e 1 e c t r . # ( P S S ) (°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 8 6 - 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 ( 1 8 1 8 ) 1832 5 1 1 -20 5 . 95 21.0 1878 1794 1832 53 1- 22 31 . 5 21.0 1808 1754 ( 1 7 3 8 ) 53 1 -22 6. 10 20.5 ( 1 7 7 1 ) ( 1 7 1 7 ) ( 1 7 5 5 ) 54 1- 23 6. 1 1 2 1.1 ( 1 7 0 9 ) 1748 ( 1 7 6 3 ) 55 1- 24 33. 66 20.0 (1 8 1 6 1758 1793 55 1- 24 6 . 59 20.0 ( 1 7 6 7 ) ( 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 ( 1 8 1 1 ) 1758 1790 99 3- 9 28 . 02 2 1.9 1877 1792 18 14 1800 1751 1782 106 3- 16 28 . 36 21.4 ( 1 8 4 5 ) ( 1 7 7 4 ) — — 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 A v e r a g e e e l 1 c o n s t a n t s : 1885 1793 1821 1801 1752 1785 w i t h s t a n d a r d de v i a t i o n : 6.34 4.20 6.70 5.64 3. 50 6.63 The c o n s t a n t s i n b r a c k e t s d i f f e r e d s u b s t a n t i a l l y f r o m t h e e x p e c t e d v a l u e and were n o t I n c l u d e d i n d e t e r m i n i n g t h e a v e r a g e v a l u e s and s t a n d a r d d e v i a t i o n s . Some o f t h e s e d i f f e r e n c e s c o u l d be c a u s e d by c o n t a m i n a t i o n o f t h e e l e c t r o d e s I n s i d e a c e l l by p a r t i c l e s o r b u b b l e s . A t i m e - s e r i e s p l o t o f t h e c e l l c o n s t a n t v a l u e s ( f i g u r e B-3) shows t h a t any d r i f t I s much l e s s t h a n t h e 87 v a r i a b i l i t y In t h e o b s e r v a t i o n s . The c o n d u c t i v i t y may a f f e c t t h e f i e l d d i s t r i b u t i o n and c u r r e n t p a t h In t h e c e l l and t h u s a l t e r t h e c e l l c o n s t a n t . Some d e p e n d e n c e i s s e e n i n a p l o t o f c e l l c o n s t a n t v e r s u s s a l i n i t y d u r i n g c a l i b r a t i o n ( f i g u r e B - 4 ) . 88 1900 - l 17 CO (0 -p c 0 -p (0 c o 0 01 G • Q 1800 - X X — I. X a X Q X Q a Q Q y — _ a - X A x a x X v 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 a f t e r 85-12-1 Figure B~3 Time-series of m i c r o - c e l l c a l i b r a t i o n constants S a l i n i t y (PSS) F i g u r e E>-4\Cel l c a l i b r a t i o n c o n s t a n t s v s . S a l i n i t y B.5 M i c r o - c e l l t i m e r e s p o n s e The r e s p o n s e o f t h e c e l l t o an a b r u p t c h a n g e i n s a l i n i t y h as been i n v e s t i g a t e d t o d e t e r m i n e t h e volume r e q u i r e d ( o r t h e t i m e r e q u i r e d a t a s e l e c t e d f l o w r a t e ) b e f o r e t h e c a l c u l a t e d s a l i n i - t y r e a c h e s t h e new v a l u e . A f t e r a s t e p - c h a n g e i n t h e s a l i n i t y a t t h e i n t a k e p o i n t , t h e l e n g t h o f t i m e f o r t h e c e l l t o r e s p o n d d e p e n d s on t h e f l u s h i n g c h a r a c t e r i s t i c s o f t h e c e l l . I n i n i t i a l a t t e m p t s t o d e t e r m i n e t h e t i m e r e s p o n s e o f t h e m i c r o - c e l l w i t h t h e AM/CT d a t a l o g g e r , t h e minimum s a m p l i n g was a b o u t 4 s e c o n d s and t h e o u t p u t showed e x c e s s i v e v a r i a b i l i t y c a u s e d by p r o b l e m s w i t h t h e A/D c o n v e r t e r o f t h e c o n d u c t i v i t y c i r c u i t . To g e t more a c c u r a t e d a t a a n d f a s t e r s a m p l i n g , an HP-3497A D a t a A c q u i s i t i o n S y s t e m was u s e d . The a r r a n g e m e n t i s shown i n f i g u r e B-5. •T-TOP CELL OUTLET SYPHON TUBE MICRO-CELL ELECTRONICS T-BOTTOM VALVE JAR S-l - P A I L •CH9 - HP-7225A PLOTTER HP-9825 COMPUTER HP-3497A DATA ACQUISITION SYSTEM F i g u r e B-5. Time R e s p o n s e - E x p e r i m e n t a l A r r a n g e m e n t The i n t a k e o f t h e m i c r o - c e l l was c o n n e c t e d t o a v a l v e w h i c h c o u l d s w i t c h t h e f l o w f r o m a j a r o f one s a l i n i t y 91 t o a p a l l o f a n o t h e r . The j a r was f l o a t e d l n t h e l a r g e r p a l l t o m i n i m i z e t e m p e r a t u r e d i f f e r e n c e s a nd t o g e t a n e a r l y c o n s t a n t d r o p i n h e i g h t b e t w e e n t h e f l u i d l e v e l s a nd t h e c e l l o u t l e t . The g r a v i t y - d r i v e n f l o w t h r o u g h t h e c e l l d i d r e m a i n n e a r l y c o n s t a n t when s w i t c h i n g b e t w e e n s a l i n i t i e s . A c t u a l f l o w r a t e s d u r i n g e a c h r u n were m e a s u r e d by c o u n t i n g t h e number o f d r o p s o v e r t i m e a t t h e o u t l e t f o r d i f f e r e n t s e t t i n g s . These r a n g e d f r o m a b o u t 0.5 t o 4 d r o p s p e r s e c o n d . C o u n t i n g showed a b o u t 825 d r o p s i n 50 m l . E a c h c e l l was c o n n e c t e d t o a m i c r o - c e l l c o n d u c t i v i t y c i r c u i t a n d c o n t i n u o u s l y p o w e r e d d u r i n g a r u n , w h i c h a v o i d s t r a n s i e n t s c a u s e d by s w i t c h i n g . The o u t p u t o f t h i s c i r c u i t a n d o f t h e m i c r o - c e l l t h e r m i s t o r s were t h e n c o n n e c t e d t o t h e H P - D a t a l o g g e r S y s t e m , w h i c h was c o n t r o l l e d by an HP-9825 c o m p u t e r . A p r o g r a m f o r t h i s s y s t e m was m o d i f i e d t o use t h e a v e r a g e t e m p e r a t u r e f r o m b o t h t h e r m i s t o r s f o r c a l c u l a t i n g t h e s a l i n i t y a n d t o s t o r e t h e c a l c u l a t e d v a l u e s on t a p e . The c o m p u t e d s a l i n i t i e s were p l o t t e d d u r i n g e a c h r u n a n d t h e o b s e r v e d f l o w r a t e s were marked on t h e p l o t s i n number o f d r o p s c o u n t e d p e r s t o p w a t c h s e c o n d s . A t low f l o w s , t h e d i f f e r e n c e l n f l u i d l e v e l s o f p a i l and j a r r e s u l t e d i n a c h a n g e i n f l o w when s w i t c h i n g b e t w e e n s a l i n i t i e s . F l o w r a t e s were c o u n t e d and marked f o r b o t h h e i g h t s . The t i m e t o a d j u s t t o t h i s c h a n g e i s unknown b u t b e l i e v e d t o have a n e g l i g i b l e e f f e c t on t h e r e s p o n s e t i m e . From t h e f i r s t t i m e - s e r i e s a t c o n s t a n t s a l i n i t y i t was f o u n d t h a t t h e o v e r a l l v a r i a b i l i t y o f t h i s s y s t e m was a b o u t 0.01 S. 92 The n e x t s e r i e s o f r u n s was done t o l o o k a t t h e c h a r a c t e r i s t i c s o f t h e r e s p o n s e f o r a r a n g e o f s a l i n i t y v a l u e s and a t f l o w r a t e s u s e d i n e x p e r i m e n t s . The o u t p u t o f t h e s e r u n s c o n s i s t s o f p l o t s o f c a l c u l a t e d s a l i n i t y f o r e a c h o f t h e t h r e e c e l l s a t d i f f e r e n t b u t s t e a d y f l o w r a t e s f r o m 0.5 t o 4 d r o p s p e r s e c o n d , and f o r s t e p s o f 0.5 t o 4.0 S i n t h e s a l i n i t y . These t i m e - s e r i e s p l o t s a r e i n c l u d e d i n t h i s a p p e n d i x . The t y p i c a l shape o f t h e r e s p o n s e c u r v e s c o n s i s t o f : a n e a r l y h o r i z o n t a l p a r t a f t e r s w i t c h i n g t h e i n t a k e , a s t e e p l i n e a r s e c t i o n o f r a p i d c h a n g e In s a l i n i t y an e x p o n e n t i a l t a i l a p p r o a c h i n g t h e f i n a l s a l i n i t y The t i m e r e q u i r e d a f t e r a s w i t c h i n s a l i n i t y a t t h e i n t a k e , f o r t h e c a l c u l a t e d s a l i n i t y t o r e a c h 90% o r 95% o f t h e f i n a l v a l u e , was g r a p h i c a l l y d e t e r m i n e d f r o m t h i s f i r s t s e t o f p l o t s : On t h e s e p l o t s , t h e t i m e a t w h i c h t h e i n t a k e was s w i t c h e d was marked a s tO and t h e s t a r t o f r a p i d c h a n g e a s t c ; t 9 0 and t 9 5 were t h e t i m e s a t w h i c h t h e c a l c u l a t e d v a l u e had c h a n g e d by 90% o r 9 5 % o f t h e s t e p i n s a l i n i t y . The r a p i d c h a n g e s t a r t i n g a t t = t c a p p e a r s l i n e a r o v e r p a r t o f t h e c h a n g e , e x c e p t a t f l o w s o f l e s s t h a n a b o u t 1 d r o p p e r 2 s e c o n d s (.03 m l / s e c ) . T h i s i s f o l - l o w e d by a c u r v e a s t h e c a l c u l a t e d v a l u e a p p r o a c h e s t h e f i n a l s a l i n i t y . D i s t a n c e s m e a s u r e d a l o n g t h e t i m e a x i s were c o n v e r t e d t o volume by m u l t i p l y i n g w i t h t h e f l o w r a t e . F o r o b t a i n i n g d e n s i t y p r o f i l e s i n t h e t a n k a r e a s o n a b l e f l o w r a t e i s n e e d e d t o t a k e s u c c e s s i v e r e a d i n g s a t d i f f e r e n t d e p t h s w i t h i n t h e t i m e i n w h i c h l a r g e r p a t t e r n s In t h e c o n v e c t i o n t a t i k c h a n g e . A s t e a d y s l o w f l o w t h r o u g h t h e m i c r o - c e l l m i n i m i z e s t h e d i s t u r b a n c e a t t h e i n t a k e p o i n t . The l e n g t h o f t i m e b e f o r e t h e r a p i d c hange ( t O - t c ) d e p e n d s on t h e l e n g t h a nd d i a m e t e r o f t h e t u b e t h r o u g h w h i c h t h e f l u i d moves b e f o r e r e a c h i n g t h e c e l l and on t h e f l o w r a t e . The volume o f f l u i d e n t e r i n g t h e c e l l i n t i m e ( t O - t c ) s h o u l d be c o n s t a n t f o r s t e a d y f l o w , b u t t h e f l o w i s b r i e f l y I n t e r r u p t e d w h i l e s w i t c h i n g s a l i n i t y a t t h e I n t a k e . The s t a r t i n g p o i n t a nd f l o w r a t e a r e a p p r o x i m a t e w h i c h e x p l a i n s t h e r a n g e i n i n i t i a l volume f r o m 0.28 t o 0.66 m l . The p l o t t e d d a t a show t h a t f o r a c h a n g e t o 9 5 % o f t h e f i n a l v a l u e t a k e s 30 t o 90 s e c o n d s and b e t w e e n 2 a n d 7 ml o f f l u i d . The shape o f t h e r e s p o n s e c u r v e c h a n g e s w i t h t h e f l o w r a t e . I n a n e x t s e t o f r u n s t h e c a l c u l a t e d t e m p e r a t u r e s , c o n d u c t i v i t y r a t i o s and s a l i n i t i e s were r e c o r d e d . The t i m e - s e r i e s p l o t s show a s e r i e s o f c a l c u l a t e d s a l i n i t y c u r v e s a t d i f f e r e n t f l o w r a t e s . These have b e e n n o r m a l i z e d f o r s a l i n i t y c h a n g e and e a c h s e c t i o n h a s b e e n r e p l o t t e d i n t e r m s o f volume r e q u i r e d f r o m t h e t i m e o f a s w i t c h i n s a l i n i t y . A p l o t o f n o r m a l i z e d s a l i n i t y c h a n g e v s . volume ( t e x t f i g . 2-5) shows t h a t t h e r e s p o n s e c u r v e s c o l l a p s e I n t o a s i n g l e c u r v e a t h i g h e r f l o w r a t e s . The f l o w r a t e and t h e s t a r t a n d end t i m e f o r e a c h segment a r e a l s o marked on t h e p l o t s . S e v e r a l t i m e - s e r i e s o f c o m p u t e d s a l i n i t i e s , t e m p e r a t u r e s a n d c o n d u c t i v i t y r a t i o s were p l o t t e d a t t h e same t i m e - s c a l e t o c h e c k t h e i r r e l a t i v e e f f e c t . A t t h e h i g h e r f l o w r a t e s ( 4 0 / 1 5 d r / s o r 0.16 m l / s ) I t t a k e s 2 t o 3 ml o f f l u i d f o r a c h a n g e o f 90% t o 95% o f t h e new v a l u e o v e r r e s p e c t i v e l y 12 t o 19 s e c o n d s . To g e t a d e n s i t y p r o f i l e o f 94 f l u i d i n t h e e x p e r i m e n t a l t a n k , t h e f l o w r a t e i s s e t by a d j u s - t i n g t h e d r o p i n h e i g h t b e t w e e n t h e f l u i d l e v e l i n t h e t a n k a nd t h e c e l l o u t l e t . I f t h e D a t a l o g g e r m u l t i p l e x e r c y c l e i s s t a r t e d 20 s e c o n d s a f t e r t h e i n t a k e i s moved t o t h e n e x t h e i g h t , t h e n t h e c a l c u l a t e d s a l i n i t y <Sc) w i l l be c l o s e t o 9 5 % o f t h e c h a n g e i n s a l i n i t y o r , a s s u m i n g S i < S2: S c = S l + 0.95CS2-S1) w h i c h y i e l d s : S2 = ( S c - . 0 5 S D / . 9 5 F o r c o n t i n u o u s m o n i t o r i n g o f t h e s a l i n i t y i n t h e t r a y o r i n t h e m i x e d l a y e r b e l o w i t a t a f i x e d p o i n t , a much s l o w e r f l o w r a t e c a n be u s e d s i n c e t h e a v e r a g e c h a n g e s o v e r t i m e a r e much s m a l l e r a n d s l o w e r t h a n t h o s e o b s e r v e d i n t h e t e s t p r o f i l e s . 9 5 96 , SALINITY (PSS) iFO I 0.100/DIV 2B 500 29 r00 —I 1 1 H H 1 1 1 1 1 1 1 1 1 1 1 1 1 , — — CD c i fD CO 1 CD 3 fD fD Sa l in i ty (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— • >—• : u i cn V © 03 (D ft) 0 0 (0 ID O a. L6 SALINITY (PSS) &RL* I 0.100/DIV f - r H 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 r o c n i *—* i 00 c n OJ o c n ra D_ T r o 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— 0 0 5 " B Z Aia / 0 0 1 - 0 i ring (SSd) A1INI1VS 98 Fiaure B-9. MICRO-CELL TIME RESPONSE CELL01 2 5 - 1 0 / 0 . 4 Figure B-10. MICRO-CELL TIME RESPONSE CELL#2 25-10-85/1. 1 - 1 . 2 S 1 - S 2 = 2 7 . 8 5 - 2 9 . 0 2 1 2 3 4 5 6 Vol ume (ml) Figure B—11. MICRO-CELL TIME RESPONSE CELL#3 2 5 - 1 0 / FILES F1.7-F1. 10 S1-S2 = 27.97-29.13 1 2 3 4 5 6 Volume(ml) B .6 S p a t i a l r e s o l u t i o n o f t h e m i c r o - c e l l s A t w o - l a y e r s y s t e m was u s e d t o c h e c k how w e l l an a p p a r e n t l y s h a r p s t e p i n s a l i n i t y a t t h e i n t e r f a c e i s r e p r e s e n t e d i n a s a l i n i t y p r o f i l e f r o m m i c r o - c e l l s d a t a t a k e n a t c l o s e l y s p a c e d po i n t s . The l i g h t e r f l u i d o f l o w e r s a l i n i t y was f i r s t p l a c e d i n t h e c o n t a i n e r and t h e h e a v i e r f l u i d was t h e n s l o w l y a d d e d a t t h e b o t t o m . The d e n s i t y i n t e r f a c e was v i s i b l e i n t h e s h a d o w g r a p h image a s a n a r r o w b r i g h t l i n e o f l i g h t w h i c h s l o w l y b r o a d e n e d due t o d i f f u s i o n a nd t u r b u l e n c e f r o m f i l l i n g . I t was s h a r p e n e d by w i t h d r a w i n g f l u i d f r o m a p o i n t b e l o w t h e l i n e . F l u i d was t h e n s y p h o n e d t h r o u g h t h e m i c r o - c e l l a t a b o u t 2 t o 3 d r o p s p e r s e c o n d i n s e v e r a l r u n s w i t h d i f f e r e n t s t e p s i n s a l i n i t y . M e a s u r e m e n t s were w h i l e s y p h o n i n g f l u i d t h r o u g h t h e m i c r o - c e l l a t a f i x e d r a t e , l o w e r i n g t h e c e l l i n t a k e t o a d e p t h a n d t a k i n g a r e a d i n g a f t e r a l l o w i n g e nough t i m e t o f l u s h t h e c e l l ( 3 0 s e c ) , t h e n m o v i n g t h e i n t a k e t o t h e n e x t d e p t h . S a l i n i t y p r o f i l e s were o b t a i n e d by p l o t t i n g t h e c a l c u l a t e d s a l i n i t i e s a g a i n s t d e p t h ( f i g u r e s B-6,7 ) . S e v e r a l p l o t s show a s p r e a d l n d e p t h b e t w e e n t h e l a y e r s o f c o n s t a n t s a l i n i t y . T h i s c a n i n d i c a t e e i t h e r a l a c k o f r e s o l u t i o n o r t h e a c t u a l shape o f t h e i n t e r f a c e w h i c h showed l o n g p e r i o d o s c i l l a t i o n s l n one c a s e . I n t h e p r o f i l e d a t e d 15-4-86 a s h a r p i n t e r f a c e i s s e e n o f 0.5 PSS o v e r 3 mm t h i c k n e s s , i n w h i c h t h e s a l i n i t y i n c r e a s e s i n 8 s t e p s o f 0.4 mm e a c h . 102 SALINITY PROFILE 11-4-86 CELL SPATIAL RESOLUTION 30.0 103 SALINITY PROFILE 15-4-86 MICRO-CELL SPATIAL RESOLUTION 2 9 . 0 SALINITY (PSS) 2 G . 5 0 J i 1 1 i 1 10 . 20 _ 30 _ 40 _ | 50 f 60 . CL. U J Q 70 J 80 90 100 . 110 - 120 _ 130 _ 140 . 150 _ 30.0 I I L 1 1 •* e- f l o w t h r o u g h o e l l abt. 3 d r / 8 e c Figure B*I3. Resolution i n 2-layer system. 104 Therm i s t o r s A P P E N D I X 1C5 APPENDIX C THERMISTORS C l T h e r m i s t o r use T h e r m i s t o r s were u s e d t o d e t e r m i n e t h e t e m p e r a t u r e o f f l u i d i n s i d e e a c h m i c r o - c e l l a n d i n t h e e x p e r i m e n t a l t a n k , t o e n a b l e a c c u r a t e c a l c u l a t i o n o f t h e s a l i n i t y and d e n s i t y o f t h e f l u i d . The t y p e o f t h e r m i s t o r u s e d i n t h e s e e x p e r i m e n t s c o n s i s t e d o f a s m a l l b e a d mounted i n t h e t i p o f a h o l l o w n e e d l e , a n d p l a c e d i n i n t h e t a n k a n d a t t h e i n l e t a n d o u t l e t o f e a c h c e l l . I n i t i a l l y , a s i n g l e t h e r m i s t o r was i n s e r t e d i n t h e f l o w a t t h e o u t l e t o f t h e m i c r o - c e l l s t h r o u g h a s m a l l g l a s s t e e . The d i f f e r e n c e b e t w e e n t h e t e m p e r a t u r e o f f l u i d i n t h e e x p e r i m e n t a l t a n k a n d a m b i e n t room t e m p e r a t u r e c a u s e d t h e v a l u e d e t e r m i n e d f r o m t h i s t h e r m i s t o r t o d i f f e r f r o m t h a t a t t h e c e n t r e o f t h e c e l l by some amount w h i c h d e p e n d s on t h e r a t e o f f l o w t h r o u g h t h e c e l l a n d on t h e m a g n i t u d e o f t h e t e m p e r a t u r e d i f f e r e n c e . To r e d u c e t h i s e r r o r a n d t o c h e c k on t h e o u t p u t o f t h e s e o l d e r t h e r m i s t o r s (some o f w h i c h were f o u n d t o d e v e l o p e l e c t r i c a l l e a k s o v e r t i m e ) a s e c o n d t h e r m i s t o r was i n s t a l l e d a t t h e i n l e t o f e a c h c e l l . The a v e r a g e o f t h e t e m p e r a t u r e s a t t h e i n l e t and o u t l e t o f t h e c e l l was u s e d i n t h e c a l c u l a t i o n o f s a l i n i t y ( s e e a p p e n d i x A . l ) . T h i s was t h e n c o m b i n e d w i t h t h e t e m p e r a t u r e i n t h e e x p e r i m e n t a l t a n k t o d e t e r m i n e t h e d e n s i t y o f f l u i d a t t h e i n t a k e p o i n t ( s e e a p p e n d i x A.2). F i g u r e C-1 b e l o w shows t h e m i c r o - c e l l w i t h t h e two t h e r m i s t o r s . 106 F i g u r e C-1 . T h e r m i s t o r s a t m i c r o - c e l l I n l e t a n d o u t l e t . T e m p e r a t u r e s a r e c a l c u l a t e d f r o m t h e m e a s u r e d r e s i s t a n c e o f c a l i b r a t e d t h e r m i s t o r s . The t e m p e r a t u r e T ( I n °C> f o r a g i v e n r e s i s t a n c e RT ( i n ohms) and c a l i b r a t i o n c o n s t a n t s A, B and C i s t h e n c o m p u t e d f r o m : T = 1/1A + B * l n ( R T ) + C * ( l n ( R T > > 3 ] - 273.15 I.1 Leaks I n i n i t i a l t e s t s w i t h t h e t h e r m i s t o r s a t t o p and b o t t o m o f e a c h c e l l , s i g n i f i c a n t d i f f e r e n c e s were f o u n d i n s e v e r a l c a s e s b e t w e e n t h e c a l c u l a t e d t e m p e r a t u r e s above a nd b e l o w t h e c e l l . E l e c t r i c a l l e a k s were f o u n d In some t h e r m i s t o r s . These l e a k s f o r m an e x t e r n a l c u r r e n t p a t h p a r a l l e l t o t h e I n t e r n a l p a t h , 107 w i t h a r e s i s t a n c e w h i c h may v a r y w i t h t h e c o n d u c t i v i t y o f t h e f l u i d o r w i t h v a r i a t i o n s i n t e m p e r a t u r e , w h i c h c a n cha n g e t h e c o n t a c t - s u r f a c e r e s i s t a n c e i n m i n u t e c r a c k s . Any c u r r e n t l e a k l o w e r s t h e t r u e r e s i s t a n c e v a l u e as a p a r a l l e l r e s i s t a n c e , w h i c h c o r r e s p o n d s t o a h i g h e r a p p a r e n t t e m p e r a t u r e : 1 / R a p p a r e n t = 1 / R t r u e + 1/ R l e a k F o r a l e a k o f 1 megohm and a t r u e r e s i s t a n c e o f 2000 ohm, t h e a p p a r e n t r e s i s t a n c e becomes 1996 ohm. F o r t h e r m i s t o r #31 t h e c a l c u l a t e d t e m p e r a t u r e w o u l d c h a n g e f r o m 20.281 t o 20.338 °C a nd t h e s a l i n i t y a t 20-30 PSS w o u l d c h a n g e by 0.3-0.4 PSS. The d i s c r e p a n c i e s i n t e m p e r a t u r e s were r e d u c e d by r e p l a c i n g t h e t h e r m i s t o r s w h i c h were f o u n d t o have l e a k s . C.2 R e - c a l i b r a t i o n f o r e x t e n d e d r a n g e The t h e r m i s t o r s were o r i g i n a l l y c a l i b r a t e d a t t e m p e r a t u r e s c l o s e t o 0 °C. F o r l a b o r a t o r y u s e , t h e r e s i s t a n c e o f t h e n e e d l e mounted t h e r m i s t o r s was d e t e r m i n e d a t t e m p e r a t u r e s up t o 25 °C i n a c o n t r o l l e d t e m p e r a t u r e b a t h a g a i n s t r e c e n t l y c a l i b r a t e d t h e r m i s t o r s . The HP u t i l i t y - p r o g r a m FITTER was u s e d t o g e n e r a t e a new s e t o f c a l i b r a t i o n c o n s t a n t s f o r t h e s e t h e r m i s t o r s , w h i c h a r e l i s t e d i n t a b l e C.1 b e l o w . Some t y p i c a l e x a m p l e s o f t h e o u t p u t f r o m t h e c u r v e f i t t i n g p r o g r a m f o r t h e r e - c a l i b r a t e d t h e r m i s t o r s i s i n c l u d e d a t t h e end o f t h i s a p p e n d i x . T h i s l i s t s d a t e , d a t a u s e d f o r t h e f i t , g e n e r a t e d c a l i b r a t i o n c o n s t a n t s , a n d t h e maximum e r r o r a n d s t a n d a r d e r r o r o f t h e e s t i m a t e . 108 T a b l e C l T h e r m i s t o r C a l i b r a t i o n C o n s t a n t s 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 + B x l n ( R T ) + C*(ln(RT))» ] - 273.15 C.3 D a t a l o g g e r c a l i b r a t i o n c o r r e c t i o n R e c a l i b r a t i o n d i d c o r r e c t t h e e r r o r i n o b s e r v a t i o n s when a d i g i t a l v o l t m e t e r was u s e d b u t t e m p e r a t u r e s d e t e r m i n e d f r o m t h e d a t a l o g g e r i n p u t s t i l l d i d n o t a g r e e f o r d i f f e r e n t t h e r m i s t o r s . The c o n v e r s i o n f r o m d a t a l o g g e r N-number t o r e s i s t a n c e v a l u e was done w i t h a l i n e a r f i t f o r t h e r e s i s t a n c e v a l u e s f o r a r a n g e o f l a b o r a t o r y o p e r a t i n g t e m p e r a t u r e s r e t u r n e d by t h e r m i s t o r #41, ( u s e d i n i t i a l l y a t t h e e x i t o f t h e f i r s t c e l l b u t r e p l a c e d due t o an e l e c t r i c a l l e a k ) . T h i s l i n e a r f i t was g i v e n b y : RT = 2526 - NT*0.25373 where RT = r e s i s t a n c e v a l u e (ohm) NT = d a t a l o g g e r N-number 109 Many o f t h e t h e r m i s t o r s c o v e r a s l i g h t l y l o w e r r a n g e o f v a l u e s . A s e c o n d o r d e r f i t t o t h e d a t a l o g g e r o u t p u t NT-numbers y i e l d s a b e t t e r f i t o v e r t h e r a n g e o f r e s i s t a n c e v a l u e s f r o m 1600 t o 2500 ohms, w i t h a s t a n d a r d e r r o r o f 0.854221 : RT = 2527.62 + N T * ( - 0 . 2 6 1 1 9 2 + NT*4.771296E-6> A t h e r m i s t o r r e s i s t a n c e o f 1800 ohms c o r r e s p o n d s t o an N-number o f 2861 when u s i n g t h e c o e f f i c i e n t s o f t h e l i n e a r f i t , b u t w i t h t h e s e c o n d o r d e r f i t t h i s N-number ( 2 8 6 1 ) y i e l d s a r e s i s t a n c e o f 1818.4 ohms. U s i n g t h e c a l i b r a t i o n c o n s t a n t s f o r t h e r m i s t o r #40, 1800 ohms c o r r e s p o n d s t o a t e m p e r a t u r e o f 23.72 °C w h i l e 1818 ohms w o u l d be 23.44 °C. A f t e r i m p l e m e n t i n g t h e above c o r r e c t i o n s , t h e v a l u e s o f t h e o b s e r v e d t e m p e r a t u r e s were f o u n d t o be i n g o o d a g r e e m e n t w i t h e x p e c t e d v a l u e s f o r f l u i d i n t h e t a n k a nd f o r a m b i e n t a i r t e m p e r a t u r e s . 110 4 T i t l e : T H E R M * 31 X - V a r i a b l e : R Y - V a r i a b i e : T C r e a t e d 0 7 - 0 4 - 8 5 O b s e r v a 11 o n ! : x/ A * 3961 . 72 Y -- 1.953 O b s e r v a t i o n 9 • • \/ A = 3854 .75 Y = = 2.B48 U b s e r v a t i o n 3: X = = 3580 . 44 y = = 4.539 O b s e r v a 11 o n 4: V A * 3101 .18 Y = = 8.282 Obse r v a t i o n 5: V = /\ s 2692 o -> . _> ._ Y = - 12.053 O b s e r v a 11 o n 6: \/ A - " ) 0 ' ' Q .38 Y = = 1b.009 O b s e r v a t i o n 7: X * = 2155 .63 Y = - 18.157 O b s e r v a t i o n 3: X = •• 1943 .39 Y = = 21.097 O b s e r v a 1 1 o n 9: \/ A " - 1G91 .93 Y = - 2 5 . 1 F I NHL RESULT OF CURVE F I T D a t a s e t t i t l e : THERM* 31 Mode] u s e d : T h e r m i s t o r E q u a t i o n : F ( X ) - 1/(A1+ A2*1n ( X ) + A 3 * l n ( X ) * 3 ) - 2 7 3 . 1 5 The e s t i m a t e d p a r a m e t e r v a l u e s a f t e r 7 i t e r a t i o n s ' . A M J = 1 .03541 /e-03 A I 2 ] = 3 . 033537e-04 A13 J = 1.520697e-07 Maximum e r r o r i s 1.220309e-03 Ihe o v e r a l l s t a n d a r d e r r o r o f e s t i m a t e i s 8.155511e-04 111 T j t i e : IHE.RMI::. FOR* 37 X V a r i a b l e : R Y~\> a r i ;b i e : T C r e a t e d 08- 1 3 86 G b s e r v a t i o n i • 1 . X = = 3694 •' i . i T O b s e r v a t i o n '} • V -/\ = 3309 .9; v •  9.96 O b s e r v a t Iori j • X = * 3IIU6 . 1 12 r ^ • 12.612 G b s e r v a t i o n 4: \/ A " = 2646 i i v i - 16.971 G b s e r v a t i o n V A " - 24 15 . 65 / - 18.483 G b s e r v a 11on IS: X = - 2322 .26 Y - 19.682 G b s e r v a t i o n 7: X = 2111 . <- V 1 < 22.27 G b s e r v a t i o n 8: X -- 1986 . 76 V = - 2 4 . 0 2 2 G b s e r v a t i on 9: X = = 1913 .41 V 1 26.091 G b s e r v a 11on 1 i i : X = =• 1864 t = = 26.002 I- i i i r i i ••:! t ii i nf (' IJRVL 611 b a t a s e t t i t l . ? : THth'M IS TOR* 37 M o d e l u s e d : T h e r m i s t o r L'q'.u-i t i o n : F f X ) = 1 / ( M 1 • H 2 • i u ( X M H J ' l n ( X ) ' 3 > - 2 7 3 . 1 5 fh>- e s t i m a t e d p a r a m e t e r v a l u e s a t U-r 6 i t o r a t i o n s : fH i J= 1.U16687e-03 M 21= 3 . 0 1 3 7 1 7 e - 0 ^ M 3 1 = 1 .331666e-07 Ua;< imuni e r r o i i s 1 . 324976,.. • U :'. the o v e r a l l s t a n d a r d e r r o r ot tr . t i ' - i a t e i s 8 . U 1623lle-U4 112  D a t a l o g g e r s A P P E N D I X D APPENDIX D DATALOGGERS I n t h i s s e r i e s o f e x p e r i m e n t s , two t y p e s o f d a t a l o g g e r were u s e d a t d i f f e r e n t t i m e s . The f i r s t was an A p p l i e d M i c r o s y s t e m s C/T d a t a l o g g e r , m o d i f i e d t o b r i n g t h e d i g i t i z e d o u t p u t i n r a n g e f o r i n p u t f r o m t h e t h e r m i s t o r s a n d m i c r o - c e l l s . When a v a i l a b l e , an HP-3497A D a t a A c q u i s i t i o n S y s t e m was u s e d w i t h i n d i v i d u a l c o n d u c t i v i t y c i r c u i t s f o r t h e m i c r o - c e l l s . The o u t p u t i n b o t h c a s e s was d i r e c t e d t o a n HP-9825 c o m p u t e r . D . l A p p l i e d M i c r o s y s t e m s C/T D a t a l o g g e r An A p p l i e d M i c r o s y s t e m s D a t a l o g g e r (S/N 170) was a d a p t e d f o r use w i t h t h e m i c r o - c e l l s : a n i n p u t p a n e l a l l o w s a number o f c e l l s a n d t h e r m i s t o r s t o be c o n n e c t e d t o d e s i g n a t e d c h a n n e l s . The t e m p e r a t u r e a n d c o n d u c t i v i t y e l e c t r o n i c s i n t h i s AM/CT D a t a l o g g e r were m o d i f i e d f o r t h e r a n g e o f c o n d i t i o n s e x p e c t e d t o be u s e d i n l a b o r a t o r y e x p e r i m e n t s . T r i g g e r e d m a n u a l l y o r a t some p r e - s e t c l o c k r a t e , t h e m u l t i - p l e x e r c y c l e s t h r o u g h t h e p r e - s e t p a t t e r n o f i n p u t c h a n n e l s . A n a l o g i n p u t s i g n a l s a r e c o n v e r t e d i n t o a d i g i t a l o u t p u t l i n e w h i c h c o n t a i n s s e r i a l number, t i m e , and numbers f o r t e m p e r a t u r e and c o n d u c t i v i t y . T h i s l i n e I s t r a n s l a t e d by an A.M. s e r i a l c o n v e r t e r a n d e n t e r e d i n t o t h e HP-9825 v i a an RS-232 i n t e r f a c e . The s a m p l i n g c y c l e f r e q u e n c y o r c l o c k r a t e i s s e t by c o n n e c - t i n g p i n #32 o f t h e e d g e - c o n n e c t o r on t h e S e q u e n c e r b o a r d t o t h e a p p r o p r i a t e p i n on t h e C l o c k b o a r d edge c o n n e c t o r . T a b l e D . l l i s t s t h e f u n c t i o n f o r e a c h p i n o f t h e C l o c k b o a r d . A f t e r s w i t c h i n g on t h e d a t a l o g g e r , t h e s a m p l i n g c y c l e s a r e i n i t i a t e d 115 a u t o m a t i c a l l y a t t h e r a t e s e t on t h e c l o c k o r c a n be t r i g g e r e d m a n u a l l y by p r e s s i n g t h e b u t t o n marked " s t a r t " . The p a t t e r n o f C a n d T c h a n n e l s w h i c h t h e s e q u e n c e r c y c l e s t h r o u g h was programmed on a ROM-chip i n t h e D a t a l o g g e r . Up t o f o u r d i f f e r e n t m i c r o - c e l l s c a n be s e l e c t e d , e a c h w i t h two t h e r m i s t o r s , a n d up t o f o u r a d d i t i o n a l t h e r m i s t o r i n p u t s c a n be a d d e d t o d e t e r m i n e t h e t e m p e r a t u r e a t p o i n t s i n t h e t a n k . These p a t t e r n s a r e l i s t e d i n t a b l e D.2 . D i p - s w i t c h e s S1-S5 o f SW1 on t h e m u l t i p l e x e r (MUX) b o a r d a r e p r e - s e t t o t h e d e s i r e d p a t t e r n number: MUX# = 1 +S1 +S2 +S3 +S4 +S5 Here and i n t h e f o l l o w i n g d i p - s w i t c h p a t t e r n s , S i = 0 i f open a n d S i = 2 < 1-" i f c l o s e d . D i p - s w i t c h e s S6-S8 o f MUX-SW1 s h o u l d be c l o s e d f o r 1 2 - b i t d a t a . The number o f c h a n n e l s o u t p u t by t h e D a t a l o g g e r t o t h e S e r i a l C o n v e r t e r i s s e t w i t h s w i t c h e s S1-S5 o f SW1 on on t h e S t o r a g e F o r m a t t e r (FMT) b o a r d : #CHNLS = 1 +S1 +S2 +S3 +S4 +S5 The f i r s t two c h a n n e l s a r e i n s t r u m e n t s e r i a l number a nd t i m e i n s e c o n d s ( a p p r o x 1 mate 1 y ) , a n d e a c h t e m p e r a t u r e and c o n d u c t a n c e r e q u i r e s an a d d i t i o n a l c h a n n e l . The HP-9825 p r o g r a m s prompt f o r number o f c e l l s a n d e x t r a t h e r m i s t o r s a n d d i s p l a y s e t t i n g s f o r MUX-SW and FMT-SW1. D i p - s w i t c h e s S6-S8 o f FMT-SW1 s e t t h e number o f t i m e s t h a t t h e d a t a w o r d s a r e o u t p u t ( o n c e i f a l l a r e o p e n ) . D i p s w i t c h e s S1-S6 o f FMT-SW2 s e t t h e d a t a o u t p u t r a t e i n m i 1 1 i s e c o n d s : T i m e / b i t = 5. 1 5 * ( 1 +S1 +S2 +S3 +S4 +S5) F o r 1 2 - b i t word o u t p u t S7 o f FMT-SW2 i s c l o s e d ( 1 0 - b i t I f o p e n ) . 116 T a b l e D . l . C l o c k B o a r d Edge C o n n e c t o r P i n F u n c t i o n s P i n # F u n c t i o n P i n # F u n c t i o n 1 o/p 256 h o u r s 18 o/p 30 m i n u t e s 2 o/p 128 h o u r s 19 o/p 56.25 s e c o n d s 3 p a r a l l e l t r a n s f e r p u l s e 20 o/p 28.125 s e c o n d s 4 s e r i a l d a t a o u t p u t 21 s e r i a l d a t a I n p u t 5 o/p 32 h o u r s 22 o/p 112.5 s e c o n d s 6 o/p 16 h o u r s 23 o/p 1.75 s e c o n d s 7 o/p 8 h o u r s 24 o/p 3.51 s e c o n d s 8 o/p 64 h o u r s 25 o/p 7.03 9 o/p 27.466 m i c r o s e c o n d s 26 o/p 14.0625 10 o/p 1 h o u r 27 o/p 429.153522 m i c r o s e c 1 1 s h i f t c l o c k 28 o/p 6.86 msec 12 o/p 2 h o u r s 29 o/p 3.43 msec 13 o/p 4 h o u r s 30 cl'ock r e s e t p u l s e o u t 14 o/p 15 m i n u t e s 31 c l o c k r e s e t 15 o/p 225 s e c o n d s 32 p a r a l l e l t r a n s f e r 16 o/p 7.5 m i n u t e s 33 V s s 17 t i m e code I n c r e m e n t o/p 34 Vdd 35 V s s T a b l e D.2. M u l t i p l e x e r I n p u t C h a n n e l C y c l i n g P a t t e r n 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 x x x x x x x x x x x x x x x T2-C2-T7 x x x x x x x x x x x x x x x T3-C3-T8 x x x x x x x x x x T4-C4-T9 x x x x x T i l X X X X X X X X X X X X X x x x T12 x x x x x x x x x x x x T13 x x x x x x x x T14 x x x x 117 The d a t a l o g g e r g r e a t l y s i m p l i f i e d t h e n e a r l y s i m u l t a n e o u s c o l l e c t i o n o f d a t a f r o m a l l t h e r m i s t o r s a n d c o n d u c t i v i t y c e l l s d u r i n g t h e s l o p e f l o w e x p e r i m e n t s . However, w h i l e t h e d a t a f r o m t h e t e m p e r a t u r e c i r c u i t g a ve v e r y s t a b l e o u t p u t , t h e r e were some s p u r i o u s jumps i n t h e o u t p u t f r o m t h e c o n d u c t i v i t y c i r c u i t . The N-numbers d i d jump a t t i m e s by up t o 10 o r more u n i t s , w h i c h c o r r e s p o n d s t o a v a r i a b i l i t y o f a l m o s t 0.1 PSS. S e v e r a l e f f o r t s were made t o i m p r o v e t h e r e l i a b i l i t y by r e p l a c i n g c o m p o n e n t s i n t h e d a t a l o g g e r a n d by i n c r e a s i n g t h e d e l a y b e t w e e n s w i t c h i n g a c e l l on and r e a d i n g t h e o u t p u t , b u t t h e c o n d u c t i v i t y r e a d i n g s s t i l l became n o i s y o c c a s i o n a l l y w i t h o u t known c a u s e . D.2 HP-3497A D a t a A c q u i s i t i o n S y s t e m The HP-3497A S y s t e m was o n l y a v a i l a b l e on o c c a s i o n . I t was u s e d i n d e t e r m i n i n g t h e t i m e r e s p o n s e c h a r a c t e r i s t i c s o f t h e m i c r o - c e l l s and t o o b t a i n d a t a f o r s i m u l t a n e o u s p r o f i l e s i n t h e l a s t two s l o p e f l o w e x p e r i m e n t s . When u s i n g t h i s s y s t e m , e a c h m i c r o - c e l l was c o n t i n u o u s l y p o w e r e d by a s e p a r a t e c o n d u c t i v i t y c i r c u i t . T h i s r e d u c e d any t r a n s i e n t s c a u s e d by s w i t c h i n g t h e c e l l s on b u t c a u s e d some c r o s s - t a l k b e t w e e n t h e c e l l s w h i c h was e l i m i n a t e d by s h i f t i n g t h e i n d i v i d u a l o p e r a t i n g f r e q u e n c i e s . S m a l l s h i f t s f o u n d a f t e r c o l l e c t i n g e x p e r i m e n t a l d a t a were s e e n t o o c c u r when t h e s y p h o n o u t l e t s o f t h e m i c r o - c e l l s were moved r e l a t i v e t o e a c h o t h e r . The H P - d a t a l o g g e r a l l o w e d much h i g h e r s a m p l i n g f r e q u e n c i e s a s w e l l a s a v e r a g i n g o f r a p i d m u l t i p l e r e a d i n g s o f e a c h s e n s o r , w h i c h f u r t h e r r e d u c e d t h e n o i s e i n t h e d a t a . 118 Membrane Salt Flux Calibration A P P E N D I X 119 APPENDIX E MEMBRANE FLUX CALIBRATION E . l S a l t and volume f l u x a n d d r i v i n g p r e s s u r e The s u r f a c e s a l t f l u x due t o t h e f r e e z i n g o f s e a w a t e r was s i m u l a t e d i n t h e s e e x p e r i m e n t s by a p e r c o l a t i o n o f s e a w a t e r t h r o u g h a p o r o u s membrane i n a t r a y . T h i s membrane was mounted b e t w e e n two l a y e r s o f c i r c u i t b o a r d , w i t h p e r f o r a t i o n s o f a b o u t 1 mm d i a m e t e r s p a c e d u n i f o r m l y a t 4 p e r cm a l o n g and a c r o s s t h e t r a y . The t r a y was s u s p e n d e d l e v e l w i t h t h e s u r f a c e o f f l u i d i n t h e e x p e r i m e n t a l t a n k , w h i c h was p a r t l y f i l l e d w i t h a m i x t u r e o f s e a w a t e r and f i l t e r e d t a p w a t e r . The method u s e d f o r e s t i m a t i n g t h e m a g n i t u d e o f t h e volume a n d s a l t f l u x t h r o u g h t h e membrane i s d e t a i l e d i n s e c t i o n 2.6 i n t h e t e x t . I n a s e r i e s o f f l u x c a l i b r a t i o n r u n s , i n w h i c h t h e b o t t o m o f t h e t a n k was k e p t h o r 1 z o n t a l , t h e s a l i n i t y o f f l u i d a t t h e c e n t e r o f t h e t a n k was t a k e n a s a v e r a g e f o r t h e w h o l e t a n k s i n c e t h e m i x e d l a y e r e x t e n d s t o t h e b o t t o m . The n e t s a l t f l u x i s t h e h i g h s a l i n i t y i n f l o w r e d u c e d by t h e low s a l i n i t y r e t u r n f l o w t o t h e t r a y , p e r u n i t t i m e and u n i t a r e a . I t was e x p r e s s e d a s : Bn = V w . ( S 2 . D 2 - S 1 . D l ) = d l S l . D l 1 . V I ( E - l ) 1000 d t 1000 A Bn= n e t s a l t f l u x ( g / c m 2 / s ) Vw= volume f l u x (cm 3/cm 2/s) S i = s a l i n i t y i n t r a y ( 2 ) and t a n k ( l ) ( g / k g o r PSS) Di= d e n s i t y i n t r a y ( 2 ) and t a n k ( l ) (g/cm 3) V l = volume o f f l u i d i n t h e t a n k (cm 3) A = a r e a o f t h e t r a y b o t t o m (cm 2) 1 2 0 The f l u x i s d r i v e n by t h e p r e s s u r e c a u s e d by t h e d i f f e r e n c e i n d e n s i t y b e t w e e n t h e f l u i d i n t h e t a n k a nd t h a t i n t h e t r a y o r r a t h e r , t h e w e i g h t o f a c o l u m n o f f l u i d In t h e t r a y a n d t h a t o f a c o l u m n o f t h e same h e i g h t i n t h e edge b e t w e e n t a n k a nd t r a y : P = ( D 2 - D 1 ) . g . h ( E - 2 ) P = p r e s s u r e ( g / c m / s 2 ) Di= d e n s i t y <g/cm 3) g = g r a v i t y = 981 (cm/s*) h = e f f e c t i v e h e i g h t o f f l u i d (cm) The f l u i d i n t h e edge s p a c e b e t w e e n t a n k a nd t r a y became s t a b l y s t r a t i f i e d a s t h e r e t u r n f l o w w h i c h r i s e s f r o m t h e m i x e d l a y e r i n t h e t a n k s l o w l y I n c r e a s e s i n s a l i n i t y . The l e s s s a l i n e f l u i d f o r m e d a s u r f a c e l a y e r o f a b o u t 2 mm i n t h e t r a y , w h i c h c a n n o t be m i x e d w e l l w i t h o u t d i s t u r b i n g t h e s u r f a c e ( a n d t h u s t h e p r e s s u r e a nd a s s o c i a t e d f l u x ) . F l u i d i n t h e t r a y and i n t h e edge s p a c e were a p p r o x i m a t e d a s 2 - l a y e r s y s t e m s w i t h t h e same s a l i n i t y i n t h e u p p e r 2 mm l a y e r , a n d t h e e f f e c t i v e h e i g h t u s e d t o compute p r e s s u r e s was t h e t r a y f l u i d h e i g h t r e d u c e d by 2 mm. E.2 F l u x c a l i b r a t i o n e x p e r i m e n t s To e s t i m a t e t h e m a g n i t u d e o f t h e s a l t f l u x , t i m e - s e r i e s d a t a of c o n d u c t i v i t y a n d t e m p e r a t u r e were c o l l e c t e d f r o m t a n k and t r a y i n a s e r i e s o f c a l i b r a t i o n e x p e r i m e n t s w i t h o u t a b o t t o m s l o p e . The s a l t f l u x was v a r i e d by u s i n g d i f f e r e n t s t a r t i n g s a l i n i t i e s a n d d e p t h s o f f l u i d In t h e t r a y . The m e n i s c u s i n t h e 121 edge s p a c e made I t d i f f i c u l t t o d e t e r m i n e t h e e x a c t h e i g h t o f t h e f l u i d . S h a d o w g r a p h p a t t e r n s d u r i n g t h e s e r u n s show a n e a r l y u n i f o r m d i s t r i b u t i o n o f c o n v e c t i v e m o t i o n s i n t h e t a n k e x c e p t n e a r t h e t a n k e n d - w a l l s where t h e s e m o t i o n s a p p e a r r e d u c e d i n a t r i a n g u l a r s e c t i o n w i d e n i n g w i t h d e p t h . T h i s I s c a u s e d by t h e s m a l l d o w n f l o w u n d e r t h e e n d - w a l l s o f t h e t r a y and t h e v e r y s l o w upward m o t i o n i n t h e edge s p a c e . Any s i m i l a r e f f e c t a t t h e s i d e w a l l s c a n n o t be d i s t i n g u i s h e d s i n c e t h e s h a d o w g r a p h image i n t e g r a t e s o v e r t h e w i d t h o f t h e t a n k , b u t i n j e c t e d dye d i d n o t show any mean c i r c u l a t i o n i n a c r o s s - s e c t i o n o f t h e t a n k . S a l i n i t y p r o f i l e s were p l o t t e d f r o m d a t a t a k e n d u r i n g s e v e r a l s a l t f l u x c a l i b r a t i o n r u n s , a l o n g t h e c e n t e r l i n e and i n t h e edge s p a c e b e t w e e n t h e t a n k and t r a y , ( f i g u r e s E-1 t o E - 3 ) . V e r t i c a l s a l i n i t y g r a d i e n t s were f o u n d j u s t b e l o w t h e membrane and i n some c a s e s c l o s e t o t h e b o t t o m , p o s s i b l y due t o i n c o m - p l e t e m i x i n g a f t e r a l o c a l s p i l l . The p r o f i l e s i n d i c a t e t h a t s a l i n i t y o f f l u i d s a m p l e d a t a p o i n t n e a r t h e c e n t r e o f t h e t a n k may be t a k e n a s a r e a s o n a b l e e s t i m a t e o f t h e a v e r a g e f o r t h e t a n k . The i n i t i a l s e r i e s o f c a l i b r a t i o n r u n s d i d show a g e n e r a l s i m i l a r i t y l n t h e shape o f t h e t i m e - s e r i e s p l o t s o f c a l c u l a t e d s a l i n i t i e s . E s t i m a t e d v a l u e s f o r volume f l u x e s were o b t a i n e d w i t h t h e e x p r e s s i o n s f o r m u l a t e d a b o v e , u s i n g a f i n i t e d i f f e r e n - c e s method: t h e r a t e o f c h a n g e i n s a l i n i t y and i n d e n s i t y was a p p r o x i m a t e d by t h e d i f f e r e n c e b e t w e e n s u c c e s s i v e o b s e r v a t i o n s d i v i d e d by t h e t i m e i n t e r v a l . I n t e r p o l a t e d t i m e , s a l i n i t y a n d d e n s i t y a r e t a k e n a s t h e a v e r a g e o f e a c h p a i r . The volume 122 f l u x e s and p r e s s u r e s f o u n d by s u b s t i t u t i n g t h e s e v a l u e s i n t o t h e a bove e x p r e s s i o n s were p l o t t e d f o r s u c c e s s i v e r u n s t o o b t a i n a s i n g l e f l u x c a l i b r a t i o n g r a p h f o r t h e s y s t e m . T h e r e i s a d o u b l i n g o f v a r i a b i l i t y by u s i n g t h i s method s i n c e a p o i n t t o o h i g h i n one s t e p w i l l be t o o low i n t h e n e x t . The p l o t t e d r e s u l t s f r o m a f i r s t s e r i e s o f e x p e r i m e n t s d i d n o t f o r m a s i n g l e c h a r a c t e r i s t i c c u r v e o f volume f l u x v e r s u s p r e s s u r e . The t r a y b o t t o m was d i s a s s e m b l e d t o i n s p e c t t h e membrane, w h i c h a p p e a r e d t o be c l o g g e d and d i s c o l o r e d i n s p i t e o f f i l t e r i n g t h r o u g h w a t e r - p u r i f y i n g c a r t r i d g e s . T h i s c o u l d be c a u s e d by o r g a n i c a c t i v i t y o r m i n e r a l p r e c i p i t a t i o n , and by d u s t f r o m t h e l a b o r a t o r y v e n t i l a t i o n s y s t e m . A new membrane w i t h 5 m i c r o n p o r e s i z e was i n s t a l l e d i n t h e t r a y , a n d a l l f l u i d s were pumped t h r o u g h a 0.45 m i c r o n f i l t e r . A f t e r a d j u s t i n g t h e s a l i n i t i e s , and a d d i n g a s m a l l amount o f b l e a c h t o c o n t r o l b i o l o g i c a l a c t i v i t y , t h e f l u i d s were pumped t h r o u g h a 0.8 o r 5 m i c r o n f i l t e r i n t o t h e t a n k and r e s e r v o i r s b e f o r e e a c h c a l i b r a t i o n r u n . The s a l t f l u x p l o t s f r o m t h e s e e x p e r i m e n t s were c o m b i n e d i n a s i n g l e g r a p h ( f i g u r e E-3) . T h i s shows t h a t , w i t h some s c a t t e r , r e p e a t a b l e r e s u l t s f o r s a l t f l u x e s t i m a t e s were o b t a i n e d f o r a r a n g e o f f l u x e s . Membrane volume f l u x c a l i b r a t i o n s were done b e f o r e a n d a f t e r t h e f i r s t s l o p e f l o w e x p e r i m e n t and a c u r v e t h r o u g h t he c o m b i n e d p l o t s ( f i g u r e E-2, a l s o i n t e x t ) was u s e d t o compute s a l t f l u x e s t i m a t e s . The f o l l o w i n g p a g e s c o n t a i n a t y p i c a l p r i n t - o u t o f t h e d a t a a n d c a l c u l a t e d v a l u e s , t h e t i m e - s e r i e s p l o t o f s a l i n i t i e s and t h e c a l i b r a t i o n p l o t s o f membrane volume f l u x v e r s u s p r e s s u r e . 123 F i g u r e E - l . MICRO-CELL TIME SERIES PLOT Membrane f l ux c a 11 brat. 1 on: 2 6 - 2 - 8 6 55.0-1 CO -P c s a l i n i t y in the tray ro o CO 30. 0 i s a l i n i t y in the tank 5 .0 —r— 90 — r :I0 Time (min) 1 30 150 270 Figure E~2. Membrane volume f l u x c a l i b r a t i o n before and a f t e r f i r s t s lope flow experiment. 126 DESCRIPTION OF EXPERIMENTS A P P E N D I ZXi TT 127 APPENDIX F DESCRIPTION OF EXPERIMENTS T h i s a p p e n d I K c o n t a i n s a b r i e f d e s c r i p t i o n o f t h e i n d i v i d u a l s l o p e f l o w e x p e r i m e n t s . I n c l u d e d a r e t h e s l o p e a n g l e , s t a r t i n g s a l i n i t i e s o f f l u i d i n t a n k a n d t r a y , s p e c i a l f e a t u r e s o b s e r v e d d u r i n g t h e i n d i v i d u a l e x p e r i m e n t , t h e t a b u l a t e d v a l u e s o f t r a y s a l i n i t i e s f r o m t h e m a n u a l l y c o l l e c t e d d a t a , v e l o c i t y maxima m e a s u r e d f r o m dye f e a t u r e s i n t h e s l o p e f l o w , t h e e s t i m a t e s o f t h e membrane s a l t f l u x a t t h e t i m e s t h a t f l o w v e l o c i t i e s were d e t e r m i n e d , t i m e - s e r i e s p l o t s o f s a l i n i t i e s d u r i n g t h e e x p e r i - ments and t h e l i n e p r l n t e r o u t p u t o f t h e raw d a t a and c o m p u t e d v a l u e s f r o m t h e d a t a l o g g e r . 1.7.8 F. 1 SLOPE FLOW EXPERIMENT #1 I n t h e f i r s t s l o p e f l o w e x p e r i m e n t , t h e b o t t o m s l o p e a n g l e was 3.3 d e g r e e s and t h e d e p t h i n t h e t a n k u n d e r t h e t r a y was 7 mm a t t h e r a i s e d end a n d 63 mm a t t h e d e e p e n d . The t r a y was f i l l e d w i t h f l u i d o f 59 p p t t o a h e i g h t o f a b o u t 34 mm, w h i l e 800 ml o f f l u i d o f 15 p p t was a d d e d t o t h e edge b e t w e e n t a n k and t r a y t o k e e p t h e l e v e l s e q u a l . A b o t t o m s l o p e f l o w became v i s i b l e on t h e s h a d o w g r a p h b e f o r e f i l l i n g a n d l e v e l l i n g was c o m p l e t e d . V e l o c i t y maxima i n t h e s l o p e f l o w were d e t e r m i n e d f r o m c o l o r s l i d e s e q u e n c e s o f dye s t r e a k s . S a l i n i t y p r o f i l e s were p l o t t e d f r o m m i c r o - c e l l d a t a t a k e n a t p o r t # 6 o v e r t = l l - 3 8 m i n ( f i g . F-2 ) . ' Quas i - i ns t a n t a n e ou s' p r o f i l e s were o b t a i n e d f i t t i n g a s e c o n d o r d e r c u r v e t h r o u g h t h e p r o f i l e p o i n t s i n t h e m i x e d l a y e r ( f i g u r e F-3) and s u b t r a c t i n g t h e f i t f r o m t h e p r o f i l e p o i n t s : S ( i n s t a n t ) = S ( p r o f i l e ) - S ( f i t ) + S ( t l ) The a d j u s t e d p r o f i l e s ( f i g u r e F-4) show a s l o p e f l o w d e p t h o f 14 t o 17 mm, w i t h a r i s e i n s a l i n i t y o f 0.6-0.7 PSS. M i c r o - c e l l d a t a were a l s o t a k e n t o c h e c k t h e d i s t r i b u t i o n o f s a l i n i t y i n t h e t a n k a l o n g t h e b o t t o m s l o p e and a l o n g t h e t o p u n d e r t h e t r a y ( f i g u r e F - 5 ) , b u t a t i m e - s e r i e s p l o t o f t h e s e p o i n t s ( f i g u r e F-6) g i v e s i n s u f f i c i e n t d e t a i l a b o u t t h e l a t e r a l d i s t r i b u t i o n . T a b l e F l l i s t s t h e c o m p u t e d v a l u e s o f s a l i n i t i e s , d e n s i t i e s and d r i v i n g p r e s s u r e s a t t h o s e t i m e s t h a t s l o p e f l o w v e l o c i t i e s were m e a s u r e d , and t h e volume and s a l t f l u x e s d e r i v e d f r o m them as d e s c r i b e d i n t h e t e x t ( s e c t i o n 2 . 6 ) . 1Z9 T a b l e F1. S a l t f 1 u x e s a n d f l o w v e l o c i t i e s - s l o p e r u n # l From dye s e e n i n s i i d e # 12-13 17-19,20-21 t a k e n a t t i m e ( m i n ) t = = 25 30 ( l i n e p r i n t e r t i m e ) max. v e l o c i t y (cm/s) v : = 0.510 0.401-0. 519 s a l i n i t y - t r a y ( g / k g ) S2 = = 57.926 57.676 f r o m C#3 d a t a f i t s a l i n i t y - m i x e d l a y e r SI = = 20.541 21.395 f r o m p r i n t e r C#2 t e m p e r a t u r e C O T - t a n k = 21 .67 21.64 t h e r m i s t o r #526 t r a y d e n s i t y ( s i g m a - t ) D2 = = 41.867 41 .683 U n e s c o E q . o f S t a t e m i x e d l a y e r d e n s i t y D l : = 13.357 14.010 M n d r i v i n g p r e s s u r e P = = 89.50 86 .87 g * h * ( D 2 - D l ) / 1 0 0 0 volume f l u x ( c m / s e c ) Vw : = 2.95e-4 2.82e-4 f r o m f i g . 2 - 1 5 s a l t f l u x ( g / c m 2 / s ) B = 1.780e-5 1 .694e-5 130 F i g u r e F - l . MICRO-CELL TIME SERIES PLOT SLOPE FLOW EXPERIMENT #1 6 0 . 0 1 co C O : : « z s a l i n i t y i n t r a y t i t i i t I I H I a co 3 5 . 0 - s a l i n i t y i n tank ( i n c l u d e s p r o f i l e s ) 10.0 Time (min) 1 20 "60" 100 140 180 F-2 S A L I N I T Y P R O F I L E S L O P E FLOW EXP#1 17.0 S a l i n i t y (PSS) 1 Q 5 2 2 . 0 1 I 1 1 I I I I I 1 PROFILES IN PORT #6 t e l l - 2 7 min going down- 2 min i n t e r v a l e t=30-38 going up- 1 min i n t e r v a l e 132 t ime (min) Figure F-3. Time-series plot of profile points. Figure F~4. S A L I N I T Y P R O F I L E S L O P E FLOW E X P # 1 16.90 S a l i n i t y C P S S ) ^ 3 0 4 0 - J 1 L 17. 70 J I • P r o f i l e a in port #8 t=ll-27 going down (o) t e30-38 going up (x) S <profile)-S (actual) - S(t) + S(t0) S(t) = 14.1185 +U.2S736 -t*.0021194) (2nd order f i t to mixed layer data) (S(t0)- S ( t - l l ) 134 32.01 SLOPE FLOW EXP#1 X s5 sa l ini ty at 2 mm above bottom o= sa l ini ty at 4 mm below tray samplinq interval 3 minutes &=r using 2nd order f i t (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. D i s t a n c e a l o n g 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 I n s l o p e f l o w e x p e r i m e n t #2, t h e s l o p e a n g l e was 3.8 d e g r e e s and t h e f l u i d d e p t h b e l o w t h e t r a y was 7 mm a t t h e s h a l l o w end and 65 mm a t t h e deep e n d . The AM/CT d a t a l o g g e r was u s e d w i t h m i c r o - c e l l s #1 and #2 t o o b t a i n d a t a f o r f l u i d i n t h e t a n k . P r o f i l e d a t a were t a k e n l n p o r t #6 a t t=39-56 min ( f i g u r e F-9) and a t t =112-130 min ( f i g u r e F - l l ) a f t e r t h e s t a r t . A l e a s t s q u a r e s l i n e a r f i t t o d a t a t a k e n s i m u l t a n e o u s l y w i t h t h e s e c o n d m i c r o - c e l l a t f i x e d d e p t h i n t h e m i x e d l a y e r ( f i g u r e F-8, F-10) was u s e d t o o b t a i n t h e q u a s i - i n s t a n t a n e o u s p r o f i l e s . S a l i n i t y maxima i n t h e s l o p e f l o w were 0.4 t o 0.5 p p t above t h o s e i n t h e m i x e d l a y e r . T a b l e F 2 . F l o w v e l o c i t i e s f r o m p h o t o s - s l o p e r u n #2 P h o t o s # : 7-10 14-17 min a f t e r s t a r t ( c l o c k t i m e ) : 55 ( 1 5 : 2 5 ) 125 ( 1 6 : 3 5 ) s c a l e : p o r t s ( c m ) / p h o t o ( m m ) : 20/74 30/81.8 dye moved on p h o t o ( m m / 1 O s e c ) : 16 8.5 f l o w v e l o c i t y max. ( c m / s e c ) : 0.43 0.312 T r a y f l u i d d a t a were o n l y t a k e n a t t h e s t a r t and end o f t h e r u n . S a l i n i t i e s a t o t h e r t i m e s were e s t i m a t e d f r o m c o n s e r v a t i o n o f volume and s a l t : V 1 * S 1 ( t ) * D l ( t ) + V 2 * S 2 ( t ) * D 2 ( t > = G ( t ) l n w h i c h VI a n d V2 were t h e t a n k and t r a y v o l u m e s , S I and S2 t h e s a l i n i t y i n t h e m i x e d l a y e r a n d i n t h e t r a y a n d DI and D2 c o r r e s p o n d i n g d e n s i t i e s . The a r b i t r a r y f u n c t i o n G ( t ) r e p r e s e n t s 137 t h e s a l t l o s s t o t h e b o t t o m f l o w , arid was l i n e a r l y p r o p o r t i o n e d o v e r t h e p r o f i l i n g t i m e . T a b l e F3 shows t h e s a l i n i t i e s c o m p u t e d f r o m d a t a o f m i c r o - c e l l #3, w i t h V l = 7 . 0 8 and V2=26.5 l i t e r s . T a b l e F4 l i s t s t h e c o m p u t e d s a l i n i t i e s , d e n s i t i e s and p r e s s u r e s and t h e d e r i v e d s a l t f l u x e s a t t h e t i m e s t h a t f l o w v e l o c i t i e s were d e t e r m i n e d . T a b l e F 3 . S a l i n i t y o f t r a y f l u i d - s l o p e r u n #2 -VC#3 RT#22 RT#40 T ( d e g . C ) S ( p p t ) s t a r t t = 55 t=125 end 2.217 1950 1883 ( e s t i m.) ( e s t i m.) 2.026 1956 1889 22. 45 22. 37 57.64 55.21 52 . 42 52 . 04 T a b l e F4. S a l t f l u x e s and slope flow v e l o c i t i e s - sloperun# 2 A t t i m e ( m i n ) t t p r t l = 55 S a l . - m i x e d l a y e r S I = 15.694 S a l i n 1 t y - t r a y S2 = 55.21 t e m p ( d e g . C ) T - t n k = 21.286 t r a y d e n s ( s i g m a - t ) D2 = 39.890 d e n s m i x . l a y e r D l = 9.794 d r i v i n g p r e s s u r e P = 94.48 volume f l u x ( cm/s) Vw= 3.17e-4 membrane s a l t f l u x B = 1.820e-5 m a x . f l o w v e l o c i t y v = 0.43 125 f r o m : 25.006 C#2 p r i n t - o u t 52.04 e s t i m . ( t a b l e F 3 ) 21.585 t h e r m i s t o r #526 37.652 U n e s c o p o l y n o m . 16.754 65.60 ( D 2 - D 1 ) / 1 0 0 0 * g * h 2.00e-4 f r o m f i g u r e 2-15 1.712e-5 B=F*S2*( D2 +1) 1000 1000 0.312 ( c m / s e c ) 13B Figure F-7. MICRO-CELL TIME SERIES PLOT SLOPE FLOW EXPERIMENT #2 time (min) Figure F~B. Time-seriee and lineor f i t 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 f i t Figure F-ll. SALINITY PROFILE a 6-3-86 SLOPERUN #2 23.60 SALINITY (PSS) 2 4 < 7 0 2 5 Q 0 * 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 I n s l o p e f l o w e x p e r i m e n t #3 t h e s l o p e a n g l e was 2.2 d e g r e e s . The d e p t h b e l o w t h e t r a y was 20 mm a t t h e s h a l l o w e n d and 51 mm a t t h e deep e n d . The AM/CT D a t a l o g g e r was u s e d w i t h m i c r o - c e l l #1 f o r p r o f i l e s , w i t h m i c r o - c e l l #2 f i x e d a t 15mm b e l o w t h e t r a y f o r s a l i n i t i e s In t h e m i x e d l a y e r a n d w i t h t h e r m i s t o r #526 f o r t e m p e r a t u r e s i n t h e t a n k . S a l i n i t i e s i n t h e t r a y were c o m p u t e d f r o m v o l t - m e t e r r e a d i n g s o f m i c r o - c e l l #3. A f t e r f i l l i n g t h e t r a y t o s t a r t t h e e x p e r i m e n t , t h e t a n k was b r i e f l y s t i r r e d t o remove c i r c u l a t i o n p a t t e r n s w h i c h m i g h t have been f o r m e d by u n e v e n f l u x d u r i n g t h e f i l l i n g . The s l o p e f l o w r e - e s t a b l i s h e d i t s e l f w i t h i n one m i n u t e , s t a r t i n g a t a b o u t 30cm fr o m t h e s h a l l o w e n d . A c o u n t e r - r o t a t i n g f l o w c e l l , a l s o f o u n d i n t h e p r e v i o u s e x p e r i m e n t , was s e e n i n t h e s h a d o w g r a p h u p s l o p e f r o m t h i s p o i n t . T h i s u p h i l l f l o w d i s a p p e a r e d when t h e s t a r t i n g p o i n t o f t h e d o w n - s l o p e f l o w moved s l o w l y t o w a r d s t h e s h a l l o w e n d . S k e t c h e s o f t h e t y p i c a l f l o w p a t t e r n s a n d t h e d o u b l e f l o w c e l l s a r e i n c l u d e d i n t h e t e x t . S a l i n i t y p r o f i l e d a t a were t a k e n i n p o r t #8 a t t=105-129 min a f t e r t h e s t a r t . A l i n e a r f i t t o s a l i n i t i e s c o m p u t e d f r o m d a t a t a k e n a t a f i x e d d e p t h i n t h e m i x e d l a y e r d u r i n g t h e p r o f i l i n g ( f i g u r e F-13) was u s e d t o o b t a i n ' q u a s I - i n s t a n t a n e o u s ' p r o f i l e s ( f i g u r e F-14>. These show t h e c o n v e c t i v e l y m i x e d l a y e r a n d a s h a r p r i s e l n s a l i n i t y o f 0.8 PSS s t a r t i n g a t 12-18 mm above t h e b o t t o m . Maxima i n t h e s l o p e f l o w v e l o c i t y were m e a s u r e d f r o m t h e d i s t a n c e dye moved i n p h o t o s e q u e n c e s . 144 T a b l e F 5 . F l o w v e l o c i t i e s f r o m p h o t o s - s l o p e r u n #3 min a f t e r s t a r t ( c l o c k t i m e ) : 60 ( 1 0 : 3 0 ) 135 ( 1 1 : 4 5 ) d i s t . dye moved on p h o t o (mm): 11-11.5 10.5-11.0 t i m e b e t w e e n p h o t o s : 11.5 12.5 s l o p e f l o w v e l o c i t y ( c m / s e c ) : 0.259-0.270 0.227-0.238 T a b l e F 6 . S a l t f l u x a n d s l o p e f l o w v e l o c i t y - s l o p e r u n #3 1 i n e p r i n t e r t ime = 60 135 mi n . a f t e r s t a r t m i x e d l a y e r S I = 21 .561 29.106 ( P S S ) t i m e - s e r i e s f i t t r a y s a l i n i t y S2 = 5 4 . 5 8 3 52.695 ( P S S ) t I m e - s e r l e s f i t t e m p e r a t u r e T- t n k = 21.420 21.877 C O t h e r m i s t o r #526 t r a y d e n s i t y D2 = 39.366 37.775 ( s i g m a - t ) U n e s c o e q n . t a n k d e n s i t y DI = 14.192 19.781 M M p r e s s u r e P = 81 .50 58.25 ( g r / c t / s 2 ) volume f l u x Vw = 2.50e-4 1.67e-4 (cm/s) f l u x c a l . p l o t m e m b r . s a l t f l u x B = 1.418e-5 0. 946e-5 g r / c m 2 / s s l o p e f l o w max . V = 0.259-0.270 0.2 27-0.2 38 cm/s f r o m p h o t o s 1 4 5   igure F-14. S A L I N I T Y PROFILE 1 1 - 3 - 8 6 SLOPERUN #3 PORT #8 > 5 . 8 0 S A L I N I T Y ( P S S ) 2 6 . 8 0 27. 80 i f t u a l p r o f i l e * a d j u s t e d p r o f i l e s by l i n e a r f i t t o d a t a from f i x e d d e p t h 148 F.4 SLOPE FLOW EXPERIMENT #4 I n s l o p e f l o w e x p e r i m e n t #4, t h e s l o p e a n g l e was 5.2 d e g r e e s . The d e p t h b e l o w t h e t r a y was 2 cm a t t h e s h a l l o w e n d and 10 cm a t t h e d e e p e n d . The AM/CT D a t a l o g g e r was a g a i n u s e d w i t h m i c r o - c e l l s #1 and #2 and w i t h t h e t a n k t h e r m i s t o r , a n d d i g i t a l v o l t m e t e r s were u s e d w i t h m i c r o - c e l l #3 t o m o n i t o r t h e s a l i n i t y o f f l u i d i n t h e t r a y . T a b l e F 7 . S a l i n i t i e s i n t h e t r a y - s l o p e r u n #4 t i me m i n — VC#3 RT#22 --> TO °C> S C p p t ) 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 S a l i n i t y p r o f i l e s were p l o t t e d f r o m d a t a t a k e n i n p o r t #5 o v e r t=97-131 min a f t e r t h e s t a r t , c o r r e c t e d f o r t h e s a l i n i t y c h a n g e i n t h e m i x e d l a y e r ( f i g u r e F - 1 6 ) . D a t a were a l s o t a k e n a l o n g t h e b o t t o m o f t h e t a n k a t p o r t #8 t h r o u g h #2 and b a c k t o p o r t #7. T h r e e d a t a p o i n t s were t a k e n i n r a p i d s u c c e s s i o n i n e a c h p o r t a t a b o u t 2 mm above t h e b o t t o m , and t h e p o i n t w i s e t i m e - c o r r e c t e d a v e r a g e s were p l o t t e d ( f i g u r e F-17>. 149 The s l o p e f l o w v e l o c i t i e s were m e a s u r e d f r o m v i d e o f o o t a g e o f dye c a r r i e d a l o n g by t h e b o t t o m f l o w , u s i n g t h e 10 cm s p a c i n g o f s a m p l i n g p o r t s i n t h e t r a y f o r s c a l e where v i s i b l e o r t a k i n g t h e a v e r a g e o f v e r t i c a l l i n e s a t t h e bac k ( s p a c e d 5 cm) and t h e u n i t s on a s c a l e a l o n g t h e f r o n t o f t h e t a n k . T a b l e F 8 . Flow v e l o c i t i e s and s a l t f l u x e s - s l o p e r u n #4 A t c l o c k t i m e = 1 4: 50 15:21 16:12 16: 48 hr:m i n 1 i n e p r i n t e r t = 20 50 102 138 m i n t r a y f l u i d S2= 52.708 51 .585 50.175 49.3445 p p t m i x e d l a y e r S l = 7.011 9.557 12.720 14.847 j p p t t a n k temp. T = 21 .053 21.392 2 1 .639 21.715 °C t r a y d e n s . D2 = 38.033 37.068 35.911 35.252 s i gma-1 t a n k d e n s . D l = 3. 295 5. 138 7 . 464 9 .049 s i gma-1 p r e s s u r e P = 112.5 103. 4 92.09 84.83 g r / c m / s 2 volume f l u x Vw= 4.00e-4 3.50e-4 3.00e-4 2.67e-4 cm/s s a l t f l u x B = 2. 19e-5 1 . 87e-5 1 .56e-5 1 .36e-5 g r /cm 2/ 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. S A L I N I T Y PROFILE SLOPE RUN #4 Port #5 t= 97-111 min K-AS=0- 2 4 — ^ 151 FiqureF-16. SALINITY PROFILE SLOPE RUN #4 Port #5 t-ll1-126 min 3 < 4 S a l i n i t y (PSS) i 3 . 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 f i t to mixed lay«r data —= adjusted prof i le 152 1 3 - 6 - 8 6 SLOPE RUN #4: S A L I N I T I E S ALONG BOTTOM SLOPE pointwiee t i m e - a d j u s t e d t=148-173 Figure F -17. Sa l in i ty d i s t r ibut ion along bottom slope. F.5 SLOPE FLOW EXPERIMENT #5 I n t h i s e x p e r i m e n t t h e s l o p e a n g l e was a g a i n 5.2 d e g r e e s and the d e p t h 2 cm a t t h e s h a l l o w e nd and 10 cm a t t h e deep e n d . A new membrane was i n s t a l l e d i n t h e t r a y . M i c r o - c e l l s #1 and #2 were c o n n e c t e d t o t h e AM/CT d a t a l o g g e r and c e l l #3 was u s e d w i t h t h e DVM's f o r t r a y . S t a r t i n g s a l i n i t i e s were 52 p p t i n t h e t r a y a n d 13 p p t i n t h e t a n k . T a b l e F 9 . S a l i n i t i e s i n t h e t r a y d u r i n g s l o p e r u n #5 t i me m i n — VC3 RT#44 RT#23 T- a v g 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 S a l i n i t y p r o f i l e s f r o m d a t a t a k e n i n p o r t #5 a t t=80-97 min ( f i g u r e F-19) and i n p o r t #3 a t t= 125-141 min a f t e r t h e s t a r t 154 ( f i g u r e F-20) were made i n s t a n t a n e o u s by s u b t r a c t i n g t h e c h a n g e i n s i m u l t a n e o u s l y t a k e n m i x e d l a y e r s a l i n i t i e s . They show a w e l l m i x e d c o n v e c t i v e l a y e r a n d a s l o p e f l o w r e g i o n o f 9 t o 15 mm t h i c k n e s s where t h e s a l i n i t y i n c r e a s e s by a b o u t 0.3 PSS. A n o t h e r p r o f i l e was p l o t t e d f r o m d a t a t a k e n i n t h e edge s p a c e b e t w e e n t a n k a n d t r a y ( f i g u r e 2-12 i n t e x t ) . S h a d o w g r a p h images a n d m o t i o n s o f i n j e c t e d dye were r e c o r d e d on v i d e o t a p e d u r i n g p a r t o f t h i s r u n . T h i s i n c l u d e s f o o t a g e o f t h e c o u n t e r - c e l l w h i c h f o r m e d u p s l o p e f r o m t h e p l a c e where t h e b o t t o m f l o w f i r s t e s t a b l i s h e d i t s e l f . V e l o c i t y maxima i n t h e f l o w were m e a s u r e d f r o m v i d e o t a p e f o o t a g e , and t h e t e m p e r a t u r e a n d s a l i n i t y o f f l u i d i n t h e m i x e d l a y e r and i n t h e t r a y a t t h o s e t i m e s were o b t a i n e d by l i n e a r i n t e r p o l a t i o n o f t h e t i m e - s e r i e s d a t a o f c a l c u l a t e d v a l u e s . T a b l e F 1 0 . Flow v e l o c i t i e s and sa l t f1uxes - sloperun #5 c l o c k t i m e t = 13:11 2 0 0 ( 1 5 : 2 0 ) 1 6 : 2 1 16:42 h r : m i n p r i n t e r t ( p ) = 71 200 261 282 m i n t r a y f l u i d S2 = 48.948 44.765 43.995 43.828 PSS m i x . l a y e r S1 = 15.835 24.773 26.406 26.915 PSS temp T - t n k = 21.568 2 1 .843 21 .863 21 .872 d e g . C t r a y d e n s D2 = 34.991 31.707 31.112 30.982 s i gma-1 t a n k d e n s D l = 9.831 16.510 17.740 18.123 s i gma-1 p r e s s u r e P = 81.45 49. 20 43.29 41 .63 g/cm/s 2 v o l . f 1 u x Vw = 2.50e-4 1.35e-4 1.25e-4 1 . 22e-4 cm/rain m e m b r . f l u x B = 1.267e-5 0.623e-5 0.567e-5 0.551e-5 g r / c m 2 / s s1 ope f l o w 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 Kl f2=1878, 1793 new membr L n 24.0n CO CO Q- o CO 14. H 4.0 30 120 210 300 Time (min) Fi a u r e f _ i g : S A L I N I T Y P R O F I L E 1 8 - 3 - 8 6 SLOPERUN #5 0 1 6 > 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 p r o f i l e data o - fi x e d depth backgnd £ - oorreoted p r o f i l e (pointwiee d i f f . ) 18.5 i 1 5 7 Figure F -20 : SALINITY PROFILE .18-3-86 SLOPERUN #5 158 F.6 SLOPE FLOW EXPERIMENT #6 I n s l o p e f l o w e x p e r i m e n t #6, t h e s l o p e a n g l e was 2.3 d e g r e e s and t h e d e p t h b e l o w t h e t r a y was 20 mm a t t h e s h a l l o w e n d and 57 mm a t t h e deep e n d . A c o n v e r g e n c e n e a r t h e t o p o f t h e m i x e d l a y e r was s e e n t o o c c u r i n s e v e r a l o f t h e p r e v i o u s e x p e r i m e n t s . T h i s c o n v e r g e n c e was c e n t e r e d n e a r t h e p o i n t where t h e down- s l o p e f l o w was s e p a r a t e d f r o m t h e u p h i l l f l o w c e l l w h i c h f o r m e d d u r i n g s t a r t - u p . The o b j e c t o f t h i s e x p e r i m e n t was t o c h e c k f o r v a r i a t i o n s i n t h e m i x e d l a y e r s a l i n i t y a l o n g t h e l e n g t h o f t h e t a n k . Any s a g i n t h e b o t t o m o r a s l i g h t bow i n t h e s i d e s o f t h e t r a y w o u l d i n c r e a s e t h e l o c a l h e i g h t o f t h e h e a v i e r f l u i d c o l u m n a n d t h u s t h e s a l t f l u x . The AM/CT d a t a l o g g e r was u s e d w i t h a l l t h r e e m i c r o - c e l l s t o sa m p l e f l u i d i n t h e u p p e r p a r t o f t h e m i x e d l a y e r a l o n g t h e c e n t e r l i n e , a b o u t 1 cm b e l o w t h e t r a y : m i c r o - c e l l #1 was u s e d a t p o r t #5 n e a r t h e c e n t e r , #2 a t p o r t #2 n e a r t h e s h a l l o w e n d , and #3 was u s e d a t p o r t #7 n e a r t h e deep e n d b u t o c c a s i o n a l l y moved t o t h e t r a y t o d e t e r m i n e t h e s a l i n i t y t h e r e . The t r a y was f i l l e d b e t w e e n 11:10 t o 11:20 t o a h e i g h t o f 34 mm w h i l e f l u i d o f 10 PSS was a d d e d t o t h e edge s p a c e b e t w e e n t a n k a n d t r a y . The v i d e o t i m e r was s t a r t e d a t 11:23:30 b u t t h e t i m e - s e r i e s d a t a a r e p r i n t e d i n m i n u t e s a f t e r 11:00 and t h u s : t < p r i n t e r ) = t ( v l d e o ) + 23.5 m i n . D u r i n g t h e f i r s t 40 m i n u t e s i n t h e t i m e - s e r i e s , t h e s a l i n i t y was h i g h e r by 0.2 t o 0.5 PSS n e a r t h e c e n t e r , and a c o n v e r g e n c e j u s t b e l o w t h e t r a y was v i s i b l e l n t h e s h a d o w g r a p h . A t t=29 o r 159 t ( v l d e o ) = 5 m i n , t h e t a n k was s t i r r e d t o remove p a t t e r n s f o r m e d d u r i n g f i l l i n g . The downs 1 o p e / u p h i 1 1 f l o w p a t t e r n s r e - f o r m e d i n a s h o r t t i m e a n d dye i n j e c t e d a t p o i n t s a l o n g t h e c e n t e r l i n e c o n f i r m e d t h i s . I n l a t e r m e a s u r e m e n t s , t h e m i x e d l a y e r s a l i n i t y was h i g h e r t o w a r d s t h e s h a l l o w e n d , e x p l a i n e d by m i x i n g o f s a l t I n t o a s m a l l e r d e p t h . The c o u n t e r - c e l l w h i c h was v i s i b l e l n t h e s h a d o w g r a p h Image d e c r e a s e d t o t h e s h a l l o w e s t 10 cm o f t h e t a n k b u t p e r s i s t e d t h r o u g h o u t t h e r u n . I t m i g h t have been s u s t a i n e d by t h e d i f f e r e n c e In s a l t f l u x n e a r t h e e n d w a l l due t o t h e a r e a w i t h o u t s a l t f l u x b e l o w t h e end o f t h e t r a y . The s h a d o w g r a p h images and s t r e a k s f r o m i n j e c t e d dye were r e c o r d e d on v i d e o t a p e d u r i n g much o f t h e r u n . F l o w v e l o c i t i e s d e t e r m i n e d f r o m t h i s a r e t a b u l a t e d b e l o w : T a b l e F l l . S l o p e f l o w v e l o c i t i e s - s l o p e r u n #6 d i s t v i d e o t i m e - i n t e r v a l d t t C p r t l v e l o c i t y (cm) ( h : m i n : s e c ) ( s ) ( m i n ) (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 t h i r d o r d e r p o l y n o m i a l f i t was done t o d a t a f r o m t h e t r a y f l u i d and f r o m c e l l #1 t o d e t e r m i n e t h e s a l i n i t y v a l u e s a t t h e t i m e s t h a t f l o w v e l o c i t i e s were m e a s u r e d , w h i c h were u s e d t o o b t a i n s a l t f l u x e s t i m a t e s . T a b l e F 1 2 . S a l i n i t i e s i n t r a y a n d t a n k - s l o p e r u n #6 t ( p r t ) S-C#3 t ( p r t ) 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 . 1 1 9 7 +t<2.3288E-5 - t * 1 . 4 4 5 4 E - 8 ) ) (rms d i f f . = 0.0265) SI = 15.8225 + t ( 0 . 0 3 3 2 5 + t ( - 4 . 4 8 5 9 E - 5 + t * 2 . 0 3 7 2 5 E - 8 ) > (rms d i f f . = 0.0867) 161 Tab le F 1 3 . F low v e l o c i t i e s and s a l t f l u x e s - s l o p e r u n #6 v i d e o t i m e r t ( v ) = 1 :54 :35 2 : 0 1 : 3 0 3 : 1 1 : 3 0 h r : m i n : s e c p r i n t - o u t t ( p ) = 1 38 145 216 m i n S - t r a y f l u i d S2 = 29 .495 29 .447 29.041 PSS S -mixed l a y e r SI = 19.610 19 .763 2 1.117 PSS tank temp T- tnk = 22.291 22 .325 22 .574 °C t r a y dens i t y D2 = 19 .963 19.917 19.541 s igma-t tank d e n s i t y Dl = 12.494 12.601 13.556 s i gma-t p r e s s u r e P = 24 .18 23 .68 19 . 37 g / c m / s 2 volume f l u x Vw = 7 . 3 3 e - 5 6 . 5 0 e - 5 5 . 5 0 e - 5 cm/s m e m b r . s a l t f l u x = 2 .205e-6 1 . 952e-6 1 .628e-6 gr / cm 2 / s f l o w v e l o c i t y V = Q.123 0.1 1-0.1 3 0.09-0.1 1 cm / s 162 F igure F~2 1 MICRO-CELL TIMESERIES 8 -5 -8 6 SLOPERUN #6 d=20-57 h=34 K=1892, 1795, 1817 Time (min) F.7 SLOPE FLOW EXPERIMENT #7 I n t h i s e x p e r i m e n t t h e s l o p e a n g l e was 5.5 d e g r e e s . The t r a y rested on the b o t t o m a t the shallow end, the d e p t h at the deep end was 78 mm. The s t a r t i n g s a l i n i t i e s were 7 PSS i n t h e t a n k and 28 PSS i n t h e t r a y . The d a t a l o g g e r was a g a i n u s e d w i t h a l l t h r e e m i c r o - c e l l s . T i m e - s e r i e s o f m i c r o - c e l l d a t a were t a k e n w i t h t=0 a t 14:00. S a l i n i t y p r o f i l e s f r o m d a t a t a k e n a t p o r t #5 o v e r t=40-59 ( s e e f i g u r e F-23) and a t p o r t #4 o v e r t=109-121 ( f i g u r e F-24) show a t y p i c a l m i x e d l a y e r a n d t h e b o t t o m s l o p e f l o w r e g i o n w i t h a r i s e i n s a l i n i t y o f 0.2-0.4 PSS i n t h e l o w e s t 8 mm. As t h e s a l i n i t y i n b o t h t h e m i x e d l a y e r and t h e s l o p e f l o w i n c r e a s e s o v e r t i m e , t h e deep e nd o f t h e t a n k becomes s t a b l y s t r a t i f i e d . T h i s c a n be s e e n i n a p r o f i l e a t p o r t #7 o v e r t = 87-100 ( f i g u r e F - 2 5 ) . The s h a d o w g r a p h image shows t h a t a f t e r one h o u r t h e m i x e d l a y e r e x t e n d s a b o u t 3 cm down f r o m t h e t r a y a n d no c o n v e c t i v e p e n e t r a t i o n i s s e e n b e l o w t h i s d e p t h . Dye i n t h e s l o p e f l o w was s e e n t o s p l i t : one p a r t c o n t i n u e s a l o n g t h e b o t t o m , t h e o t h e r f l o w s a l o n g t h e i n t e r f a c e where i t i s e n t r a i n e d i n t o t h e m i x e d l a y e r by t h e v e l o c i t y s h e a r . S h a d o w g r a p h images o f t h e o n s e t o f c o n v e c t i o n a n d t h e s t a r t - up o f t h e s l o p e f l o w were r e c o r d e d on v i d e o t a p e . The v i d e o t i m e r was s t a r t e d a t 13:48 so t [ v i d e o l = t t p r t ] - 12. The s l o p e f l o w was s e e n t o s t a r t up v e r y c l o s e t o t h e s h a l l o w e n d s o o n a f t e r t h e s a l t f l u x t h r o u g h t h e membrane became v i s i b l e on t h e s h a d o w g r a p h a s a s l o w l y d e s c e n d i n g c u r t a i n o f l i n e s . The d e s c e n t was n e a r l y e v e n a l o n g t h e t a n k e x c e p t s l i g h t l y f a s t e r i n t h e a r e a where a 164 c o u n t e r - r o t a t i n g c e l l f o r m e d i n p r e v i o u s e x p e r i m e n t s . No s u c h c e l l was s e e n t h i s t i m e . A c l o u d o f d y e , i n j e c t e d i n t h e s t a b l e l a y e r n e a r t h e deep end o f t h e t a n k , s l o w l y d i f f u s e d b e l o w t h e s h a r p i n t e r f a c e w i t h t h e m i x e d l a y e r . I t was e n t r a i n e d above t h i s a n d l i f t e d i n t o t h e r e t u r n c i r c u l a t i o n . The s l o p e f l o w v e l o c i t y was d e t e r m i n e d f r o m v i d e o f o o t a g e o f dye movement: T a b l e F 1 4 . F l o w v e l o c i t y a n d s a l t f l u x - s l o p e r u n #7 dye moved 5 cm i n : d t ( v i d e o ) = 2: 25 :55-2:26:37 =42s and : d t = 2: 26 :37-2:27:26 =49s s l o p e f l o w max. v = 0.102-0.119 cm/s t i me 16:14 t [ p r 1 = 138 m i n u t e s a f t e r s t a r t S - t r a y f l u i d S2 = 26.552 PSS S - m i x e d l a y e r S I = 16.871 PSS t a n k temp T - t n k = 24.179 °C t r a y d e n s i t y D2 = 17.2106 s i gma-1 t a n k d e n s i t y DI = 9.930 s i g m a - t p r e s s u r e P = 23.569 g/cm/s 2 volume f l u x Vw = 6.33e-5 cm/s m e m b r . s a l t f l u x B = 1.710e-6 g r / c m J / 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. S A L I N I T Y P R O F I L E S L O P E R U N #7 K = 1 8 9 2 , 1 7 9 5 , 1 8 1 7 167 Figure F-24. S A L I N I T Y P R O F I L E S L O P E R U N #7 K = 1 8 9 2 , 1 7 9 5 , 1 8 1 7 168 Figure F-25. S A L I N I T Y P R O F I L E S L O P E R U N #7 K = 1 8 9 2 , 1 7 9 5 , 1 8 1 7 169 F.8 SLOPE FLOW EXPERIMENT #8 I n e x p e r i m e n t #8, t h e b o t t o m s l o p e a n g l e was 5.1 d e g r e e s , a n d a t t h e s h a l l o w e nd t h e d e p t h u n d e r t h e t r a y was 12 mm. The HP-3497A D a t a A c q u i s i t i o n s y s t e m was u s e d f o r a l l t h e r m i s t o r s a n d f o r t h e o u t p u t f r o m t h e i n d i v i d u a l c o n d u c t i v i t y c i r c u i t s w h i c h p o w e r e d t h e t h r e e m i c r o - c e l l s . The s y s t e m was c o n t r o l l e d w i t h an HP-9825 c o m p u t e r w h i c h s t o r e d a l l d a t a on t a p e , p r i n t e d t h e c a l c u l a t e d v a l u e s f r o m e a c h s e n s o r a nd p l o t t e d t i m e - s e r i e s d a t a o f c a l c u l a t e d s a l i n i t i e s . S i m u l t a n e o u s s a l i n i t y p r o f i l e s were o b t a i n e d f r o m d a t a t a k e n n e a r t h e m i d d l e o f t h e t a n k and a t 20 cm t o e i t h e r s i d e . The i n t a k e s o f m i c r o - c e l l s C # l , C#2 a n d C#3 were l o w e r e d t h r o u g h p o r t s #7, #5 and #3 r e s p e c t i v e l y , a n d s e t t o t o u c h t h e s l o p e d b o t t o m . S i m u l t a n e o u s d a t a were t a k e n a t s u c c e s s i v e d e p t h s a f t e r r a i s i n g t h e i n t a k e s o f t h e m i c r o - c e l l t o g e t h e r t o t h e same h e i g h t above t h e b o t t o m ( s e e f i g u r e F - 2 6 ) . F i g u r e F-26. A r r a n g e m e n t o f m i c r o - c e l l s 170 I n t h e f i r s t s e r i e s o f p r o f i l e d a t a , t a k e n o v e r a p e r i o d o f 20 m i n u t e s , t h e i n t a k e s were l o w e r e d t h r o u g h t h e c o n v e c t i v e l y m i x e d l a y e r a n d t h e s l o p e f l o w r e g i o n t o t h e b o t t o m a nd r a i s e d a g a i n . S e c o n d o r d e r c u r v e s were f i t t h r o u g h t h o s e s e q u e n c e s o f d a t a f r o m e a c h c e l l w h i c h i n an e x p a n d e d t i m e - s e r i e s ( f i g u r e F-28) a p p e a r e d t o be p a r t o f t h e m i x e d l a y e r : S ( t ) = A + B t + C t 2 M i c r o d a t a - f i l e number c o e f f i c i e n t s o f 2nd o r d e r f i t : - c e l l f r o m t o and t o 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 S i m u l t a n e o u s q u a s i - i n s t a n t a n e o u s p r o f i l e s were o b t a i n e d f r o m : S ( c o r r ) = S ( a c t u a l ) - S ( f i t ) + S ( f i t a t s t a r t ) a n d i n t h e p r o f i l e s so o b t a i n e d , t h e m i x e d l a y e r s a l i n i t i e s o f e a c h i n d i v i d u a l s t a t i o n a r e t h e same a t t h e s t a r t a n d end o f t h e p r o f i l e s e q u e n c e ( f i g u r e s F - 2 9 , 3 0 ) . A s e c o n d s e t o f s a l i n i t y p r o f i l e s , f r o m d a t a t a k e n a b o u t 85 m i n u t e s l a t e r , ( f i g u r e F-31) shows t h a t t h e s a l i n i t y i n t h e b o t t o m c u r r e n t d o e s n o t r i s e a s much ab o v e t h a t i n t h e m i x e d l a y e r as i n t h e e a r l i e r s e t . The l a t e r p r o f i l e f r o m m i c r o - c e l l #1 i n p o r t # 7 n e a r t h e deep end shows a n e a r l y l i n e a r s t r a t i f i c a t i o n f r o m h e a v y f l u i d w h i c h c o l l e c t e d i n t h e b o t t o m . D i f f e r e n c e s i n t h e shape o f p r o f i l e s f r o m m i c r o - c e l l s #2 and #3 d i d n o t c h a n g e o v e r t h a t t i m e . T e s t s done a f t e r t h i s e x p e r i m e n t show t h a t a s u d d e n s h i f t i n c o n d u c - t a n c e may o c c u r w i t h a s h i f t i n r e l a t i v e p o s i t i o n o f t h e o u t l e t t u b e s o f t h o s e m i c r o - c e l l s w h i c h s y p h o n i n t o t h e same b o t t l e . 171 t a t a c a to t a c a c a DATA 1 0 - 3 1 - 8 6 HP-DATALOGGER • i L 11 0 E L OJ-P QJ4-e <H I — 09 4- +r ca 0) CT) II 6 ̂ • r t C -P CD o Figure F~27. Time-series slope flow exp#8 300 SEC/DIV i i t i t M I C R O - C E L L S A L I N I T Y T I M E S E R I E S P L O T Fiqure F-Z9, S A L I N I T Y P R O F I L E 3 S L O P E RUN m 9. 55 40 E E o _u V > 0 _Q 0 ID 20 •rt a; 10 - 0 S a l i n i t y (PSS) g > g 5 I l l 10. 15 i / / / t= l l : 58-12: 06 ' quasi-instantaneous' profiles, using 2nd order f i t . Cl : port#7 C2 i port#5 C3 t portl?3 1 7 4 FIGURE F-30. S A L I N I T Y P R O F I L E S L O P E RUN #8 9. 90 40 30 - E E E 0 -P 0 -0 > 0 J) 0 •rt X 10 " S a l i n i t y ( P S S ) 1 0 - 2 0 I I L_ C2 Cl 10. 50 _L I t - 12:06™12t 17 F#i 110-132 'quaoi-inetantaneoue' p r o f i l e a ueing aeoond order f i t through mixed layer data Cl C2 C3 port#7 port#5 port#3 h=13mm, AS=0.38-0.46 0 175 S A L I N I T Y P R O F I L E FIGURE F-31. S L O P E RUN #8 0 S a l i n i t y <PSS) i g > 3 1 I L_ 1 3 . 6 1 quasi-inetantaneoue p r o f i l e e (correoted f o r change i n s a l i n i t y i n the mixed l a y e r during p r o f i l i n g ) . Simultaneous p o i n t s at equal height© above the e l c p i n g bottom*, spaced 20 cm: in port#7 (deep) cell # 2 i n port#5 (middle) oell# 3 i n port#3 (shallow) t=13:42-13t 56 (data F6-46) AS = 0.31-0.37 176

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