Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
UBC_1987_A6_7 H36_4.pdf [ 9.74MB ]
[if-you-see-this-DO-NOT-CLICK]
Metadata
JSON: 1.0053226.json
JSON-LD: 1.0053226+ld.json
RDF/XML (Pretty): 1.0053226.xml
RDF/JSON: 1.0053226+rdf.json
Turtle: 1.0053226+rdf-turtle.txt
N-Triples: 1.0053226+rdf-ntriples.txt
Original Record: 1.0053226 +original-record.json
Full Text
1.0053226.txt
Citation
1.0053226.ris

Full Text

A LABORATORY  STUDY OF SLOPE FLOW  INDUCED BY A SURFACE SALT FLUX by Bon J . van H a r d e n b e r g 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 in  THE DEPARTMENT  We a c c e p t t h i s to  OF OCEANOGRAPHY  thesis  the r e q u i r e d  THE UNIVERSITY  as c o n f o r m i n g standard  OF BRITISH COLUMBIA  April  1987  (c)Bon J . van Hardenberg, 1987  In  presenting  degree  at  this  the  thesis  in  University of  partial  fulfilment  of  of  department publication  this or of  thesis for by  his  or  her  representatives.  Oceanography  15 A p r i l 1987  nF-firt/ft-n  for  an advanced  Library shall make  it  agree that permission for extensive  It  this thesis for financial gain shall not  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  that the  scholarly purposes may be  permission.  Department of  requirements  British Columbia, I agree  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head  of  copying  my or  be allowed without my written  ABSTRACT  The the  salt  expulsion  drainage of brine  layer, This  which  experiments into  dye r a n g e d  of  and  flow  0.24  using  1 . 63* 10 depths  experimental Bo  gravity the  than  ment. T h i s to  Arctic  This  arrangement,  flow  Using  field  interaction  interface  that  between  slope angles  fluxes  a rise  showed  in  salinity  layer.  with  predicted  model  computed  fora from  this  results  turbulent the data of  i n a quiescent  evidence  model  between  profiles  magnitude environ-  of the experiments or  low r a t e s i s required  f l o w s and the t u r b u l e n t  ii  conductivity  up t o t w o o r d e r s o f  indicate  a different such  with  closely  f o r flows  to visual which  salt  densities  without shear, using  factors  were  Fluid  F o r bottom  the entrainment  predicted  data,  from  and small-volume  i n the mixed  agreed  experiments  i s contrary  suggests  those  entrainment  those  t h e movement  7 a n d 17 mm  at a density  current,  measured  the s a l i n i t y  2  flow i s  angle.  purpose.  g/cm /s,  membrane  i s s e t a t an  and a t computed  between  Pedersen.  slope  larger  _ &  mixed  laboratory  a down-slope  0 . 0 9 t o 0.66 c m / s .  for this  t o 0.92 p p t a b o v e  Entrainment  by  of the tank  and  regions.  through a porous  show t h a t  thermistors  a n d 5.5°,  a convectively  was s i m u l a t e d i n  water  images  from  developed  2.2° _ 5  salt  of seawater  in shallow coastal  maxima i n t h e s l o p e f l o w ,  micro-cells  slope  a t the surface  Shadowgraph  were d e t e r m i n e d  1.82*10  the i c e creates  by p e r c o l a t i n g  injected  between  by t h e f r e e z i n g  t o the bottom  when t h e b o t t o m  Velocity of  flux  a tank.  induced  from  extends  buoyancy  caused  of entrainment. to e x p l a i n the environment.  TABLE  OF  Abstract Table  CONTENTS  i i  of c o n t e n t s  i i i  List  o f f i gure s  v i  List  of p h o t o s  x  List  of t a b l e s  x i  Acknowledgements  1  -  xii  INTRODUCTION  1.1 A r c t i c  1  subsurface  1.2 L a b o r a t o r y  2  -  EXPERIMENTAL  1  METHODS  5  arrangement  5  visualization  Thermistors  determination  and m i c r o - c e l l s of c e l l  Time r e s p o n s e  2.3.4 S p a t i a l  7  f o r density  2.3.2 C a l i b r a t i o n 2.3.3  flow  3  2.3 I n s t r u m e n t a t i o n 2.3.1  and s l o p e  study  2.1 Tank and t r a y 2.2 Flow  intrusions  9 9  constants  12  characteristics  13  resolution  15  2.4 D a t a a c q u i s i t i o n  17  2.5 E x p e r i m e n t a l  19  procedure  2.6 D e t e r m i n a t i o n 2.6.1  Salt-  2.6.2 S a l t 2.6.3  2.6.5  and volume flux  Membrane  2.6.4 S a l t  o f membrane  flux  Arctic  salt  flux  fluxes  calibration salt  flux  determination  and e n t r a i n m e n t  salt  flux  and c o n v e c t i o n d e p t h  i i i  21 21 22 24 28 37  3 -  E X P E R I M E N T A L R E S U L T S AND I N T E R P R E T A T I O N 3.1  Slope  angles,  3.2 S h a d o w g r a p h 3.3  Injected  3.6  4 -  and s a l t  flux  observations  44  and s a l i n i t y  fluxes  40 41  dye  3.4 S a l i n i t i e s 3.5 S a l t  starting salinities  40  and flow  profiles  50  velocities  57  Interpretation  62  SUMMARY AND C O N C L U S I O N S  67  BIBLIOGRAPHY  70  Appendix  A - S A L I N I T Y AND D E N S I T Y C A L C U L A T I O N  73  A.l  74  Sa U n i t y  A. 2 D e n s i t y  Appendix  76  B - CONDUCTIVITY B. l C e l l B.2  MICRO-CELLS  construction  Micro-cell  Determinattion  B.5 M i c r o - c e l l B. 6 S p a t i a l  Appendix  80  electronics  B.3 AM/CT D a t a l o g g e r B.4  79  time  81  conductivity  electronics  of c a l i b r a t i o n constants response  resolution  Thermistor  of the m i c r o - c e l l s  use  106 107  Re-calibration  C.4 D a t a l o g g e r  102  105  C. 2 L e a k s C.3  83 91  C - THERMISTORS C l  82  range  108  calibration correction  109  iv  f o r extended  Appendix  D - DATALOGGERS D.l  Applied  114  Microsystems  D. 2 H P - D a t a A c q u i s i t i o n  Appendix  Appendix  E - MEMBRANE F L U X  datalogger  115  System  118  CALIBRATION  E. l S a l t  and volume f l u x  and d r i v i n g  E. 2 F l u x  c a l i b r a t i o n experiments  119 pressure  120 121  F - D E S C R I P T I O N OF E X P E R I M E N T S  127  F. l S l o p e  flow  experiment  #1  129  F.2 S l o p e  flow  experiment  #2  137  F.3 S l o p e  flow  experiment  #3  144  F.4 S l o p e  flow  experiment  #4  149  F.5  Slope  flow  experiment  #5  154  F.6  Slope  flow  experiment  #6  159  F.7 S l o p e  flow  experiment  #7  164  F.8 S l o p e  flow  experiment  #8  170  v  LIST  Fig.1-1  Typical  Arctic profiles  Fig.2-1  Apparatus  for  2  flow experiments  2-3  Micro-cell  with  2-4  Micro-cells  in experiments  2-5  Volume r e q u i r e d  2-6  Micro-cell  2-8  Data a c q u i s i t i o n  2-9  Data a c q u i s i t i o n :  AM/CT d a t a l o g g e r  18  2-10  Data a c q u i s i t i o n :  HP-3497A d a t a  19  2-11  Flux  2-12  Salinity profile  in t a n k / t r a y  2-13  Salinity profile  i n the  2-15  Membrane  2-16  Diagram  2-17  Entrainment  2-18  Time s e r i e s p l o t of i n t e r f a c e and mixed l a y e r s a l i n i t y  thermistors  to  7 10 11 14  spatial resolution  16  of  - manual  force  volume  flux  interface at  initial  2-20  Entrainment  2- 21  P r o f i l e s and  vs.  input  17  system  ...  23 edge  25  tray  vs.  26  pressure  entrainment  interface  depth  of  mixed  27 definitions  2-layer  system  by  layer  penetrative  ice  thickness  Sketch  of  typical  3- 2  Sketch  of  downhi11/ups1 ope  3-3  Mixed  v i  and  31  34 salinity, 35  convection  36  - field  39  data  shadowgraph p a t t e r n  time-series  29  depth  stratification  Fig.3-1  layer  shadowgraphs  flush cell  - driving  Interface  for  7  Diagram  and  arrangement  FIGURES  2-2  2-19  of  slope  in winter  OF  flow c e l l s linear  fit  42 43 52  3-4  A c t u a l and  adjusted s a l i n i t y  3-5  Micro-cell  time-series - slope  3-6  S a l i n i t y rate and  bottm  3-7  Slope  3-8  Flow  3-9  Slope  Fig.A-1  o f change  profiles  53  f l o w exp#3  i n mixed  54  layer  flow  flow  56  velocity  velocity  vs. s a l t  flux  60  vs. slope angle  61  flow diagram  Conductivity ratio  62  vs. s a l i n i t y  A-2  Density  vs. s a l i n i t y  Fig.B-1  Diagram  of  78  micro-cell  assembly  Micro-cell  B-3  T i m e - s e r i e s of  B-4  Cell  B-5  Time r e s p o n s e  B-6  Micro-cell  time  response  - C#l  time-series  96  B-7  Micro-cell  time  response  - C#2  time-series  97  B-8  Micro-cell  time  response  - C#3  time-series  98  B-9  Micro-cell  response  curve  - C#l  99  B-10  Micro-cell  response  curve  - C#2  100  B-ll  Micro-cell  response  curve  - C#3  101  B-12  R e s o l u t i o n i n 2 - l a y e r system  - 5 PSS  103  B-13  R e s o l u t i o n in 2 - l a y e r system  - 0.5  104  C-2  vs.  81  B-2  Fig.C-1  constants  77  temperature  micro-cell  c a l i b r a t i o n constants  c a l i b r a t i o n constants  Thermistors Thermistor  vs. s a l i n i t y  - experimental  at m i c r o - c e l l  arrangement  inlet  c a l i b r a t i o n curve  vii  85  and  PSS outlet  ...  89 90 91  107 113  Flg.E-1 E-2 E-3 Fig.F-1  Membrane  flux  calibration  Membrane volume f l u x c a l i b r a t i o n b e f o r e and a f t e r f i r s t s l o p e f l o w Membrane  volume  Micro-cell  flux  calibration  time-series plot  F-2  Salinity  F-3  Time-series  F-4  Adjusted  profiles  F-5  Salinity  distribution  F-6  Time-series  Flg.F-7  - time-series  profiles  Micro-cell  plot  plot  - slope  of p r o f i l e - slope  F-8  Time-series  F-9  Salinity  F-10  Time-series  F-ll  Salinity  plot  profiles plot  profiles  Fig.F-12 M i c r o - c e l l  and l i n e a r - slope  and l i n e a r - slope  and l i n e a r  ..... 131 132 133  exp#l  134  data  - experiment  135 136  #2  fit  139 140  exp#2  141  fit  142  f l o w exp #2  time-series plot plot  #1  the c e n t e r l l n e  flow  .... 125 126  exp #1  of d i s t r i b u t i o n  time-series plot  curves  points  flow  along  experiment  - experiment  flow  124  - experiment  #3  146  F-13  Time-series  F-14  Salinity  profiles  - slope  flow  Fig.F-15  Salinity  profiles  - slope  f l o w exp#4  151  F-16  Salinity  profiles  - slope  flow  152  F-17  Salinity  distribution  along  viii  fit  143  147  exp #3  exp#4  bottom  slope  148  153  Fig.F-18 Micro-cell  time-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  - slope  flow exp#5  158  profiles  Fig.F-21  Micro-cell  time-series plot  - experiment  #6  163  Fig.F-22  Micro-cell  time-series plot  - experiment  #7  166  F-23 S a l i n i t y  profiles  - slope  flow exp#7  167  F-24 S a l i n i t y  profiles  - 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 m i c r o - c e l l s  F-27 M i c r o - c e l l  - experiment  time-series plot  - experiment  F-28 Expanded t i m e - s e r i e s and curve  fit  #8 #8  170 172 173  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  profiles  - slope  flow exp#8  175  F-31  profiles  - slope  flow exp#8  176  Salinity  ix  LIST  Photo  1.  Experimental  tank  and t r a y  Photo  2.  Shadowgraph  image  of slope  Photo  3.  Interface  Photo  4.  Dye  Photo  5.  Velocity  Photo  6.  Dye a t s h a l l o w  Photo  7.  Bifurcation  Photo  8.  Waves  Photo  9.  Dye  Photo  10.  OF  PHOTOS  5 flow  8  entrainment  i n the mixed maxima  layer  flow  flow  45  47 48  end of slope  stratified  Dye a n d s h a d o w g r a p h  ...  46  end of tank  i n dye a t lower  x  and slope  i n dye  i n slope  in stably  28  region  49 49 162  LIST  Table  TABLES  2.0  Micro-cell  2.1  Entrainment  in 2-layer  2.2  Entrainment  In l i n e a r  2.3  Entrainment  from  3.1  Starting  conditions  3.2  Compiled  results  Table  Bl.  Micro-cell  calibration  constants  87  Table  Cl.  Thermistor calibration  constants  109  Table  Dl.  Clock board  edge  Table  D2.  Multiplexer  input  Table  FI.  Salt  fluxes  and  flow  velocities  F2.  Flow  velocities  from  photos  F3.  Salinity  F4.  Saltfluxes  F5.  Flow  velocities  from  photos  F6.  Salt  fluxes  flow  velocities  F7.  Salinities  F8.  Salt  F9.  Salinities  F10.  Flow  Fll.  Slope  F12.  Salinities  F13.  Flow  velocities  F14.  Flow  velocity  Table  calibration  OF  of  fluxes  flow  field  data  f o r slope  flow  slope  flow  . ..  fluid  experiments  ..  41  ....  58  tray  flow  and  ln tray  and  and  and  x i  - s l o p e r u n # l ...  - sloperun#2  - sloperun#3  - sloperun#4  138 ....  - sloperun#5  ...  ...  flux  - sloperun#6  - sloperun#7  150 154  ...  156 160  - sloperun#6  fluxes  145 149  - sloperun#6 tank  139 145  sloperun#5  fluxes  130 137  - sloperun#3  during  salt  salt  117  - sloperun#4  salt  velocities  pattern  - sloperun#2  velocities  tray  117  - sloperun#2  velocities  33 38  experiments  channel cycling  i n the  velocities  32  connector pin functions  i n the and  system stratification  from  flow  and  13  Arctic  tray and  constant K  161 ...  162 165  ACKNOWLEDGEMENTS  The of  author  Ocean  provided for  i sgrateful  Sciences  i n Sidney,  the required  the experimental  provided  development also  goes  Ocean  equipment, advice  R.B.  This contracts  Sudar provided  to the technical  work  problem  staff  a n d much o f t h e f u n d i n g  n r . FP941-4-1919  guidance  system.  of the Frozen o f Ocean  funded  advice  system  i n the  Special Seas  Sciences  thanks  group in  of  Sidney,  operational.  under Government  and FP941-5-1290.  xi i  o f U.B.C. who  and the academic  invaluable  to get the experimental  was p a r t i a l l y  and  the project.  measurement  a t the Institute  B.C. who h e l p e d  funding  complete  of the s a l i n i t y  Physics  this  w o r k , a n d t o D r P.H. L e B l o n d  to successfully late  D. R. T o p h a m o f t h e I n s t i t u t e  who s u g g e s t e d  encouragement, f u r t h e r  required The  t o Dr.  of  Canada  1 -  1.1  Arctic  subsurface  Typical salinity figure of  up  the  oceanographic p r o f i l e s  and  1-1)  temperature  meters. T h i s  and  of  forms as  this  contains  generally the  sea the  to  form  intrusions  water  there  the  in thickness,  feature  'a' as  location where  it  faster and  was  cause  or  of  Ocean Melling  the  depths Lewis  up  Sea  (see  near  to  the  large rise  depths  freezing  caused the  layer  increase  in  with  water  In many of  salinity  l a y e r were  of  the  found  of  ice below  in temperature.  mixing  by  Below  Atlantic profiles, up  to  30  temperature  minima  (see  T h i s c o l d e r w a t e r most  likely  was  mixed the  surface  surface  moved to  profiling  200  Beaufort  overturning  flow.  layer  had  meters  (1982)).  1  in  a higher  the  depth  station  salt of  Perkin  flux.  or The  i n t r u s i o n where  flows out  other  salinity  possibly  Such s l o p e  (see  some  a higher  intrusions penetrating to  the  subsurface  Deep W a t e r .  1-1).  of  i n t e r f a c e from  c h a r a c t e r i z e d by  s h e l f drainage  and  a small  sub-surface  water  c o l d water  at  where a  winter  layer extending  The  f r e e z i n g rate caused  at  i n the  ice/water  i s gradual  water at  saltier  found  current  by  flow  is isothermal,  freezes.  a convectively where  a  colder  in figure  surface  the  Arctic  into this  ice  to c o n v e c t i v e  pycnocline  meters  formed  at  i s accompanied  thermocllne  origin  salt  slope  taken d u r i n g  the  layer  i s o h a l i n e due  expulsion  that  under  show a w e l l - m i x e d  t o 50  point,  i n t r u s i o n s and  INTRODUCTION  as could  into and  a  the  Lewis  slope be  the  Arctic (1979),  TEMP.°C. 0  -2  1  2 0 -\ 40 -Q TJ  60  UJ fv ID  8 0  to  100  32.7  u cr CL 1 2 0 14 0 -  temperatures  T  S 29-11-79  STATION: 0 9 160  30  31  —r~  32  34  33  35  SALINITY Figure  As tely as the  s e a water  o f the s a l t  forms.  brine  from a s y s t e m  of d e n d r i t i c  i c e . The  water  influx  of s a l t  interface  column  more  channels that  causes a d e n s i t y  (1972) l o o k e d a t h a l i n e  rejected  salt  was  f o r i c e growth  rates  2  seen  from  the  o v e r t u r n i n g of by  Foster  a  7.8  under  pattern  r a n g i n g from  0.3 t o  in  at  convection  t o form  velocities  drains  develops  increase  in convective  immedia-  salt  the i c e . L a b o r a t o r y s t u d i e s  o r s t r e a m e r s w i t h downward  0.23 cm/s  is expelled  Subsequently,  and r e s u l t s  below  and by E l l i o t t  i c e . The  plumes to  some  the i c e w h i c h  (1969) sea  freezes,  from  ice/seawater the  1-1. T y p i c a l A r c t i c p r o f i l e s i n w i n t e r ( F r o z e n Seas R e s e a r c h Group, IOS)  of 0.09  cm/day.  A  field  study  described parts vely  o f the B e a u f o r t  bottom.  An  layer  uneven  normal  1.2  into salt  gradients current  along  at higher  series  auspices  layer  flux  the d e p t h  into  which  will  create  salt  horizontal  at levels  downslope  below  currents  simple  magnitude observed  British  over  Columbia,  was c o n d u c t e d  under  visualize determine  tank  water through  fluid  velocities  flux  Shadowgraph  into  3  induced  by a  which  s e t a t some by s l o w  t h e t a n k , and  to o b t a i n e s t i m a t e s  of  images and dye were used  flow.  the  and m a i n t a i n e d the  i n t h e c o n v e c t i v e l y mixed  i n the s l o p e  control-  was s i m u l a t e d  f l u x e s which g e n e r a t e d  motions  flows  the bottom  a membrane  f o r m u l a t i o n was d e v e l o p e d  flows.  under  Ocean  o f the e x p e r i m e n t s , with  The s u r f a c e s a l t  of the s a l t  slope  of  the  bottom.  i n each  in a plexiglass  t o examine  scale,  a sloping  were o b s e r v e d  of s a l t  slope  will  study  slope angle.  percolation  t h a t of  levels.  flux  were c o n d u c t e d  the  i t i s mixed.  a  compensating  of l a b o r a t o r y experiments  flows  to  t h e amount o f  i n t u r n can cause  and i n t r u s i o n s  s u c h as  may e x t e n d with  slope  is  the c o n v e c t i -  vary  surface effects;  i n Sidney,  Slope  small  seas,  will  o r a bottom  c o n d i t i o n s and on a s m a l l  surface  a  in this  growth  o f the Ocean P h y s i c s Group a t t h e I n s t i t u t e  Sciences led  In s h a l l o w  i s d r i v e n by f r e e z i n g  i t and w i t h  from  during  Sea i n the Canadian A r c t i c ,  the b o t t o m  mixing  by s e a i c e  (1970).  i n the d e n s i t y w h i c h  Laboratory A  rejection  which  The d e n s i t y  flowing  occur  salt  by Lake and L e w i s  mixed  salt  of  A series  layer  to  and t o  of m i c r o - c e l l s  were  developed  withdrawn the  from  points  micro-cell  micro-bead compute  the  weaker  dye of  of  cm/s  profiles  indicate  salinity  rises  1.82e-5  to  following  density  i n the  mixed  cm  0.5  t o 0.92  depths ppt  (appendix  the  in with  flow  the to  that  mm  i n the  and  injected  with  bottom.  17  to  A).  slope flow  Movement o f  above  above  fluid  the c o n d u c t i v i t y  slope  of 7  of  fluid  determined  fluid  layer.  at about  of  salt  fluxes  sections  those  found  orders smaller.  can  be  used  the  same  current,  a  peak  Salinity  in which  the  convectively  slope flow  magnitude This  of  was  orders of data,  buoyancy  The  from i n the  computed  magnitude  but  larger  mixing depths  velocity  convection,  was  than  is also field  characteristics  c o n s i d e r e d as  factors  slope flow  larger  to A r c t i c  i s used  to the p o w e r t n ) .  field  The  (e+n)  ranged  scale  were  W*,  which  therefore  nearly  cases.  entrainment  series  (10  to c h a r a c t e r i z e  in both  notation  several  in Arctic  several  the  The  to denote  than  When  in these experiments  1 . 6 3 e - 6 g/cm'/s.  e s t i m a t e s were  their  the  i n the  flux  and  of  with  distribution  salt  ment.  combined  of  layer.  Estimates  this  temperatures  experimental tank,  slope flow  0.24  conductivity  i n s h a d o w g r a p h s show  opposite flow velocity  t a n k . The  were  and  motions  t o 0.66  mixed  i n the  salinity  shows a 0.09  and  the e l e c t r i c a l  i n the  thermistors,  Patterns a  to obtain  calculated  experiments  those  predicted  contrary  a by  were  show  that  over great distances  4  gravity  inserting  data  up  o r d e r s of  t o two  for a quiescent  to evidence  data which  turbulent  from such from  the  environ-  experiments  flows the  from  maintain  source.  2 - E X P E R I M E N T A L METHODS  2.1  Tank a n d t r a y  A  series  made of cm  laboratory experiments  12 mm t h i c k  long,  The  of  arrangement  plexiglass.  was p a r t l y  filled  at  Photo  1.  photo  one end t o c r e a t e  w i t h a m i x t u r e of  level  tank,  by  a s l o w s e e p a g e of h i g h e r s a l i n i t y w a t e r this  tray.  (a M l l l l p o r e between  from s e a  The t r a y b o t t o m c o n s i s t e d filter  two l a y e r s  perforations.  salt  The  membrane, of  0.8  fiberglass  tray  was  filled 5  2-1). and  water.  of  the  i c e was  fluid  of a p o r o u s  bottom membrane  size)  mounted  with  aligned  to  several  boards,  w i t h sea  in  simulated  t h r o u g h the  micrometer pore circuit  87.5  tray  surface  the  of  and the e x p u l s i o n o f  were  1 and f i g u r e  f r e s h and s e a  w i t h the  tank  a s l o p i n g bottom  E x p e r i m e n t a l t a n k and  t r a y was s u s p e n d e d  in a  inside dimensions  23cm wide and 25cm deep (see  t a n k was r a i s e d  A  The  was c o n d u c t e d  water  millimeters sides was  taped  added  fluid an  were  above  return  that  salinity  I n some  to increase  pump was u s e d with  shut.  percolates  equal  the height to which  of the experiments  the s a l t  through  flux.  t h e membrane  flow of the l i g h t e r  to s t i r  the f l u i d  reservoir  were  kept  The v o l u m e s  slots  i n the  pure  sea salt  When t h e h i g h into  fluid  the tank  salinity  this  to the tray.  i n the tray,  i n a back-up r e s e r v o i r  i n the tray.  levelling  causes A  and exchange  to help maintain the of f l u i d  c o n s t a n t d u r i n g each  small  i n tank,  i t  higher  tray  and  r u n and the system i s  self-levelling. A series were  o f 6 cm l o n g c o p p e r  mounted  10 cm  intervals  shallow  from  tank  and  d e n s i t y.  tray  exchange  tank  These  fluid  from  conductivity  with  the sampling  without  i n the bottom line,  access  tubes  that  and t r a y  or ports were  pump u s e d  pumps w h i c h  to maintain constant  6  used  from t h e #1 t o #8, to  inject  and depths  t o determine  and l e v e l l i n g  i n the reservoir.  the small  7.5 cm  of the arrangement  tubes  diameter  of the t r a y , a t  starting  micro-cells  and the c i r c u l a t i o n i twith  inside  various locations  2-1 s h o w s a d i a g r a m  reservoir,  shown  the centre  o f 1.6 mm  the s h a l l o w end of the tank,  through  Figure  to  along  or t o withdraw  the  the  t h e membrane  end of the tank.  numbered dye  through  tubes  in  salinity  of the  tank,  slots,  the added  t o mix t r a y  f l u i d and  The  return  micro-cells  t h e syphoned  levels.  are fluid  reservoir Figure  2.2  Flow  from  focused  tank  f o r slope  a source  2-2).  This  lenses  beam  a translucent  shadowgraph  into  a nearly  mylar  film  the tank  parallel  was p r o j e c t e d t h r o u g h  beam ( s e e  the side  on t h e o p p o s i t e  was  side  of  the  to  form  Images.  approximately  C  experiments.  placed at a distance behind  by c y l i n d r i c a l  onto  camera  flow  visualization  Light  figure  2-1. A p p a r a t u s  7  meters pro j e c t o r slot  tank c r o s s - s e c t i on  iiia  r  ID]  2-2. D i a g r a m  d cy1i ndr lenses  transp.film Figure  a  of arrangement 7  f o r shadowgraphs  During  the e x p e r i m e n t s ,  due c o n v e c t i v e the  image.  bottom slope  layer  were  photo  2).  or p a r c e l s therefore  The  image fluid,  in  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  deflections  represents  was  of some sank  f l o w was a l s o  d i l u t e d with  match the the of  i n the  the  integrated  flow line  motions of  over  slope  sampling  fluid  flow d e n s i t y . tubes along  of  injected of  of  (see  streamers  the  tank  and  patterns.  flow  i n an  the  i n the c o n v e c t i v e most  S  small  i n j e c t i n g dye,  mixed l a y e r  mixed  patterns  slope  the c e n t e r l i n e  mixed l a y e r ,  the  circulation  The dye was  the dye was e n t r a i n e d  t h r o u g h the  image  v i s u a l i z e d by  from t h e  in  the w i d t h of  c a n n o t show any c r o s s - s e c t i o n a l  slope  index  lines  P h o t o 2. S h a d o w g r a p h The  of w r i n k l e d  f l o w and the c o m p e n s a t i n g  v i s i b l e as  of  i n the r e f r a 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  shadowgraph  the  variations  which  attempt  to  t h r o u g h one tray.  While  m o t i o n s as  it  i t was c a r r i e d a l o n g  as  dye  streaks  slope the  i n the slope  angles  over  distance  photo  2.3  a range  that  and s l i d e  sequences  salinity to  determination  flow  velocities  f l u x e s were i n a known  o r on v i d e o  tape  flows  and  taken  manually  time  from  interval  in  determination  used  were  in combination  i n the c o n v e c t i v e l y or with  different  footage.  conductivity cells  and  at  determined  mixed  a datalogger  developed  with  a q u a n t i t a t i v e d e s c r i p t i o n of f l u i d  slope  top  moved  for density  small-volume  obtain  The  of s a l t  t h e dye  Instrumentation Several  flow.  thermistors  densities  layer.  The  and p r o c e s s e d  for  i n the  data  using  were  a  desk-  taken  from  computer.  2.3.1  Thermistors  To d e t e r m i n e different cells ml  (figure  in  the tank The  or tray  micro-cells  glass  tubing  Micro-bead  consisted  ( o f 1.8  mm  from  by  volume  syphoning  of four  were  platinum  3.0  mm  inserted  micro-cell.  9  0.15 point  foil  The  scale  electrode  by  segments of  outside  diameter).  average  r e s i s t a n c e s was  Salinity  of about  i n the flow  to c a l c u l a t e the s a l i n i t y  of the P r a c t i c a l  micro-  i t from a  long) separated  i n s i d e and  their  conductivity  of the m i c r o - c e l l s .  b y 5 mm  thermistors  ratio  one  tank,  internal  sampled  through  diameter  determined  conductivity  a small  was  and o u t l e t of each  ratures  mials  with  2-3). F l u i d  ( o f 3 mm  c o n d u c t i v i t y of f l u i d  i n the experimental  developed  rings  inlet  micro-cells  the e l e c t r i c a l  points  were  and  of the  at  tempe-  combined with using  the  (see appendix A l ) .  the  the  polyno-  The  density  computed another the  by c o m b i n i n g  Stable  of  equation  salinity  of State  of f l u i d  withdrawal  influence  from  of the c e l l s  were  point  i n the tank  the temperature  obtained with  l n the tank  are described  from  (appendix A2).  the m i c r o - c e l l s .  flow patterns.  was  using the polynomials of  f o r seawater  through  a point  the g e n e r a l  with  i n the tank  and r e p e a t a b l e r e a d i n g s  syphoning  details  this  thermistor located  Unesco  slow  of the f l u i d at the intake  did  not  Dimensions  i n appendix  continuous  The  low  rate  perceptibly and  assembly  B.  NEEDLE  Figure One along along  cell  was  a track the  2-3. M i c r o - c e l l mounted  over  on a v e r t i c a l  the tank  centerllne  with thermistors traveller  which  t o one o f t h e s a m p l i n g  i n the tray.  10  Data  points  was  tubes for  moved spaced  salinity  profiles of  the  for  of  fluid  intake  in the  tube  simultaneous  to s u c c e s s i v e depths. readings  mixed l a y e r  to determine  the  cell  third  salinity. of  at  (1  was used  to 3 d r o p s / s e c ) .  rent  cells  to the  fluid  levels  and volumes used  Figure  2-4.  ln background s a l i n i t y  to monitor the slow change  to r e t u r n  fluid  t r a y and to the  at  A small  tank  tray  pump  with  rate two  diffe-  to maintain the  fixed  the s a l t t—  1 1  in  of  to c a l c u l a t e  experiments  used  and  a fixed  from the o u t l e t s  2-4.  M i c r o - c e l l s in  was  tip  in the c o n v e c t i v e l y  was syphoned through the c e l l s  0 . 0 5 - 0 . 1 5 ml/s  shown ln f i g u r e  A second c e l l  a f i x e d depth  the change  was used  Fluid  pump-heads  tank were o b t a i n e d by lowering the  fluxes,  as  2.3.2 C a l i b r a t i o n of c e l l The  electrical  the  salinity  so  the o u t p u t  cell  of  the  of the f l u i d .  A  voltage  cell  product  (K) was  a t S = 35 PSS and T=15 computed from  (2.1)  1/R  (2.2)  RR  through  (VC) was a l i n e a r  constant  of conductance  values  An e l e c t r o n i c  (1/R) f o r f l u i d  cell  (RR) i s t h e n  The  c o n d u c t i v i t y i n the m i c r o - c e l l s  conductance  salinity.  constants  of a g i v e n expressed °C.  micro-  temperature  and  i n ohms r e s i s t a n c e  output  ratio  v o l t a g e as the  constant: A = -2.6008e-8  = K.(A + B.VC)  B = -4.5954e-4  o f A and B were o b t a i n e d voltages  with  designed  The c o n d u c t i v i t y  = A + B.VC  output  was  f u n c t i o n o f the  the m i c r o - c e l l  and c e l l  circuit  changes  for.a  by l e a s t  series  squares  of h i g h  linear f i t  accuracy  standard  res i s t o r s . In  a number  datalogger (see  was  section  voltages  and  The which  I t was  constant  RR  cell the  micro-cell  an A p p l i e d M i c r o s y s t e m s  micro-cell  found  that  and t h e r m i s t o r  the d i f f e r e n t  conductivity circuit  required different  the d a t a l o g g e r  (2.3)  to take  by the i n t e r n a l  f o r the c e l l  from  used  2.4)-.  used  micro-cells  of the e x p e r i m e n t s  values  c u r r e n t s and to d r i v e  the  A and B  the c o n d u c t i v i t y r a t i o  numbers ( N C ) :  = K'.(R'tB'.NC)  constants salinity  readings  f o r the c o n s t a n t s  K to c a l c u l a t e  C/T  were c h o s e n of a f l u i d  conductivity ratio  as t h o s e  sample,  A'=  5.53084e-5  B'=  1.3290e-7  integer values  calculated  and t e m p e r a t u r e , 12  from  was c l o s e s t  for the to  the  value  determined  with  was  frequently repeated  due  to a g i n g  calibration table  2.0  Table  below  Calibration  to ensure  or e l e c t r o d e constant  2.0  a Guildline  (see  appendix  Micro-cell  of  The  the  average  for  constant  occurred  values  of  the  listed  K  f o r the AM/CT d a t a l o g g e r : ( s t d . dev. f o r 18 s a m p l e s )  1885 (6.3)  1793 (4.2)  182 1 (6.7)  for separate c o n d . c i r c u i t : ( s t d . d e v . f o r 12 s a m p l e s )  1803 (5.6)  1752 (3.5)  1783 (6.7)  As  the of  cell  flush  to  to  f o r each 3 drops  steps for  the  against  The  before  the  i n the the  t o 5 PSS.  volume For  tubing  results  are  through  and  as a  syphon the  shown  at  the  To  the  flow  1#3  tubing The  i n t a k e p o i n t was  determi-  ml/s)  of  the  i s the  2-5.  the  response  rates ranging  was  and  an  time  and  from a b o u t 1 for  salinity  response by  total  curves  plotting salinity  product  of  flow  volume  to  flush  r a t e s , the  micro-cell  13  intake  were n o r m a l i z e d  which  in figure  micro-cell,  obtain typical  fraction  flow  to a  i s taken.  to 0.15  results  required,  these  at  ( o r 0.05  salinity  intake  a reading  cells,  second  0.5  the  in s a l i n i t y  m i c r o - c e l l s the  time.  intake  per  between  change  and  it,  of  changes at  must p a s s  a sudden change  ned to  fluid  Cel  characteristics  salinity  amount  in  details).  Cel1#2  Time r e s p o n s e  K for:  had  m i c r o - c e l l s are  B table B.l  calibration  shifts  calibration  Cel1#1  2.3.3  constant  t h a t no  fouling.  f o r each  Autosal. This  found  to be  about  4  the step rate the ml.  MICRO-CELL TIME RESPONSE  Fiqure 2~5. Volume required to flush the c e l l  2.3.4  Spatial  The  fluid  resolution  syphoned from the  intake point  c a n be c o n s i d e r e d as a p o i n t s i n k salinity  i s an a v e r a g e  measure o f t h e s p a t i a l sharp  interface  by p a r t l y  then s l o w l y p i p i n g s h a r p e n i n g the below  shadowgraph. a fixed  For 0.5 the  Fluid  by s y p h o n i n g f l u i d was  visible  of d e p t h  micro-cells, calibration  to the bottom from a p o i n t line  and just  in  a at  spaced  depths. between  from d a t a t a k e n a c r o s s  steps over a  few  milli-  2-6).  o f the d i m e n s i o n s and a s s e m b l y of the c e l l  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 and i n appendix  was  sea water,  with a step in s a l i n i t y  show a s e t o f d i s t i n c t (figure  interface  2 d r o p s p e r s e c o n d and r e a d i n g s were  profiles plotted  A detailed description  given  profile.  then syphoned t h r o u g h the m i c r o - c e l l  of about  5 ppt, s a l i n i t y  calculated  r e g i o n . Some  as a b r i g h t  30 s e c o n d s a t s u c c e s s i v e c l o s e l y  interface  meters  was  the  a container with diluted  such t w o - l a y e r systems  and  in a s a l i n i t y  water of a h i g h e r s a l i n i t y  interface  flow rate  taken a f t e r  filling  micro-cell  i s then the e x t e n t to which a  system w i t h a sharp d e n s i t y  interface  i t . The  i n a f l o w , and  d r a w n from a s m a l l  resolution  appears b l u r r e d  A two-layer f l u i d obtained  of f l u i d  to the  B.  15  c o n s t a n t s and the s p a t i a l  of the  electronics, resolution is  0  29.0  10  .  20  .  SALINITY J  1  (PSS) i  ,  i  29.5  30.0  —i  30 _ 40 _ |  50  5 60  J  CL LU Q  70  J  80 90 100  _  110  _  120  _  130  .  140  .  150  _  flow through c e l l : abt. 3 dr/aec  R e s o l u t i o n of  interface  in 2~layer  sjystem yst 1—  160 r i q u r e 2-6.  M i c r o - c e l l spa-tial r e s o l u t i o n  16  Data  2.4  In with tage  acquisition  the i n i t i a l a switch from read  were  entered  which  from  circuit  conductivity circuit  micro-cell  In t u r n .  v i a thekeyboard to apply  voltmeters into  values,  magnetic  tape  plot  The o u t p u t  (DVM's).  thecalibration  t h e raw data and  and store  t h e d a t a on  1  VC"  DVM  RT"  DVM  TAPP  HP-7225 PLOTTER  HP-9825 COMPUTER EXPERIMENTAL Figure  were to  2-8. D a t a  voltage separate The clock  acquisition  of theexperiments,  t h e HP-9825.  sensing  Microsystems internal  themicro-cells. current  used  micro-cell calibration  AM/CT d a t a l o g g e r interval  - manual  could  to cycle  input  the m i c r o - c e l l s and thermistors  The d a t a l o g g e r  f o r use w i t h and  LINE PRINTER  TANK  i n t e r f a c e d v i a an Applied  modified  f o r the  (see figure 2-8).  SWITCH  most  computer,  relations  print  s e l e c t e d parameters  MICRO-CELL ELECTRONICS  In  vol-  The n u m b e r s  a n HP-9825 d e s k t o p  and m i c r o - c e l l s t o thedata,  computed  was u s e d  and ther e s i s t a n c e s of the thermistors  a set of digital  was p r o g r a m e d  thermistors  a small  t o power each  this  were  tests,  by  (AM/CT)  conductance  17  circuit  The d i f f e r e n t this  constants  circuit  a l l sensors  required  or at  and then  was  driving  (see section  be t r i g g e r e d m a n u a l l y  through  datalogger  2.3.2). a set transmit  the  data  v i aa serial  converter  to  t h e HP-9825 c o m p u t e r  the  AM/CT d a t a l o g g e r  the  tray  used  fluid  with  a n d an RS-232  (seefigure  was l i m i t e d  was o u t o f r a n g e ,  interface  2 - 9 ) . The s a l i n i t y  a n d when  module range of  the conductivity  the separate  small  of  circuit  was  t h e DVM's.  AM/CT  SERIAL CONVERTER  HP-7225 PLOTTER  DATA LOGGER RS-232  1  TAPE T-TNK EXPERIMENTAL  the l a s t  System for  rapid  averages readings  were  variability  Some  small  s h i f t s were  and  later  testing  conductivity. provided the  slope  This  Data  found  revealed outlet  a separate  of each  that  t h e most d e t a i l e d  with  rapid  sequences  cause  18  Acquisition circuit  sampling  rate,  sensor  circuit  and a l s o  showed  continuously from  powered. experiments  lnrelative a change  t h i s arrangement  p r o f i l e s of density  flow.  Data  f o r each  any s h i f t  could  datalogger  conductivity  sensor),  were  i n data  tubes  obtained  a more  readings  the c e l l s  AM/CT  an HP-3497A  allowed  taken  because  the micro-cell  with  of multiple  less  of  acquisition:  experiments  combined  micro-cell.  automatic (5  2-9. D a t a  several  was u s e d ,  each  HP-9825 COMPUTER  TANK  Figure In  HP-LINE PRINTER  y  position  i n apparent  ( f i g u r e 2-10)  distribution  in  CIRCUIT  "A"  CIRCUIT  "B"  CIRCUIT  "C"  CONDUCTIVITY ELECTRONICS  HP-7225 PLOTTER  TAPE HP-9825 COMPUTER HP-3497A C#l  C#2  C#3  ZZfcJ  t :  T-TNK  EXPERIMENTAL  The of  Figure  2-10.  raw d a t a  from  magnetic  with  water  salinity  were  were  was  fluid  ratio,  printed  plotted were  mixed  the computed  salinity  intake  the p r i n t - o u t .  d u r i n g each later  and saved  during The  from  time  Profiles  these  data,  (In section  on  profiling  salinity  experiment.  plotted  values  and d e n s i t y f o r  on a l i n e - p r i n t e r  with  tap water  i n one  f o r the experimental tank,  water  in another  tray  and r e s e r v o i r  of  as i s  3).  tank  and  tank  t o c r e a t e low  salt  f o r the high s a l i n i t y  fluid  The  fluids  or to reservoir  and  tray-filling pail  tank  a  filter  t o remove  most 19  were  was  i n some r u n s .  experimental micron  on  and  System  procedure  sea  0.8  LINE PRINTER  HP-3497A  the experimental r e s u l t s  Experimental Sea  sensor c i r c u i t  i n the tank  described  2.5  each  s e t and noted  points  salinity  acquisition:  tape. Depths of the m i c r o - c e l l  manually  series  Data  conductivity  of the c e l l s  were  J  TANK  temperatures,  each  DATA ACQUISITION SYSTEM  organic matter  added to used  pumped  in  to the through  and were  left  for  at least  one d a y t o s t a b i l i z e  and  t o de-gas which  riment.  For the i n i t i a l  into  bubbles  until  the beginning high edge  between  pressure  that  This  level  with  fluid  and t r a y  the  establish was  itself  maintained  but  in  later. were  one c a s e  after  by t h e s a l t usually  the slope  i n photo  bottom  a period  f l o w was s t i l l  sequences  the f l o w p a t t e r n s and t o determine  experimental  initial  results  flux  due  In e x c e s s  which  image  as  plumes.  extended  to to  experiment  each  of  fluids.  f l o w was s e e n  and  experiment.  of 3 to 5 about  hours,  15  hours  of injected  o r on v i d e o flow  are described in section  20  the  of small  seen  slope  filled  at  t h e two  images a n d t h e movement and s l i d e  was  levels  of each  throughout  over  drained  was a d d e d i n  levels  layer  the s t a r t  taken  fluid  curtain  then  tray.  the tray  between  a mixed  flux  was  i n the shadowgraph  A down-slope  shortly  The s h a d o w g r a p h  recorded  study  were  of the  was  lowered  and the tank  in fluid  expe-  the a i r  The t r a y  a rapid  in density  was  remove  the f l u i d  to prevent  evenly descending  of the tank.  Observations  to  t o keep  o v e r t u r n i n g produced  bottom  tapped  depth  o f c o n v e c t i o n was s e e n  and n e a r l y  Convective  The t r a y  low s a l i n i t y  by a d i f f e r e n c e  sensor  the tank  fluid.  the bottom  while  was d o n e  caused  start  slowly  The  and g e n t l y  due t o t h e d i f f e r e n c e  The a  low s a l i n i t y  to the desired  tank  on t h e  w e t t i n g o f t h e membrane,  of an e x p e r i m e n t a l r u n ,  salinity  same h e i g h t . to  was  temperature,  r e a d i n g s d u r i n g the  i n the p e r f o r a t e d boards.  horizontally  the f l u i d  with the  adversely affect  the tank  trapped  lowered  At  would  to the top with  sideways  room  to a v o i d the formation of bubbles  surfaces  filled  a t ambient  3.  tape  dye to  velocities.  2.6  D e t e r m i n a t i o n o f membrane s a l t  The  salt  the  height  the  fluid  i n tank  and that  Initial  and  volume  estimates  salinity  of f l u i d  the  of change  tray (2.4)  Bn=  difference  flux  of the net s a l t of f l u i d  flux  i n the t o t a l  amount  volume  per unit  taken  tank.  Into  the tank  by  that  The n e t s a l t  tray,  taken  per unit  flow  forms  a thin  partly  mixed  reservoir  into  fluid.  from  flux  flow  surface layer  of s a l t  (gr/cm /s) 2  fluid  volume  A  = membrane a r e a  volume  l n the tray  (cm ) 3  and 1 f o r those  i n the tray  salt  ln  The  which  exchanges only  reduced  slots  2-11).  In  flows  bottom,  the l e v e l l i n g  therefore  3  2  at which  (see figure  (cm )  (cm )  a t the top of the tray  21  or ppt) 3  = reservoir  2.4 w i l l  combined  (gr/cm )  Vr  area  is  area:  (gr/kg  through  known  flux  i n the  of tray  = salinity  Is the rate  the  The n e t s a l t  i t b y t h e pump w h i c h  Equation  and  S2  t h e membrane  In the r e t u r n  obtained  flux  f o rproperties  through  the  Bn = n e t s a l t  V2 = t r a y  the  determines  were  i n the tray  and r e s e r v o i r .  d(S2*D2)*(V2+Vr) dt 1000 A  2 Is used  charac-  layer.  D2 = d e n s i t y  Suffix  of  between  a n d t h e membrane  buoyancy  mixed  Is a function  fluxes  in tray  and r e s e r v o i r  the density  of t h i s  time-series  volumes  membrane  i n the tray  i n the convectively  Salt-  rate  the porous  i n the tray,  The m a g n i t u d e  turbulence  the  through  of f l u i d  teristics.  2.6.1  flux  flux  the  return  is  only  tray  and  yield a  rough  initial in  estimate  tray  and  The  amount  must  the  equal  volume (2.5)  the  amount  (2.6)  B  The  be  from  expressed  flux  calibrate  convective the fluid  taken  per  end  by  the  membrane  tank  through  the  tank  to the  of  volume  this  flux  membrane  tray,  and  salt  the  flux:  (cm /cm /s) 3  of  fluid  from  flux  the  net  product  of  salt  the  mixing  fluid.  2  volume the  flux  and  tray:  (gr/cm /s) 2  membrane  salt  flux.  was  done  In these  and  volume  fluxes,  i n which  the  bottom  of  experiments  motions,  with  walls  of  the  a nearly end  the of  The  the  average  the  effects  tank.  a p o i n t near  Estimates  Bn=_d dt  the  the  reservoir  salt  indicated  of change  incomplete  and  F=  B=  the  tray  volume  images  from  to  i n terms  i s then  unit  due  calibration  to represent  volume.  B  is driven  horizontal.  (2.7)  flow  flux  salt  experiments  rate  of  entering  = F*(D2*S2) 1000  shadowgraph  of  return  convection  To  near  flux  exchange  fluid  salt  of  Salt  kept  net  Bn=F*(D2*S2-Dl*Sl) 1000  membrane  of  of  F can  The  2.6.2  the  slow  the  flux  of  net  (S1*D1)*V1 1000 A  22  flux  density  tank  p a t t e r n s of  of d i m i n i s h e d  rate  change  the  series  of change  was  lines  uniform d i s t r i b u t i o n  c e n t e r of  salt  i n s a l i n i t y and  the  a  in of  activity  in s a l i n i t y  the  tank  was  then  f o r the  whole  tank  fluid  were  obtained  i n the  tank:  from  the  With flux  the  through  density and  fluid  In  the  the  (2.8)  P  edge  =  and  membrane  difference  in  tank  of  between  tank  by  same  level,  pressure  of  equal  height  and  tray:  with:  LEVELLING  the  the  columns  (D2-Dl)*g*h  Ay  at  is driven  fluid  space  tray  P  = pressure  D  = density  h  =  g  = gravity  tray  the due  in  salt  to  the  the  tray  (gr/cm/s2) (gr/cm3)  fluid =  height 981  (cm)  (cm/s2)  SLOT  me m b r a n e  TANK  Figure  2-11.  Salinity tray the  Flux  - driving  2-12)  Increasing  In  the  the  a  driving  pressure,  stable the layer  did  light  show a of  layer a  at  of  the  the  the  2-13) top  in was  simple  columns  s a l ln 1 ty.  23  by  space  between  stratification  rising  slots  correction  fluid  edge  stable  fluid  (figure  s t r a t i f i c a t i o n s with  height  in  levelling  tray  formed  force  fluid  salinity  through  salinity  Dl  p r o f i l e s of  (figure  return  Si,  to  from  the  show the  tray,  and  this  tray.  To  2-layer 2-3  and  caused  by  mixed  that  made by  the  the  tank  layer  profiles return calculate  approximating systems mm  of  to  and  of  flow the these  reducing  common  upper  The  driving  calculated the A  tank,  from  obtained  (figure  2.6.3  of  before  estimate velocity  fluid  least  fitted  and a f t e r  flux  through  i n the tray  sets  the f i r s t  fluxes  were  and  in  approximations.  o f membrane  slope  flow  flux  experiment  determination  t h e membrane  was m e a s u r e d  by l i n e a r from  curve  the tank,  using  tion  graph  flux  was c a l c u l a t e d  Several develop  series  the data  and t r a y  numeric clogging readings  from  was a l w a y s  o f t h e membrane of f l u i d  depths  were  estimated  from  flux  24  were  available.  the  The  corresponding  and the  temperature  (appendix  from  experiments  A).  the c a l i b r a -  or  were  salt  done  The r a t e o f c h a n g e  very  similar,  varied,  but  tray.  to  i n the  individual  i n p a r t d u e t o some  i n successive experiments i n tank  points  2.6.  methods.  f o r t h e volume  points  2 - 1 5 ) a n d t h e membrane  calibration  acquisition  salinities were  data  of State  slope  time  data  were  was o b t a i n e d  (figure  the  were  from  Equation  equation  of flux  data  salinities  flux  flow  densities  results  those  volume  o f membrane  layer  that a  at that  a few t r a y  calculated  the Unesco  corresponding  Salinities  mixed  from  layer  when n e a r b y  f i t when o n l y  was t h e n  computed  a t the time  d u r i n g an e x p e r i m e n t ,  interpolation,  pressure  densities,  flux  and i n the mixed  o r w h e n no n e a r b y  driving  salt  the t i m e - s e r i e s .  squares  taken,  tank  for fluid  2.6 t o 2.8 a n d t h e s e  was  i n the tray  available  The  data  volume  2-15).  obtained  in  series  curve  Membrane s a l t  To flow  time  and c o r r e s p o n d i n g  using equations  calibration  data  a  pressures  or to  poor  25  22.0 0  4  Salinity J  L  A,  (PSS) J  it  5  2  I  I  I  L  E E  Profile 10  J  at  the  i n t h e "tray centre  Q(U  a 20  J  30  J  40  J  50  J  60  bottom o f  i  1  1  1  tray  1  1  1  r  Figure 2-13. S a l i n i t y p r o f i l e in the tray. 26  27. 0  Figure 2- 15.  MEMBRANE VOLUME-FLUX vs PRESSURE c a l i b r a t i o n data f o r sloperuns  2.6.4  Salt  flux  Several slope, slope by  and  separate  salt  salt  flux  into  entrainment. bright  The  line  fluxes  In t h e  either  c r e a t e d an  in density  due  3).  line  slowly  2 - l a y e r system,  the  across  This  the  elements  interface  the  became  of  salt  was  flux  visible  line the  3.  those  or  faded  s m a l l and  Interface 28  bottom In  the  caused  a  linear  which  slowly  In d e p t h  due  to  shadowgraph  p a t t e r n s i n the  upper  as  layer  q u i e s c e n t r e g i o n below  moved d o w n w a r d due line  into  layer  i n the  clear  used  entrainment  and  as  the  the  to  entrainment.  step  individual  penetrated through i t .  Photo  without a  shear.  well-mixed  to the  s e p a r a t i n g the  to  interface  absence  upper  interface  similar  2 - l a y e r system  a  c o n v e c t i v e t u r b u l e n c e from  (photo  were c o n d u c t e d  t o measure  convective turbulence  increased  In  of  flow experiments,  stratification  of  experiments  over a range  The  a  entrainment  entrainment  in  density  convective  The e n t r a i n m e n t mixed  The  layer  with  following  densities  used  velocity  is  measured  as the deepening  time:  diagram  Ve defines  to formulate  = dY/dt  the dimensions,  interface  of the (2.9)  velocities  and  entrainment:  Dw  I  D DL Tank  and  tray  2-layer  Y  == m i x e d  layer  H  == d e p t h  of f l u i d  L  == b o t t o m  AW ==  tray  Ae == t a n k  Figure  The as  a  depth  membrane  Vw == m e m b r a n e  l n tank stratlf.  Dw == t r a y  area  Interface  D  area  2-16. D i a g r a m  of Interface  volume  fluid  =- m i x e d  velocity  layer  flux  density density  De == d e n s i t y  at  DL == d e n s i t y  a t depth  entrainment  Interface  c a n be  vertical  the mixed  velocity  Y and buoyancy  scale  W*  f l u x Q using  = (Y.Q) ^ 1  1 gr/cm^  = gravity  simple  from  dimensional  = [Y.Vw.g.(Dw-D)\^ L  Dref=  derived  acceleration 29  Dref'  L  definitions  i n t e n s i t y of the convective overturning  W*  g  stratification  Ve == e n t r a i n m e n t  depth  of l i n e a r  linear  system  expressed layer  analysis: (2.10)  The  ratio  of  interface  by  Bo  the  versus a  expressed Ri  number  inertial  describes  convection been  the  by  either  as  that  ratio  rate  these at  of  flux  equals In The  the the  mass  the  sum  is nearly  1/Ri  =  salt  values  Vw  depth  f o r the  Richardson  Froude  Fr  number  flux  adds  Bo  Pedersen  written  as  predicts  a bulk  flux  layer  lower  (2.12)  mass r e q u i r e s  mass t o  In mixed the  (2.11)  2  the  volume  and  lower  layer  that  i n the  the tank  layer:  density  mass  Ae.tY.D  +  Is c o n s t a n t .  (H-Y).Del  i s d e s c r i b e d f o r the +  velocity (figure  scale  was  obtained  2-17).  velocity  and  30  Table  (2.13)  2 - l a y e r system  by:  De.(H-Y)]  dtL = Ae . f V e . ( D - D e ) + Y.dD1 Aw.(Dw-D) L dt  entrainment  interface  has  constant:  (Vw.Aw)(Dw-D) = A e . _ d f Y . D  of  overall  and  tank i s :  c o n s e r v a t i o n of  The  the  penetrative  W* g.Y.(D-De)/Dref  c o n s e r v a t i o n of  2-layer system,  or  at  = V e . ( D e - D ) * 0.20 (Dw-D).Vw  T  of changes  i n the  =  2  M '= and  of  internal  to entrainment,  experiments,  which  an  force  stratification  h y p o t h e s i s d e r i v e d by  Rf  In  Importance  density  (1978) or as  number RfT,  Richardson  buoyancy  ( 1980) :  entrainment the  the  a non-d1 m e n s l o n a l  Fr  The  to  relative  stabilizing  Kantha  Pedersen  force  from 2,1  J  (2.14) J  video observations lists  n o n - d 1 mens 1 o n a l  the  computed  parameters.  F i g u r e 2-17.  Entrainment at of 2-layer  31  interface  system.  The  analysis  The  ratio  density layer  was d o n e  of tray  using the data  to tank  o f t h e 5-23-86  a r e a was A w / A e = 0 . 8 2 4 ,  De=l.00926 (g/cm ) and t h e r a t e 3  density  Table  was n e a r l y  i n 2-layer  Entrainment Vw.e-4 (cm/s)  W* (cm/s)  Rf T  min)  Ve .e-4 < cm/s)  42  1.3308  1 .0528  0. 157  0. 2 2 2  54  1 . 9600  1.0618  0. 196  66  2.5892  1.1035  75  3.0611  90  3. 8 4 7 6  t  In the  the case  mass  under  the lower  o f change  c o n s t a n t dD/dt=6.076e-4  2.1  experiment.  i n the mixed  g/cm /s. 3  system Fr .e-3  Ri  6.01  3.834  261  0. 2 2 3  8.80  4. 4 9 5  223  0.217  0. 227  1 1 . 42  5. 2 6 5  190  1.1631  0.214  0. 2 3 2  13.19  6 . 170  162  1.3334  0.169  0. 246  15.65  9. 2 7 5  108  of a s t r a t i f i c a t i o n the tray  to that  Ve/W* .e-4  which  2  Is l i n e a r  to a depth  c o n s e r v a t i o n o f mass  f o r the l i n e a r l y  (Vw.AwXDw-D)  stratified  time-series  plots  layer  depths  a t the c o r r e s p o n d i n g mixed  graph,  shows t h a t  depth  2-18) were c o m b i n e d  of the i n i t i a l  layer  stratification,  the step  case i s :  J  f o r interface  mixed  A profile  (figure  (2.15)  = A e . d [ Y . D+ (De +DL) . ( H - Y ) 1 dt 2 L  The  L  depth i s :  M = Ae.^Y.D + ( L - Y ) . ( D L + D e ) j and  layer  in salinity  and s a l i n i t y  t o show salinity plotted  s o _d.(De)= d(D) dt dt 32  Interface  (figure in this  2-19). same  across the interface i s  constant, or: De-D= c o n s t  the  i n the  or  A  linear  Vw =  Ae .[Ve.(2D-De-DL) + ( Y + L ) . d D l Aw(Dw-D) L 2 2 d t i  least-squares f i t to the interface  footage,  f o r points  In the n e a r l y  linear  depths  (2.16)  from  video  part of the p r o f i l e ,  ylelded: Y = 5.30 + ( t - 2 4 ) * 6 0 * l . 1 2 8 e - 3 and  thus a constant entrainment  ( Y i n cm, t i n m i n )  velocity: Ve =  Values were  forflux,  computed  from  scale  velocity  u s i n g t h e above  the linear  and non-dimensional  derivations.  stratification  1.128e-3  parameters  The r e s u l t s  experiment  (cm/s)  are listed  f o r data in  table  2.2 be 1ow. Table  2.2  t (min)  Vw.e-4 (cm/s)  W*.e-2 (cm/s)  Rf  30  1 .686  2.58  40  1 .960  50 60 The with  0. 107  6.01  4 . 365  2. 46  2 . 80  0. 0 9 4  8.80  4 .032  2. 34  2 . 246  3. 0 0  0. 084  1 1 . 42  3 .76  2. 25  2 . 550  3. 2 0  0. 0 7 6  13. 19  3 .52  2. 17  convection  (1976),  stratification Fr .e-2  the  results  inlinear  Ve/W*  computed  sources  Entrainment  results  T  o f these  experiments  hypothesis f o rentrainment b y Bo P e d e r s e n  when p l o t t e d by  Bo  a s shown  Pedersen  of compiled  and Jurgensen  i n f i g u r e 2-20.  33  show g o o d  due t o  (1980) and agree  i ngraphs  Ri  2  free  with data field  agreement  penetrative from  other  and laboratory  (1984) and  by  Kantha  E n t n a i n m e n t by c o n v e c t i o n Linear- s t r a t i f i c a t i o n 5-30-86  and mixed layer s a l i n i  34  Figure 2-19. Interface depth vs. mixed layer 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  i i i : i i! i  : e v  1  — . ' . I  1.1  -1 10  t a  , c o n v e c t i o r1 -  l i n e a r s t r~ a t i f .  • €  -2 10  10  m  A  x  into-  a  *  /  -3  -  , c o n v e c t i o in  into  -  2 ~ l a y e r e yetem 2 Fr = r  V\ Yg AD /D f re  10  -4 -3  10  ,1  -2  10  1  ll  L1I l  -1 10  1_i—i  i i 111 10  I  -  • ,  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 si,si W i l l i s and Deardorff (1974)- laboratory A Farmer (1975)- s o l a r heating under lake i c e +  BvanH (1986) - laboratory salt flux  36  2.6.5  Arctic  To the et  compare  field, a l ,  1974)  The  ice  used  Froude  density  salt  salinity  of  salt salt  D i as  0.9  i n the  F  Bay  following  g/cm .  The  3  the  time  the  ice  i s the  ice.  into  table  for  entrainment  flux  F and  Using  the  The  salt  several  shows  velocity  buoyancy  W*=  CY.Q] ' 1  flux orders  flux 3  from of  laboratory,  however,  field  the  in  the  bring  f o r the the  Arctic  (Gade  buoyancy  flux,  above  mixed  a  mixed  in  notation.  layer  salinity  e s t i m a t e d as  1971  and  ppt  and  3.0  was  Sm  obtained  by  between o b s e r v a t i o n s . product  of growth,  simplified layer  can  model,  then  be  density  the  amount  expressed  as  :  following  velocity  encountered  Canadian  ice growth  over  F The  i n the  to d e r i v e values number  into  expelled  flux  w i t h those  i c e s a l i n i t y S i was  flux  and  conditions  of c o n v e c t i o n Y between October  interpolation  The  depth  i c e t h i c k n e s s H,  depth The  convection  Cambridge  included  1972.  linear  a  were  observed  April  from  and  data  and  laboratory  data  entrainment  and  saltflux  and  (dH/dt).Di.tSm  the  field  Ve=  dY/dt,  Q=  F.g  d a t a and  ice growth  (g=gravity),  estimated  magnitude the  from  s m a l l e r than  large  f o r the  experiments.  37  depths scale  - S i l  the  c o r r e s p o n d i n g Froude  freezing  values  =  of  derived  salt  convective  these those  velocity  values  (dH/dt),  number  the  (2.17)  mixed W*  scale  Fr.  field  data  used  in  layer  close  to  Is the  i n the those  Table Date days 10/12 10/29 37 12/5 78 02/21 52 04/14  the  Arctic  field  Mixed l a y e r Incr Ve S a l i n Dens (m) (cm/s ( p p t ) (sigma) .e-4) 3. 1  0 <11.5> 23 <37> 51 <95> 139 <147.5> 156  26 .5 21 . 27 0. 407 <27 . 15> <21 .30> 27 .8 22 . 32 0. 8 9 0 <28 . 35> <22. 77> 28 .9 2 3 . 21 <23. 38> 1 .47 1 <29 . 1> 2 3 . 54 29 . 3  1 .3 6. 0 7. 5  data  Ice Thk Incr Growth (cm) (cm) (cm/s .e-5)  2. 1 1  in brackets are linear  dates  Days  Depth (m) 16 . 6 < 18 .5> 19 . 7 <20. 35> 21 . 0 <24. 0> 27 . 0 <30. 75> 34. 5  17  Values  2.3 E n t r a i n n e n t f r o m  interpolations  23  1 .5 6 6  28  0. 876  88  1 .306  17  0. 3 3 3  between  those  of o b s e r v a t i o n .  Salt Flux (g/cm /s) .e-7 2  Buoyancy Flux (g/cm/s ) .e-4 3  W* (cm/s)  Ve /W*  Fr  Rf  2  T  .58  17  3.31  3. 25  0. 8 3 9  2.517  1 .63  I  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. 2 8 5  52  0.783  0.768  0.618  2 . 38  3. 9 6 0  0.61  computed  values for  The agree  entrainment e ff l ciency  w i t h t h e 0.20 p r e d i c t e d  observations, and  the  spaced  values  over  b y Bo P e d e r s e n  a period  f o rentrainment  neglect  any a d v e c t i o n of s a l t  reverse  e s t u a r i n e flow suggested  or  from  any e n t r a i n m e n t  caused  o f s i x months  d e r i v e d from  by t i d a l  were few  (figure  these  2-21),  field  f l o w s o r by t h e type  by t h e s l o p e  by I n t e r n a l  38  but there  waves.  flow  data of  experiments,  r  ~i  s.  >  30  S E P T . 14.1971 O C T . 12.1971 O C T . 29.197! DEC . 5,1971 —«»» FEB .21 .1972 APR . 14.1972  1  I fCL  ci 60 i_  J  26  28  SAL.  30  i  J  -I  +1  «  +3  (°C)  TEMP.  (%o)  '  Seasonal changes in water column temperatures and salinities at Cambridge Bay, winter 1971 and 1972. 1  -i  5 LU Z  U  r  2.0 1  r\S.K£--  -5 1-0  I  *~  0.5  LU  U  0 O  J  N 1971  L  J  I  F  M 1972  L  A  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 - E X P E R I M E N T A L R E S U L T S AND  Slope  f l o w s were  with  different  Salt  flux  the A  Slope The  of  during the  salt  between  the  salt  tank flux  i n tank  and  tray.  water  f o r the  lower  o-f t h e pure  reservoir fluids were  3.1  under flow  Sea  salt  and  fluxes,  by  s a l t was  to obtain i n tank  monitored  salinity and  with  tray. a  during  b e f o r e the  through  into  start  membrane fluid  salinities  used  where  the  h e i g h t of  initial  mixed  taken  fluxes  i n the  of  in the  tray  and  conductivities  were  AM/CT D a t a l o g g e r c i r c u i t . sea  5.5°.  2  salt  the  was  and  gr/cm /s.  fixed  range  i s determined  conducted  experiments.  was  i n the  a digital  slope  of  2.2°  data  1.63e-6  the  difference  salinities  and  of  the  the  Table  to  by  range  and  micro-cell  1.82e-5  In e a c h  The  experiment  fluxes,  tray  in  slope angle  and  reservoir within  observed  experiment.  tray  from  from  of experiments  s e t between  angles, starting salinities  the  fluids  slope angles,  ranged  was  bottom  each  in a series  e s t i m a t e s computed  slope flow  and  bottom  experiments  3.1  Induced  INTERPRETATION  For  the  differences  the  higher  sea  water  for  of  40-60  ppt  the  tray  In these cases  separate conductivity  circuit  voltmeter.  lists the  the  tray,  bottom the  e x p e r i m e n t s , and  s l o p e a n g l e , the  starting the  fluxes.  40  range  salinities  depths  of  f o r each  of computed  fluids of  membrane  the salt  Table Exp #  3.1  Starting  Conditions f o r Slope  Tray-h (mm)  1  3.3  34  63  7  59  15  2  3.8  34  65  7  58  7  18 . 20 - 1 7 . 1 2  3  2 .2  34  51  20  58  8  14.18  4  5 .2  34  100  20  53  7  21 .89 - 1 3 . 6 4  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  end  the  of  end  the  flow the  dye  near fluid  first  and  resting  amount  below  initial  at  second  the  on  the  fluid  tray  tests,  slope flow  2  bottom  and  became  the  at  of  -  the  20  shallow in  at  the small  shadowgraph to  tray  tank  9.46  the  very small  the  the  -16.94  depths  contribution  Therefore,  s h a l l o w end  Salt fluxes (g/cm /s*e-6) 17.80  neither  distinct  s h a l l o w end.  depth  of  the  d i d show a n y  the  subsequent  3.2  In  tray  the  volume  angles.  injected  the  tank,  wedge-shaped slope  of  Sa1inity(ppt) Tray Tank  Experiments  Angle (degr)  With  Tank-depth Max(mm)Min  Flow  was  was  experiments  and  mm  filled  with  the denser  fluids  i n the  the  nor slope  raised  7 mm  im  so the  in nearly a l l  experiments.  Shadowgraph o b s e r v a t i o n s When t h e  selected  tray  was  height,  space  between  began  to p e r c o l a t e  convection  tank  started  nearly  and  the  and  tray  through as  a  reached the  field  almost  membrane of  41  small  tray  and  fluid  to  i n the  the edge  the  same  level,  salt  i n the  tray  bottom  and  plumes  or streamers.  It  became  visible  wrinkled a  line  speed  i n the shadowgraph  segments,  estimated  magnitude  A downslope  flow  c u r t a i n reached  the  mostly  end  parallel the the  experiments vertical  return  flow  the  shallow  became to  visible,  start  from  imposed  at  on  the  region  after  the  flow  and  3-1  to start  from  tank: the  shallow became during  by  of the  associated  below).  pattern  up v e r y  through  close  the  of the experiments  a t 20 t o 30 cm  of  in  the bottom  shadowgraph  the s a l t f l u x  42  segments  overturning  (see figure  seen  end of the  images s e e n  convective  of t y p i c a l  part  8) show a d e f l e c t i o n  by t h e s l o p e  but i n several  initially  and near  page  after  towards  shadowgraph 2,  u s u a l l y was  end soon  of the l i n e  region,  i n photo  3-1. S k e t c h flow  depending  a t the shallow  typical  i n the mixed  slope  descending  up s h o r t l y  t o d i s p l a y a bend  patterns  pattern  Figure The  The  (seen  line  flow  to start  i n the mixed i t .  one c m / s e c ,  orientation  image b e g a n  with  general  seen  the bottom  vertical  of the tank  than  evenly  small  flux.  was  this  shadowgraph  s l o w l y and f a i r l y  at less  of the s a l t  image a s a c u r t a i n o f  the shallow  to  membrane  i t was end of  seen the  tank  and t o form  figure did  3-2).  a counter-rotating cell  In these  re-establish  under  the tray  introduced  cases,  again  flow  after  patterns  by uneven c o n d i t i o n s w h i l e  the experiments,  the i n i t i a l  descent  in  the shadowgraph  was s l i g h t l y  faster  the slope  flow  was s e e n  the  slope  flow  gradually  the  uphill  flow  cell  20  minutes.  (2.3  degrees),  last the  the u p h i l l  fluid  have  been  I n some  The s t a r t i n g  the shallow  #6, w h i c h  had the lowest  flow  decreased  lines  of the  and o f t e n disappeared  cell  the  the tray.  i n the area  to start.  10 cm a t t h e t o p o f t h e s l o p e ,  point of  end, over slope  in length  but p e r s i s t e d  tray  while 8  to  angle to the  throughout  e xpe r i m e n t .  Figure The but  In experiment  might  cells  of the c u r t a i n of  moved t o w a r d  shortened  which  there (see flow  stirring  filling  of  where  from  the downslope/uph111  themselves  t o remove  uphill  3-2. S k e t c h  slope  then  flow  to slown  o f downs 1 o p e / u p h i 1 1  appeared  to accelerate  down a n d r e a c h 43  some  flow  from  cells  the s t a r t i n g  equilibrium within  point about  20  t o 30 cm d o w n  accurately As at  the slope,  measure  beyond  any increase  the experiments  convective the  turbulence  tank.  at  an  along  flow  the line  was s e e n from  the  the s t a b l y  to  speed.  fluid collected  patterns  associated  into the deeper  to separate  increasing distance interface with  i n the flow  and the h e a v i e r  d i d not penetrate  The s l o p e  i t was n o t p o s s i b l e  or decrease  progressed  the deep end o f the tank,  which  from  part  of  the bottom  the end of the slope stratified  with  and  fluid  at  move the  deep end. On  several  graph  Images  through  the  streamers the  mixed  into of  occasions,  points  membrane  i n the t r a y .  The l e a k s  stratified these  have  layer  Some  to occur  i n one  and  through  penetrating  flux,  on v i d e o  profile  a small  into a micro-cell during  part  they a r e  i n the s a l i n i t y from  cut small  i n the deeper  when a s t r e a m e r  instance  as  faster  to the s a l t  variability  been caused  was s y p h o n e d  forms  tubes  showed  observed  which  contributed  sampling  slightly  motions  i n t h e shadow-  leak  profiling,  footage.  I n j e c t e d dye Small  amounts  sampling  tubes  was m i x e d  with  of  descending  the other  t o be m i n o r .  was s e e n  3.3  fluid  than  While  intermittently as  seen  where  layer  may  were  of the p o i n t s  the s t a b l y  believed  leaks  a t some  of denser  the tank.  pinhole  the f l u i d  seen  to sink  of food  set along some  salt  l n the tank. through  dye were  i n j e c t e d through  one o f  the c e n t e r l i n e of the t r a y . water  to a density  During  injection,  the c o n v e c t i v e l y  44  mixed  slightly a line layer,  the  The  dye  above  that  o f d y e was i n which i t  was d e f l e c t e d flow  toward the  pattern,  similar  When the dye was i n the  s h a l l o w end of to  the  s h a l l o w end of  4.  Dye  Where the dye features above  mixing, slope  the  which  flow.  depth city  formed,  of  bottom.  The  density  by the c o n v e c t i v e the  i n the  tank  These  tank  friction  twice at  the  features that  of  flow,  moved  of  vee-shaped  about  3 t o 6 mm  much of  dispersion  turbulence  suggest a shear the h e i g h t  interface  of  was e q u a l  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 45  and  the  flow  were c a r r i e d a l o n g  limited levels  The v e e - s h a p e d  that  ( p h o t o 4).  bottom w i t h o u t n o t i c e a b l e  indicates  to  through  motions  m i x e d l a y e r and s l o p e  features  overall  shadowgraph.  was c l o s e  s h o w i n g a v e l o c i t y maximum a t  w h i c h w o u l d be i f the  i n the  l i n e sank t h r o u g h the b o t t o m  the b o t t o m .  length  Its  seen  t a n k by the  s t r e a k s made d u r i n g d e s c e n t  m i x e d l a y e r were d i s t o r t e d  Photo  lines  more d i l u t e d and  mixed l a y e r ,  t o w a r d the  the  the  in  the from the  flow with  a  maximum v e l o -  to t h a t of  at  the  convective  turbulence the  dye  lower  a t the from  u p p e r edge of  t h i s edge w h i l e  p a r t of the  each in  Velocity  timed  from the  photo or s l i d e  Velocities  the  in  photo  distance  or  this  conditions  from the  at various dye  in video  from  the  times  in  t o n g u e s moved tape  footage.  observations  made  of  the  slope,  since  the  region appeared steady  and  not  much a f f e c t e d  by  a t the e n d s of the  tank.  velocities  ranged  time d u r i n g  e a c h e x p e r i m e n t as  I n s e v e r a l o f the  f r o m 0.09  top  stretches  5).  t h a t these  sequences,  some of  dye  estimated  were g e n e r a l l y d e t e r m i n e d  b e t w e e n a b o u t 30 t o 60 cm flow  (see  entrained  friction  maxima i n  maximum f l o w v e l o c i t y was experiment  slopeflow  bottom  t o n g u e of d y e .  P h o t o 5. The  the  t o 0.52 the  experiments, 46  cm/s  salt dye  The and  flux  measured  flow  decreased  with  diminished.  w h i c h was  injected  In  the  edge between slots causes  into  tank  the  stable  and  tray  by  the  last  4 t o 6 cm  tray  experiments  (see photo  Photo  slope  the deep end  flow  experiment, did  appear  the r e t u r n  of the  f o r the  lifted  slowly  and  tank  slope  6.  raised  f l o w from  and the  carried  by  was  seen  to the  tank. This  i n the edge s p a c e .  a t the s h a l l o w end  down-slope  slowly  was  stratification  under  At  tray  to be  Dye  flow  injected  mixed  into  the c o n v e c t i o n but d i d n o t  a n g l e s and  salt  fluxes  used  the flow  in  these  6).  Dye  a t s h a l l o w end  o f the  tank  entrained  the dye  into  velocities  slowed  convective  motions  to p e n e t r a t e c l o s e r  47  of from  the mixed  down near  i n the  tank the s l o p e layer. later  the deep end  t o the bottom  i n the  flow When  part o f the  of  was the an tank  shadowgraph  edge  between  s l o t s  into  causes  tank  the  s t a b l e  under  the  l a s t  4  tray  6  at  cm  down-slope  for  experiments  (see  s l o w l y slope  the  by  the  of the  was  the  deep  l i f t e d  the  6.  in  tank  slope  s l o w l y  r e t u r n  shallow  photo  Photo  At  tray  s t r a t i f i c a t i o n  tray  to  and  the  angles  Dye  at  the  and  c a r r i e d tank.  space.  seen  to  s a l t  f l u x e s  the flow  i n j e c t e d  mixed  but  to  This  Dye  be  c o n v e c t i o n  end  of  the  and  e n t r a i n e d  shallow  tank  the into  slowed  experiment,  c o n v e c t i v e  motions  to  and  d i d  into not  used  the flow  in  these  6).  v e l o c i t i e s  appear  from  edge  was  the  flow  d i d  flow  end  by  r a i s e d  penetrate  c l o s e r  47  end  dye the  down  to  near the  of  tank  from  the  mixed in  the  the  l a y e r . l a t e r  deep  bottom  slope  in  end the  flow When  part of  of the  was the an tank  shadowgraph  Image.  I n the c o u r s e  the  slope  it  formed  was  a stably stratified was  seen,  I n s e v e r a l of t h e e x p e r i m e n t s ,  heavier  o f the  in which  fluid  tank, no  where  convective  l a y e r of n e a r l y the dye  i t reached  this  from  i n the  uniform  slope  stable fluid  flow (see  i n photo 7 ) .  P h o t o 7. The  region  below a mixed  s e e n t o b i f u r c a t e where  arrows  the  f l o w a c c u m u l a t e d a t the d e e p end  penetration depth.  of an e x p e r i m e n t ,  slope  stratified  flow lower  Bifurcation  of s l o p e  flow  l i f t e d o f f the b o t t o m on r e a c h i n g p a r t of the  interface  was  were  not  visible  dye,  I n j e c t e d i n the c e n t r e  move  but  tank.  Dye  o f t e n s e e n t o c l i m b up and i n the  the  s l o w l y d i f f u s e d b e l o w the  mixed l a y e r (see  photo  travelling over  shadowgraph (see of  9). 48  the  along  the  waves w h i c h  photo 8).  stratified sharp  steep  stably  A cloud  region,  interface  did with  of not the  Along of  the  the  the  tank,  slope  Since  flow  This in  the  the  of  the  opposite  less  organized  3.4  in this  micro-cells fluid  and  i n the  velocity  1 ml/s  (2  increased  the  salt  layer  from  the  ends  the  depth  of  l n the  dye  or  i n the  time  the  change  actual  through  slope  rise  and  the  layer top  of  the  lines reached  be  carried  and  in a  much  convective  eddy  increases  of  must  continuity.  flow  velocities  mixed  were  taken  the  various flow the  as  in  the  slope.  (as  cells  described at the  salinity to  salinity in s a l i n i t y data: 50  take  a  a  a  and  in  the  in s e c t i o n  2).  calibration before  an  mixed  s e r i e s of were  fixed  rate  of  constants  experiment.  layer  data  obtained  point  and  densities  depths  constant  i n the  profiles at  thermistors  l o c a t i o n s and  u s u a l l y checked  the  from  salinities  second),and  needed  profile  for  d i f f u s e d by  toward  slope  per  flow  there  profiles  at  flux,  'Quas1-instantaneous' tracting  In  deflection  to  temperatures,  t r a y and  drops  being  data  m i c r o - c e l l s were  to  from  seen  in the  seen  i n the  salinity  syphoned  the  much s l o w e r  while  i n the  from  i t was  at  to determine  was  Due  tank,  experiments,  Fluid  the  away  is constant,  slope  A f t e r dye  layer decreases  l a y e r and  for  cm  as  tank  bottom  exist  image.  the  mixed  about  30  velocity,  l n the  the  to  manner,  Salinities  of  seen  flow  the  fluid  direction  The  During  about  p e r c e p t i b l e changes  flow  above  shadowgraph  motions.  slope no  the  of  flow  already  deep end  depth  were  In  volume  return was  or  the  images.  the  a  of  there  shadowgraph  be  part  slowly  points. by  i n the  submixed  S(profile) in  which  the  profile  mixed and  value  linear  periods  of time  profile  points  3-4)  which  points tank).  near  either  mixed  f i t through  i n the mixed  the underside  Time-series indicate that  curve  gives  layer  salinity  profile  using  l a y e r then  flow  was s e e n  the  salinity  rose  mixed  layer.  Appendix  flow  experiment  times  (figure  a s a 7 t o 17 mm  a brief  computed  mixed  taken  above  least  f o r short  time-adjusted (figure  (except f o r enters the  i n the  mixed  a second  order  f o r the change  b y 0.24 t o 0.92 PSS  with  the  the s a l t  data  observation  an experiment  F gives  of a  became v e r t i c a l  o f t h e t r a y where  i n the p r o f i l e s  taken.  s u b t r a c t i n g the  the slope  t h e l a y e r was w e l l  a better approximation  was  taken  o r by s u b t r a c t i n g  through  p l o t s of s a l i n i t y  during  point  i n the mixed  3-5). thick  The  slope  layer  where  the value  in  d e s c r i p t i o n of each  results,  at  i n the  were  layer salinities  A line  f o r longer  data  by p o i n t w i s e  the mixed  3-3).  indicates that  the p r o f i l e  change  the data  are the s a l i n i t i e s  layer salinity,  for this  (figure  that  (3.1)  c a l c u l a t e d from  the f i r s t  was made  i n the computed  squares  time  ( t l ) that  adjustment  'smoothed'  layer  i s the s a l i n i t y  S(mixed) and S ( t l )  depth,  a t the time  change a  S(actual)  l a y e r a t t h e same  The  - S(mixed) + S ( t l )  = S(actual)  the slope  time-series plots  and  prof i1es. Excessive  noise  i n some  micro-bead  thermistors  salinities  were  good  of the data  a t the m i c r o - c e l l s ,  re-calculated using  thermistor, offset  was c a u s e d  by h a l f 51  by  faulty  a n d i n some  the temperature  from  the averaged d i f f e r e n c e .  cases the  X  ime (min)  Figure 3~3. Time-series and linear f i t  Figure 3-4. Actual and adjusted s a l i n i t y profiles  53  Figure 3~5. MICRO-CELL TIME-SERIES SLOPE FLOW EXP#3  In a separate were the of  same h e i g h t a b o v e the tank  a n d 20 cm  experiment,  series 27)  data  the bottom, to either  indicate  the  of r a p i d  from  this  that  (figure  the rate  the  and slope mixed  salinity many  and  layer  during  points  F-28)  flow.  match the  those  salinity  from As  heavy  wedge  of f l u i d  motions profile about of data  fluid  were  formed  seen  3 cm  fluid  thick  (figure  order curve  near  salinities  i n t h e edge  stably  stratified:  up f l u i d  between  bottom  of i n c r e a s i n g  55  time  In b o t h  flow  was mixed  data  from  d a t a . When  used  (figure F-30  a t the end  would  weakening  in salinity  collected  in  profiles  i n the  #7,  when  Salinity  flow,  from  images.  this  wedge  A was  stratification profiles  (figure  rising  bottom,  few c o n v e c t i v e  shadowgraph  and t r a y  salinity  in  (figures  shows t h e s t a b l e  tank  F-  the slope.  i n the  the return  with  but persistent  i n experiment F-25),  (figure  was  profiles  a t the deep end of the tank.  taken  brought  #7  Time  #8  time-series  a t the deep end i n which  to penetrate  taken at port  sensor.  profile  A small  the slope  The u s e o f  to c o l l e c t  2 0 cm a p a r t d o w n  from  middle  f o r the change  layer  was s e e n  to  to correct  a second  the mixed  spaced  data  frequent sampling,  along the slope  f i t through  the  F-26).  of s a l i n i t y  'quas1- 1nstantaneous'  gradient  locations  of change  required  at the s t a r t .  near  3-6) a n d e x p e r i m e n t  A curve  taken,  F-31) f o r which  profile  readings f o r each  c a n t h u s be u s e d  were  (figure  a l l o w e d more  locations  the time  to obtain  but located  side  multiple  same a t d i f f e r e n t  layer  successive  the Intakes of a l l three m i c r o - c e l l s  HP-3497A D a t a l o g g e r System  andiaveraging  was  flow  t a k e n by r a i s i n g  the  a  slope  2-12)  from  the mixed  from also  the tank, layer.  12.6 -I-  CD CD  a.'  >-  TIME-SERIES-OF MICRO-CELLS SPACED 20 CM APART intake of Cl in port #7 C2 tn port. #5 C3 in port #3 intakes at equal height  (deepest) (middle) (shallowest) above botto m  intakes raised to 20 mm (mixed layer) ""V  cn  if:"  11.6  CO  s t a r t of slope flow reaches: . ^v//* j lis C3; / • J r? :Cl 4mm above bottor  CM  C3  10. 6 F i qure 3-6.  TIME: 300SEC/DIV S a l i n i t y r a t e of change i n mixed l a y e r and bottom f l o w .  A  sequence  near  the bottom  ports in  of m i c r o - c e l l a n d 6 mm  data  below  but  data  the  upper  3.5  Salt  The  along  taken  the slope  and flow  after  start,  salinities  values  and  overall salt  tank  slope  listed  behaviour flux  of s a l t  calculated  slowly  into  and t r a y  calculated  results  3.2  experiments  slide  lists  sequences  reduced  flow  were  were  o r from  of  salinities monitor  experiment  as the  data  6,  the s a l t  of s a l i n i t y  at  flux  i n the  was tray  as o u t l i n e d  in section  2.6.  t a b u l a t e d f o r each  experiment  and  plots  time  and s a l i n i t y  experiments values  t after  m a x i m a Vmax  video  in salinity  i n an e x p e r i m e n t  determined,  the compiled  velocity  set  to  the d i f f e r e n c e  For the times  i n the tank,  of slope angle  slope  conductivity  experiment  d u r i n g each  of the i n d i v i d u a l  below  temperatures,  micro-  system.  the t i m e - s e r i e s  description  over F-17).  t h e r m i s t o r s and  d u r i n g each  the t i m e - s e r i e s  The  with  of  decreased  flow v e l o c i t i e s from  from  These  fluids.  layer  ment,  show a h i g h e r s a l i n i t y  printer.  the tank  i n the mixed  Table  (figure F-5),  on t h e l i n e  of the  and  the  the tray  f o r each  as a t i m e - s e r i e s  plotted  included  distribution  (sigma-t)  were  which  sampling  densities  were  between  #4  #1  velocities  observations  influx  or under  the raw d a t a  and the c a l c u l a t e d  The  in successive  t o see a d i s t i n c t  during experiment  fluxes  ratios,  experiment  p a r t of the s l o p e , and a t the deep end ( f i g u r e  time  cells  the  the tray  d i d n o t show e n o u g h d e t a i l  the s a l i n i t y  taken during  footage  57  of  profiles  i n appendix  from  measured injected  F.  the slope  starting  the  from  in  flow  experi-  photo  or  dye, computed  salt  fluxes  f o rtimes  slope  flow  mixed  layer  (El)  and with  Cd=  (from  h and r i s e  (E2) bottom  3.2 C o m p i l e d  the velocity  in salinity  profiles),  4.2e-2/(h.Vmax)  Table  #  depth  a t which  slope t Vmax s a l t f l x 6 (min) (gr/cm /s (cm/s) *e-5) 2  of slope  flow depth (mm)  determined, that  entrainment  i n the without  Cd ( s e e s e c t i o n 3 . 6 ) w h e r e :  El= h.g'sinG/V  results  dS above  and computed  drag  was  and  2  flow  Salinity (PSS)  dS  E2 = E l - Cd  experiments drag Cd  Entrainment El E2  14-17  20. 54  0. 68  0. 053  0. 217  0. 163  1 .820  9-9.5  15. 69  0. 57  0. 108  0. 183  0. 075  0 . 34  1 .080  9- 1 1  25 .01  0. 40  0. 124  0. 2 1 1  0. 087  60  0. 26  1 .418  8.5-9  21 .56  0. 86  0. 185  0. 393  0. 208  1 35  0. 23  0. 946  20  0. 47  0. 498  50  0. 47  0. 436  102  0. 40  0. 373  12. 72  0. 25  0. 066  0. 209  0. 144  1 38  0. 35  0. 332  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  13-17  13. 10  0. 34  1 3. 3  2 3. 8  3 2. 2  4 5 .•2  5 5 .2  8 5 .1  25  0. 51  1 .780  30  0. 46  1 .694  55  0. 42  I 25  16 '  58  1 .36 1  The  tabulated  corresponding the  slope  (figure tical  bars  measured angle  were  i s not but  the  next  used  slope  ranged  from  flow  profiles  and  little  mixed  the  bottom  The  magnitude  slope  p l o t s to  relation  f o r the  relation  range  the  of  used  visible  the of  fluxes  3-8).  Ver-  range  velocity  angles  fluxes  salt  (figure  between  both  dependence  i n d i c a t e the  d e s c r i b i n g the  increasing salt  the  of  angles  in  the  and  slope  i n the  expe-  rise  in  is further explored  flow  depths,  estimated  from  7  17  There  no  to  the  mm.  upper p a r t  of  of  slope  associated  with  d i s p e r s i o n . The that  region,  the  i n the where  salinity  slope in  i n the  flow,  between  most  where  detailed  shear  weak d e n s i t y  level  turbulence  of  part  i s more  of  the  and  carried here  slope  dye along  is greatly  flow  rapidly diffused.  and  gradient.  is strongly stratified maxima a r e  59  profiles,  interface  velocity  upper  dye  layer:  shows a  flow  the  sharp  bottom  dominate,  the  from  was  c o n v e c t i v e l y mixed  convection  part  'tongues'  reduced  at  the  penetrative lower  the  f l u x e s to check  on  i n the  been p l o t t e d a g a i n s t  section.  The  the  the  distinct  velocity  with  on  have  salt  velocities  and  flow  The  and  velocities.  riments,  the  angles  flow  3-7)  velocities  and  in  in i ai *  CM  in  m  co O  OJ  0  CM  i— I aai cn  a-8  c 0  ai o Cu 0 0  OJ  •—I »—« >V  in  £ c  3-rrr  O  C3-Q  -P -P o  CM OJ  OJ  _£>  0  01 CP  c 0 L L a 01 ,a L L a ai -£> a 01  CM  tn  E  L 0 C _Q  OJ  in Q  •rt  Q  in i ai 4c  OJ CM  GTO  OJ  in 0  —rrP OJ 1  1  ^  in  co OJ  in in" CM •  IT) CD  60  0. 70numbers are bars  salt  indicate  fluxes  range i n  (*e~5) velocities  12. 67 17. 80 16. 94  $18.  20  10. 80  0. 35H \  21.89 18. 72 * 15.59 $ 13. 64  CO  14. 18 9. 46  E  0 -P  •|HJ 0  1.95 1.63  o  I—I  1.71  >  0. 00 + 0  T  4  T  Slope angle  gure 3 - 8 .  F I ow  veloci  vs.  slope  angle  T  6  (degrees)  3.6 I n t e r p r e t a t i o n Density  currents  separately  in geophysical  many r e s e a r c h e r s . two  mechanisms  flux  induces  (reduced)  a slope  is  balanced  reaches  which  h  which  turbulence state  by t h e f r i c t i o n  =  g'  depth  i s the reduced  i n slope  Do=  of environment  by  The  flow  i s slowed  a t the i n t e r f a c e which  a t the bottom  = ( t i +tw) Ds  flow  (3.1) (3.2)  g.Ds-Do Dre f  ti=  friction  at interface  tw=  friction  a t bottom  factor  V = averaged  9  = slope  Ve= e n t r a i n m e n t  flow  ->v  7 \ h w '  3-9. S l o p e  62  flow  interface:  3  = gravity acceleration  Ve  force  g'=  K = drag  angle  is  environment.  and a t the  K. V  of  down by  when t h e g r a v i t a t i o n a l  gravity:  salt  by t h e component  g  Figure  studied  the surface  i n the o v e r l y i n g  of the flow  Ds= d e n s i t y density  i s driven  and by s h e a r  a steady  been  and i n the l a b o r a t o r y  involved:  the slope.  h.g'sinG in  flows  have  s e r i e s of laboratory experiments the  flow,  by c o n v e c t i v e  flow  convection  are simultaneously  a t the bottom  The  fluid  In this  g r a v i t y along  friction modified  and p e n e t r a t i v e  " / vmax  diagram  n-  e  speed  velocity  Conventional  turbulent  by  Richardson  an o v e r a l l  inverse  of the square  Pedersen,  density  plumes have  number R i ( K a n t h a , of the densimetric  =  1 Fr  Such g r a v i t y fluid  from  turbulent  currents  flow.  This  is  proportional  is  the entrainment  environment  by M o r t o n ,  factor  and Turner  currents  linearly  to include  i n terms  of v a r i a b l e s  A=  dependent  h.V.g'.  properties equations  No a s s u m p t i o n s in could  a cross then  and Turner V.  gravity  distance  that  a  (Ve/V) constant the  the assumption  for  dependence driven  of the en-  turbulent the depth  slope of the  V which are  x and by the buoyancy  made a b o u t  flux  the d i s t r i b u t i o n  s e c t i o n of the flow.  Ve  along  h a n d mean v e l o c i t y  distance were  (1956)  attain  the  plumes l e d  The r a t i o  currents with  into  entrainment  of free  integrated over  depth  on d o w n s l o p e  downstream  i s 'entrained*  a Richardson  currents  by f l o w  distance  (1959) m o d i f i e d  and d e s c r i b e d  specified  with  velocity  E. G r a v i t y  factor,  only  (Bo  (3.3)  distance  Taylor flow  V and spread  Ellison  with  trainment  flow,  number F r  i s c h a r a c t e r i z e d by an  spread  t o t h e mean  velocity  gravity  Froude  i sthe  2  i n depth  inflow  V e . The l i n e a r  the assumption  slope.  grow  a quiescent  to  mean  1975) w h i c h  = h.q'cosG V  2  velocity  characterized  1980) : Ri  as  been  The  of  conservation  be r e d u c e d t o :  mass  _d(h.V) dx  = E.V  (3.4)  momentum  _d(h.V ) = h.g'sinG dx  buoyancy  _d(h.V.g') = -h.V.N (x) dx  - Cd.V  2  2  63  2  (3.5) (3.6)  in N  which =  Cd  i s the  (-_g_. d @ ) @o dz  coefficient  i s the  1 / 2  local @o  In  these  were  high  The  enough  t h a t any  tion),  terms  i n the  in which  case  Richardson  and  number.  substitution  of  that  the  small  motion  eqations  or:  = h . g ' s i n 9 - Cd V  3.4  and  V . _ d ( h . V ) + h.V.dV = E.V dx dx = Ri.tanG  3.3  be  enough  (E)  ignored. to  neglect  approxima-  only of  numbers  depends  on  equation  3.5  yields:  =  2  and  Reynolds  (Boussinesq  factor  (drag),  density.  could  Algebraic manipulation  =  E  reference  considered of  friction  frequency  effects  entrainment  _d(h.V ) dx 2  i s the  assumed  equations the  bottom  buoyancy  molecular  d e n s i t y d i f f e r e n c e s were  inertia  the  d e r i v a t i o n s i t was  of  h.g'sinG  -  Cd.V  2  - Cd  (3.7)  2  For  slope  interface, is  c u r r e n t s dominated the  reduced  to  a  by  bottom  friction  simple  relation:  turbulent entrainment  can  be  ignored  E(Ri)= In the  the lower  estimated  present  experiments  part  the  of  observed  and  w h i c h y/& a  first  to  height  of  the  and  low  flows,  equation  3.7  Ri.tanG  levels the  the  of  bottom  (3.8)  turbulence  in  friction  was  from: Tw  in  with  and  at  = *? i s t h e order  y of  the  = ji.dU dy  kinematic  approximation maximum  flow depth,  = Cd.@.U  viscosity,  f o r dU/dy  velocity  based  on  = v.  1 y.V  (3.9)  2  above  shadowgraph  about  i s the the and  1.4e-2  ratio  bottom dye  cm /s 2  of  Vmax  (about  1/3  observations),  thus: Cd  = 64  4. 2 e - 2 h.V  (3.10)  The  depth  averaged  entrainment slope  velocity  factors,  was  f l o w s shown by  V,  used  i n the  e s t i m a t e d from  LOfquist  velocity  the  and  laboratory  literature  ment  factor  E The  = Ve/V  The  between  experiments to  bottom case for  2.2°  The  and  (Cd)  quiescent  3.7  density  such  distances,  and  f o r the  Pedersen  indicate be  (3.11)  (1980)  that  the  by:  by  experiments.  data  the  to  two  well  as  the  interaction  between 65  f l o w s was  used  here  in turbulent  and  for  calculated  flows would the  data  characteristics  the  every  magnitude.  field  a different  the  o r d e r s of  This contradicts  flows maintain their that  including  predicted  values  Arctic  were  that  flows  bottom  flow  3.2)  (E2), in nearly  exceeded  large  slope  (table  ( E l ) . While  between  that  of  above  values  up  The  environment  present  3.10  factor  difference.  suggests  in a quiescent  from  and  factors  as  from  entrain-  approximated  describes gravity  indicate  findings  slope  = Vmax/1.12  Bo  i n the  these  environments.  loose  experimental  for  2.76e-3 t o 6.9e-3 f o r s l o p e  friction  reduced  entrainment  would  account  used  calculated  which  entrainment their  from  entrainment  formulation  in  that  5.5°  quiescent environment  compare  profiles  (3.12)  range  factors  computed  to  work  by  flows can  w i t h o u t bottom  friction  the  would  using equations  1.84  the  h i s own  values for entrainment  entrainment  0.08  from  the  = 0.072 s i n 9  e q u a t i o n 3.12  angles  data compiled  for sub-critical  predicted  from  and  of  (I960): V  Field  computation  model  rapidly present  which  show  over  great  is required  t u r b u l e n c e and  shear.  to  The  intensity  of t u r b u l e n t  image  appears  slope,  which  upward  out of the flow.  data  much could  in table  and  would  higher lead  3.2  cause  motions  seen  In t h e mixed  l a y e r than  to net entrainment The R i c h a r d s o n  using  equation  considerable  i n the  i n the bottom  o f m a s s a n d momentum  numbers c a l c u l a t e d from  3.3 r a n g e  damping  shadowgraph  from  2.10  to  of the turbulence  19.5  at  the  i nterface. In are  a two-layer  idealized  system,  the v e l o c i t y  by a d i s c r e t e s t e p  slope  flow  and the environment.  data  the  d e n s i t y changed  flow  and  the v e l o c i t y  layer  fluid  With  since  the  details  might  be o b t a i n e d  the and  of  of s a l i n i t y  slope  Integrated  used over  the growth i f a longer profiles  to assess the  the depth  extended  developed o r decay slope  taken  shows t h e d i s t r i b u t i o n  c a n be  with  from  upward  of I t i s s t r a i n e d along  Instrumentation  more  shape  some  was  for  66  in  the  slope  Into  the  mixed  these  used.  at different  the  experimental  by t h e  of such  friction.  experiments  slope  currents  The c h a n g e  i n the  locations  along  o f mass w i t h i n t h e s l o p e  the down-slope  depth.  profiles  a t the I n t e r f a c e between In p r o f i l e s  slowly  profile  and d e n s i t y  change  in  mass  flow, when  4 - SUMMARY AND  In the  a s e r i e s of laboratory experiments,  f r e e z i n g of sea water  water  through  a porous  was s i m u l a t e d  membrane  two-dimensional  bottom  when t h e b o t t o m  of the tank  Low  values  slope  of s a l t  were c a l i b r a t e d  membrane.  In  that  the constant  convection these  as  not agree  due  in part  rine  closely  to salt  Shadowgraph  were  patterns carried  weaker the 0.09  flow  this  efficiency  assumptions  The s m a l l with  A  by t h e c o n v e c t i o n angle.  starting  experiments system  f o r free  with  confirmed penetrative  be e x t e n d e d  for  values  into  by s l o p e  of convective  flow  i n the opposite  entrainment  which  may  i n the experimental  tank d i d  i n the mixed  direction  was s e e n  layer,  slope  from  which  flow.  A  superimposed  on  V e l o c i t y maxima i n t h e s l o p e  67  estua-  regions.  o u t by a b o t t o m  measured  be  i n the perimeter  motions  and smoothed  0.66 cm/s w e r e  o f computed  the bay by the r e v e r s e  images o f t h e f l u i d  pattern.  were a p p l i e d t o a s e t  the predicted values,  advected  caused  along  convective to  below.  by s e l e c t e d  i n t e r f a c e entrainment  entrainment  tank  density d i f f e r e n c e s across the  stratifications,  data.  circulation  show  controlled  from  due t o  fluxes.  field  did  Induced  was s e t a t a s m a l l  i n t e r f a c e entrainment  Arctic  a plexiglass  was  flux  by a p e r c o l a t i o n o f s e a  p r e d i c t e d b y Bo P e d e r s e n c o u l d  low s a l t  The of  several  and l i n e a r  flow  fluxes,  conditions,  two-layer  into  the s a l t  CONCLUSIONS  the progress  of  flow  of  tongue  features and  in  injected  photographs  Salinity flow  and  profiles  were p l o t t e d  conductivity  videotape  of  fluid  from  have  0.05  on  recorded  a  ppt,  require  over extended  The  salinity  profiles  0.92  ppt  17  above  mm  and  g/cm /s. allows  a  slope  model  the the  flow,  and  salt  and  the  the  look  with  a  mixed  v e l o c i t y maxima m e a s u r e d  model  for  predicting  environment computed were values  by  by  several for  the  a  of  quiescent  well  from  flow,  environment.  of  depths  the  0.24 of  7  to  1.63e-6  within  possible  to  currents.  difference the  between  profiles,  and  applied  the  from  a  flow  than  the  to  quiescent  Entrainment  slope  to  micro-cells  be  were  fluid  larger  convective  distribution  current.  magnitude  68  with  density  the  by  1.82e-5 and  bottom  of  better  maintained  flow  flow  these  i n the  from  mixed  density  determined  These  of  and  slope  for  the  from  use.  i t may  gravity  inserting data orders  of  and  salinity  slope  entrainment  turbulent  of  slope  purpose.  flush  between  the  flow,  layer  to  achieved  longer  behaviour  slope  this  value,  at  slides  i n the  for  i n the  fluxes  and  thermistors  region  resolution  down-slope  of  layer  color  from  periods  show a  mixed  spatial  depth  flow  the  4 ml  in s a l i n i t y  more d e t a i l e d  the  The  rise  calculated  The  2  a  a  layer  in calculated  about  readings  and  mixed  developed  resolution  of  footage.  obtained  stable  turbulence,  in sequences  i n the  data  micro-cells  micro-cells than  dye,  factors  experiments predicted  The  conclusions  - Low to  calibrated freezing  a porous ting -  from  these experiments  salt  fluxes  to simulate salt  were a c h i e v e d by  membrane.  starting  The  depths  percolating  magnitude  and  are:  density  was  sea  confirmed that  predicted  by  - A surface a  slope  Bo  salt  interface  to these  sloping  bottom  in  higher  salt  fluxes  (figure  t o 5.5°  i n the  e x p e r i m e n t s , t h e r e was  lation -  -  the  between  slope flow  flow  High  resolution  from  small-volume  these  velocity 3-5),  velocity  salinity  e x p e r i m e n t s and  salt  fluxes. produced  slope  flow  experiments  flows  were  several  into  were  by  from  their  suggests  that  from  larger  a different between  env i r o n m e n t .  69  data  contrary Arctic  is required  slope flow  and  for  the  gravity those  to  visual  field  data,  environment  over great d i s t a n c e s .  model  the  from  than  f l o w s under a t u r b u l e n t  characteristics  interaction  or  data  for turbulent  evidence  maintain  3-6).  o b t a i n e d from  inserting  f o r a quiescent environment,  such  (figure  re-  thermistors.  predicted  show t h a t  distinct  micro-bead  magnitude  the experiments  no  s l o p e s of  developed  a model  orders of  f o r bottom  for  micro-cells,  with  calculated  increase  slope angle  profiles  used  factors  the  efficiency  always  show a n  but  and  conductivity  Entrainment  which  low  without  flow.  - Maxima  2.2°  selec-  differences.  applied  over a  due  through  by  the c o n s t a n t e n t r a i n m e n t  Pedersen flux  water  controlled  Entrainment experiments across a density shear  expulsion  to the  This  describe turbulent  BIBLIOGRAPHY  Benjamin,  T.B. 1 9 6 8 . G r a v i t y c u r r e n t s a n d r e l a t e d J . F l u i d Mech. 31, 209-248  phenomena.  Bo P e d e r s e n ,  F. 1 9 8 0 . A m o n o g r a p h o n t u r b u l e n t e n t r a i n m e n t a n d f r i c t i o n i n two-layer s t r a t i f i e d flow. Paper 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 D e n m a r k , 397 p p .  Bo P e d e r s e n ,  F. a n d C. J u r g e n s e n , 1 9 8 4 . 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 d u e 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  Deardorff  J.W., G.E. W i l l i s a n d D.K. L i l l y , 1 9 6 9 . L a b o r a t o r y i n v e s t i g a t i o n of non-steady 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 M e c h . 3 5 , 7-31  Deardorff  J.W.  Deardorff  J.W,, G.E. W i l l i s a n d B.H. S t o c k t o n 1 9 8 0 . L a b o r a t o r y s t u d i e s o f the 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 mixed l a y e r . J . F l u i d Mech. 100, 41-64  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 the t o p o f a mixed 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  Elliott,  J.A.  1972. C o n v e c t i v e m o t i o n s under s e a i c e . F r o z e n Seas Research Group, I n s t . o f Ocean S c i . S i d n e y , B.C. U n p u b l i s h e d , 17 p p .  Ellison,  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 s t r a t i f i e d f l o w s . J . F l u i d M e c h . 6, 423-448  Fofonoff,  Foster,  Gade,  ln  N.P. a n d R.C. M i l l a r d J r . , 1 9 8 3 . A l g o r i t h m s f o r c o m p u t a t i o n of fundamental p r o p e r t i e s of seawater. 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, 5 3 p p . T.D.  H.G.,  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 the f r e e z i n g of s e a w a t e r . J.Geop.Res. 74,6967-6974  R.A. L a k e , E . L . L e w i s a n d E.R. W a l k e r , Oceanography of an A r c t i c Bay. Deep-Sea Res. 21, 547-571 70  1974  Heidt,  Kato,  F.D.  H.  Kantha  1 9 7 7 . 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 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 M e t . 12, 439-461  a n d O.M. P h i l l i p s , 1 9 6 9 . On t h e p e n e t r a t i o n o f a turbulent layer into a s t r a t i f i e d fluid. J . F l u i d Mech. 37, 643-655  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 of 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 system. 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.  Kullenberg,  Lake,  R.A.  Linden,  G. 1 9 7 7 . E n t r a i n m e n t v e l o c i t y I n 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, 3 2 9 - 3 3 8 and E.L. during  P.F.  LOfquist,  Long,  stratified  1 9 7 5 . The d e e p e n i n g of a mixed 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  K.  R.R.  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 growth. J.Geophys.Res. 75, 583-597  1960. F l o w stratified  1 9 7 5 . The density  and s t r e s s near an i n t e r f a c e between l i q u i d s . P h y s . o f F l u i d s 3, 1 5 8 - 1 7 5  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 i n t e r f a c e s . J . F l u i d Mech. 70, 305-329  Meagher,  T.B.  Melling,  H.  Millero,  F . J . , C.T. C h e n , A. B r a d s h a w a n d K . S c h l e i c h e r , 1 9 8 0 . 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.  A.M. P e d e r s o n a n d M.C. G r e g g , 1 9 8 2 . A l o w - n o i s e c o n d u c t i v i t y micro-structure Instrument. IEEE J . o f Ocean.Eng, pp.283-290  and. E . L . L e w i s 1 9 8 2 . 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 a n d t h e i r e f f e c t on t h e A r c t i c Ocean p y c n o c l i n e . Deep-Sea Res. 29, 967-985  a n d R.R. L o n g 1 9 7 1 . An e x p e r i m e n t a l Investigation of 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,  1 9 6 7 , The u s e 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 niques l n the study of flow 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  Perkin,  R.G.  and E.L. L e w i s 1978. M i x i n g J.Phys.Ocean. 8, 873-880  Perkin,  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 c a l c u l a t i o n . J.Geop.Res. 8 3 , 466-478  Perkin,  R.G.  a n d E . L . L e w i s 1 9 8 0 . The P r a c t i c a l 1 9 7 8 : F i t t i n g the Data. I E E E J . o f O c e a n i c E n g . O E - 5 , 9-16  Phillips,  O.M.  i n an A r c t i c  Fjord,  Salinity  and  Scale  1 9 7 2 . T':>o e n t r a i n m e n t interface J . F l u i d M e c h . 5 1 , 9 7 - 1 18  Thorpe,  S.A.  Turner,  J . S . 1 9 6 8 . 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 o n turbulent entrainment across a density interface. J . F l u i d Mech. 3 3 , 639-656  Turner,  J . S . 1973. "Buoyancy 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 p p .  Turner,  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 b y B.A. W a r r e n & C. W u n s c h , M I T P r e s s , C a m b r i d g e , p p . 2 3 6 - 2 6 2  Walin,  G.  Wyatt,  L.R.  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 of 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  1971. C o n t a i n e d non-homogeneous f l o w under 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. 48, 647-672 1 9 7 8 . The e n t r a i n m e n t f l u i d . J . F l u i d Mech.  72  interface in a 86, 293-311  gravity  stratified  SALINITY AND DENSITY  COMPUTATION  APPKNDIX  73  A  APPENDIX  A.l  Sal  salinity  calculated  Salinity  of  from  R  Scale  used  electrical  CALCULATION  s e t of polynomials  (Lewis  the conductance  and P e r k i n , ratio  Scale  known  of the f l u i d  and  as the  (i.e.  T and p r e s s u r e  a n d 15 °C) t h e n  Salinity  pressure  is  temperaPractical  1980).  a t temperature  pressure  Practical  i n the convection experiments  conductivity,  i s the conductivity  atmospheric the  of f l u i d s  using a standard  If  AND D E N S I T Y  in i ty  The  ture  SALINITY  A  ratio  P to that S  the s a l i n i t y  is calculated  the  at  in units  of  from:  Q = 1+P(A1+P(A2+P*A3))/(1+T(B1+T*B2)+R(B3+T*B4)) U = C0+T(C1+T(C2+T(C3+T*C4))) Y =W"  W = R/(Q*U)  F=(T-15)/(1+.0162(T-15))  2  S=E0+F*F0+Y(E1+F*F1+Y(E2+F*F2+Y(E3+F*F3+Y(E4+F*F4+Y(E5+F*F5))))) in  which  P  i s the pressure  S  i s the s a l i n i t y  grams/ki1ogram mediate  i n bars,  i n PSS ( u n i t s  T the temperature  are close  or parts-per-thousand),  results,  and A i through  i n °C,  to the formerly  Q, U, W,  Y, F a r e  F i are constants  with  used inter-  values:  Al=2.070e-5  C0=0.6766097  E0=0.0080  F0=0.0005  A2=0.637e-9  C1=0.0200564  El=-0.1692  Fl=-0.0056  A3 = 3 . 9 8 9 e - 1 5  C2=1. 104259e-4  E2 = 2 5 . 3 8 5 1  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  E5=2.7081  F5=-0.0144  B3=0.4215 B4=-0.003107  74  For since  laboratory P=0  These 2  to  42  polynomials are  this  extended  range  higher To  defined  parts-per-thousand.  to  25  range, of  calculations  °C  shows  create  refractometer,  calibrated indicating Practical  (see  and  and  are  simplified  this  S c a l e may  be  e s t i mates.  75  sea  fluid,  found  v a l u e s computed  Salinity  are  conductivity  pure  not  ratio  defined over  temperatures  and  salt  was  extend  added  obtained with  Autosal  result,  were  units  from  an  from to  A-1).  the G u i l d l i n e  micro-cell  salinities  polynomials smoothly  fluxes,  d o u b l i n g the  that  the  of  for laboratory  these  v a l u e s of  from  of  figure  higher salt  Salinity  dilution  that  f o r a range  A l t h o u g h PSS  a graph  salinity  v a l u e s of S  water.  these  at atmospheric pressure.  outside  17  experiments  after  from  to agree  a  the  within  from  the above  used  with  to  an  optical  2-to-l output  sea  volume of  several  the ppt,  formulas f o r the  caution  as  reasonable  A.2  Density The  is  Unesco E q u a t i o n of S t a t e  used  to calculate  sigma-t  =(D-1)*1000  pressure P  and  fluid  f o r sea water D  densities  from  salinity  ( b a r s ) from  S  i n g/cm  (PSS),  the f o l l o w i n g  (Millero, or  3  in units  temperature  of  T  (°C)  s e t of 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 . 4 3 7 1 3 e - 3 i - T ( 1 . 1 6 0 9 2 e - 4 - T *5 . 7 7 9 G 5 e - 7 ) )  C=1965 2 . 2 1 + T < 1 4 8 . 4 2 0 6 + T ( - 2 . 3 2 7 1 0 5 + T ( 1 . 3 6 0 4 7 7 e - 2 - T * 5 . 1 5 5 E=  A+S(-9.9348e-7+T(2.0816e-8+T*9.1697e-10))  F=  B + S ( 2 . 2 8 3 8 e - 3 + T ( - l . 0 9 8 1 e - 5 - T * l . 6078e-6 ) ) +S  G=  C+S(54.6746+T(-0.603459+T(0.0109987-T*6.167e-5) ))  H=  G +S  3 , 2  1980)  3/2  288e-5)))  * 1 .9 1 0 7 5 e - 4  ( 0 . 0 7 9 44 + T ( 0 . 0 1 6 4 8 3 - T * 5 . 3 0 0 9 e - 4 ) ) + P ( F + P * E )  J = 9 9 9 . 8 4 2 5 9 4 + T ( 0 . 0 6 7 9 395 2 + T ( - 9 . 0 9 * 2 9 e - 3 + T * 1 . 0 0 1 6 8 5 e - 4 ) ) K=  J + T«(-l . 1 2 0 0 8 3 e - 6 + T * 6 . 5 3 6 3 3 2 e - 9 )  L = 0 . 8 2 449 3 + T ( - 4 . 0 8 9 9 e - 3 + T ( 7 . 6 4 3 8 e - 5 + T ( - 8 . 2 4 6 7 e - 7 + T * 5 . 3 8 7 5 e - 9 ) ) ) M=-5.7 2 4 6 6 e - 3 + T ( 1 . 0 2 2 7 e - 4 - T * l . 6 5 4 6 e - 6 ) N=  J+S*K+S " *M+S *4.8314e-4  D=  N/1000/(1-P/H)  :  Similar these also  2  = density  i n gr/cm  simplify  for salinities  since  relation  P=0  r a n g i n g from  for laboratory  between s a l i n i t y  polynomials,  i s nearly  f o r the temperatures  (see  A-2).  figure  Densities  o f t h e membrane  (atmospheric  over  used  flux  76  during  used  They  pressure).  the extended  were  Scale,  PSS.  plotted  in laboratory  so d e t e r m i n e d  salt  Salinity  0 t o 42  and d e n s i t y ,  linear  salinities  estimates  3  to the p o l y n o m i a l s of the P r a c t i c a l  are v a l i d  The above  2  from range  the of  experiments t o compute  the experiments.  Figure  A - l . CONDUCTIVITY R A T I O v s S A L I N I T Y for laboratory temperatures T-25  S a l i n i ty  22 21 20  0  15  30  45  S a l i n i ty  E0  75  CONDUCTIVITY  MICRO-CELLS  A P P E N D I X  79  B  APPENDIX  MICRO-CELLS  B  A s e t of small developed tank. a  to determine  As f l u i d  flow  rate  into  inside  A  small  an  from  the c e l l  added  and the s a l i n i t y  using  (see appendix  the tank  from  another  of State  B.l  construction  The  electrodes segments Figure  made  from  B-1  shows  l.D.  the  electrical  the s a l i n i t y  converts  this  of  the  conductance  was c a l i b r a t e d t o  and o u t l e t  and the average  this  located  yield  the  density  salinity  a diagram  of the  Salinity  at the intake and the using  point  temperature the Unesco  by t e c h n i c a l s u p p o r t consist  of four  foil  o f 0.6  of the c e l l  80  temperature  i n the tank,  tubing  d i mens 1 o n s .  micro-  is calculated  of the P r a c t i c a l  thick platinum glass  of the  (appendix A.2).  of Ocean S c i e n c e s ,  o f 1.8 mm  experimental  micro-cells, at  i n the m i c r o - c e l l  f o r Sea Water  o f 0.002"  with  at the i n l e t  micro-cells, constructed  Institute  (0.15 ml/s),  A . l ) . The f l u i d  Equation  Cell  one o f t h e s e  the polynomials  thermistor  In an  was  fluid.  of f l u i d  i s computed  conductivity cells  of f l u i d  changes  which  the c o n d u c t i v i t y r a t i o  Scale  the  2 drops/sec  of the  were  thermistors,  in  through  voltage,  ratio  Thermistors cell,  the s a l i n i t y  electronic circuit  output  conductivity  four-electrode  i s syphoned  of about  conductance fluid.  volume  staff  ring-shaped  and separated mm  with  wall the  at  by  thickness. principal  GLASS TUBING SECTIONS 1 .8mm I . D . - 3mm O.D, COLOR CODED L E A D S FROM E L E C T R O D E S  0.002" PLATINUM F O I L ELECTRODES, EACH 5mm WIDE  PVC T U B I N G  Figure The  electrodes  of  heat  B - l . Diagram and g l a s s  shrink  soldered  spacers  tubing,  were  held  and c o l o r coded  to the e l e c t r o d e s .  with  epoxy  in a protective  were  made,  using  B.2  of m i c r o - c e l l  t h e same  sleeve.  materials  assembly i n place  by  electrical  The c o m p l e t e d  PVC  COVER  leads  assembly  Three  such  and p h y s i c a l  sections  was  were sealed  micro-cells  dimensions.  Micro-cell electronics The  four  electronic microcell Fluid line  electrodes  circuit  which  into a linear samples  Autosal  micro-cells resistance  o f t h e m i c r o - c e l l were converts  function  the conductance  of the output  o f a known s a l i n i t y ,  bench  salinometer,  calibration at a salinity  constants  connected  were K,  (1/R) of the  voltage (VC).  determined used  with  to obtain  expressed  a Guild-  values f o r  i n ohms o f  o f 35 p p t a n d a t e m p e r a t u r e  8 1  to an  cell  o f 15 °C.  The the  conductivity  product  ratio  of conductance  (RR) o b t a i n e d from and c e l l  1/R == c e l l  RR == K . ( A + B . V C )  The  There  was  output  no  drift  voltage  d a t a was u s e d  was  2.2065e-4  B.3  AM/CT D a t a l o g g e r The  circuit.  RR  == c o n d u c t i v i t y = cell  A  = -2.6008e-8  B  =  which  a correlation  conductivity  was o r i g i n a l l y  RR  -4.5954e-4  with  a high  about  factor  squares  designed  coefficients:  for cells  deviation .  conductivity  with  a constant  the micro-cells 1800 ohms.  ratio  The  i s given by:  NC = AM/CT d a t a l o g g e r o u t p u t  A =  constant  5.53084e-5  B = 1 .3290e-7  82  f i t to  different  K'= c e l l and  linear  t h a n 0.9999  c o n s t a n t o f about  with  i n the  electronics  b e t w e e n N-number a n d c o n d u c t i v i t y = K ' . ( A + B.NC)  of use.  found  The s t a n d a r d better  precision  6 months  1 0 0 ohms b u t w a s m o d i f i e d f o r u s e w i t h  h a v e a much h i g h e r c e l l  relation  A a n d B.  ratio  constant  dependence  A least  to calculate  with  after  or temperature  voltage  K  AM/CT D a t a l o g g e r h a d a s l i g h t l y I t  about  and checked  of the c i r c u i t .  the  of  == o u t p u t  coe ff l c i e n t s :  r e s i s t o r box,  conductance  VC  c o e f f i c i e n t s A a n d B were d e t e r m i n e d  decade  is  constant:  1/R == A + B.VC  and  the micro-cell  A and In  number of  trial  variability  of  several  data raw  was  of  the  less  a  tests,  than  +  the  conductivity were  taken  sudden  the  problem.  could  an  Small  change  The  the  tests  immediate seconds  that  change  i n the  of  salinity  and  of  the  through  flow  to draw  the  the  to  the  or  to d i s r u p t the  B.4  the  computed  to  known  with  a  the  the  PSS). three  datalogger observations micro-cells  could  by  for  be  caused  small  particles  not  eliminate  did  micro-cell  electrode  change  In t h e  level.  d i d not  which The  depend  The  use  of  more  shocks  which  cause  or  the  causes  in about  computed  on  cells  potential  flow  the a  5  value  magnitude peristaltic  than  doubles  small  the  particles  current  pattern  ce11 .  m i c r o - c e l l s were salinity.  calculated  +0.025  three  the  D e t e r m i n a t i o n of c a l i b r a t i o n The  using  salinity  previous  through  of  and  cell.  micro-cells.  fluid  temperature  s e r i e s of  caused  to  abrupt  variability  to  used  a l l fluids  i n the  the  p o s s i b l y due  ins ide  rate  salinities.  raw  observations  adhering  any  variability, bubbles  flow  bubbles  returns  time,  Filtering  d i d show  20  of  stability  ( + 0 . 0 0 7 °C>,  output  Several  i n the  conductance  to  pump  periods  flow.  the  (corresponding  Increased.  Deviations  the  of  digit  i n the  the  constant  c o n d u c t i v i t i e s was  v a r i a t i o n s i n the  obstructing  determine  several  last  3 units  of  longer  simultaneously.  i n the +  to  variability  variability  circuit  over  the  2  l a r g e r range  micro-cells,  were done  measurements at  c o n d u c t i v i t y about As  by  runs  Cell  salinity  calibrated  constants  equal  constants  to  were  that  83  by  using  then  fluid  chosen  determined  with  samples  which a  yield  of a  Guildline  Autosal  bench  micro-cell between  at several  the value determined calibrations  salinities. which  the  cell  which the of  tubing  dard  o f 1.89  Initially,  salinity This path cell  electrodes from  exchange inside  value  to occur  but exchanging  changed  constants.  84  to  break  conductivity  #2, t h e d a t a w i t h o u t a n a  the calculated  were  those  stansalinity  o f 2 0 °C.  closest  to the  the leads of p o t e n t i a l  the v a r i a b i l i t y  and caused  fluid  v i a t h e pump o r o n e  i n apparent  changes  when  the  f o r K o f 1765 w i t h  electrodes  of electrodes  agree  dependence  of d r i p p i n g  l o o p formed  the Datalogger to n e a r l y  the c e l l  found  o f 20 P S S a n d a t e m p e r a t u r e  reduced  3  An  temperatures and  contact with  instead  a change  which  the current  of the c e l l ,  current  ,  t o be  a g a i n s t ^temperature a t  were  electrical  current  each  t o 0.20 m l / s ) .  f o r temperature  constant. For cell  0.024 a t a s a l i n i t y  centre  made  counted  the c a l c u l a t e d  plotted  t o check  l o o p had an average  deviation  0.05  repeated at several  and caused  i n the c e l l  rates  through  the Autosal.  t o the tank  An e x t e r n a l  the other c e l l s  external  (about  In c o n d u c t i v i t y  was p u m p e d b a c k  thus  using  were  Shifts  flow  f o r K t o make  calculated  outlet  flow.  and  by  B-2).  was s y p h o n e d  steady  The v a l u e s o f K w e r e  t h e y were  (figure  fluid  p e r second  v a l u e was c h o s e n  These  The  different  1 and 4 drops  Integer with  salinometer.  half  the  a small  in  the  calculated  the i n i t i a l  effective  change  and  value.  potential  i n the values of  MICRO-CELL CALIBRATION , CELL#2 T = TEMP <°C>  22.0  21.0 1790 _J  1770  jM.0  23.0  I  1  J X  x  x  x  X X  x x  x  X  x<  *x  X  oell  outlet  no e x t e r n a l  1750  J  1730  J  1710  drip©, loop  x X  X  oell  o u t l e t immereed,  external  eleo.  loop  x  x  1590  iqure  B-2. Micro-cell constants vs. temp.  85  Cells wetting of  have been r e p o r t e d and d r y i n g .  theelectrodes  No  significant  cell  i n more  strongly  than  size  fluid  of constant  This  contact  surface  bubbles. particle  in  explained  each of  mixed  ofcalculated down i n  constant by a and  value.  decreasing coalescing  may d i s l o d g e a n y  and r e s t o r e  f o r thec e l l  constants  with  checks term  K which  thesmall  were  thecorrect  used  different  electrodes,  resulting  differ  electronic  f r e q u e n t l y done  behaviour  a r e Included  calibration  below.  a well  significantly  circuits  as  was  previously.  the long date  on t h e c e l l  i s  to the  a drift  conductivity circuit  values  obtained  Calibration track  datalogger  f o r thec e l l  those  d i d show  be c a u s e d  i nthec e l l  due  using  due t o t r a p p e d  tapping  trapped  and voltage  values  from  light  i nthe c e l l  t o the former  could  first  value.  AM/CT  current  i nsalinity  a t an electrode  o r bubble  calibration  output  of  i n K.  of the  o r bubbles  instances,  b y a jump b a c k  Occasional  some s h i f t  thetime-series plot  theDatalogger  cycles  characteristics  i ntheconstant  particles  I n some  salinity,  drop  and cause  The c o n d u c t a n c e  by minute  followed  apparent  The  a year.  of thec e l l .  o f S from  thesurface  o f t h e new c e l l s ,  affected  salinity,  may a l t e r  c h a n g e was f o u n d  small  values  This  t© ' a g e ' I n s u c c e s s i v e  In t h i s  constants  Each c a l i b r a t i o n  f o r both  systems t o  of themicro-cells. Print-outs of appendix  f o r each  constant  4 to 8 observations.  86  cell  listed  and t h eaveraged a r e shown below  value  i ntable B . l  i s an  average of  Table Day #  B.l Micro-cell  Date  Average  dataloqqer KI K2 K3  31 . 15  22.0  31 . 34 31 . 5 0 31 . 34 7 .8 3 7. 52 2. 74 4. 8 3 30. 3 4. 97 5 . 95 31 . 5 6. 10 6. 1 1 3 3 . 66 6 .59 2 0 . 56 22. 60 2 5 . 85 2 5 . 94 2 7 . 40 3 5 . 56 28 . 02 28 . 36 31 . 6 0 16 .40 28 . 49 26 . 8 3  21.7 21.8 21.8 21.1 20. 7 19. 1 19.2 20.5 20.5 21.0 21.0 20.5 2 1.1 20.0 20.0 21.6 20.9 21.1 21.3 21.3 21.6 2 1.9 21.4 21.3 20. 4 19.6 21.3  1879 1878 1882 1885 1876 1886 1891 1897 1897 1888 1885 1878  values be  value  particles values  1795  1822  1884  1792  1816  1877 1792 (1845)(1774) 1888 1798 1892 1795 1884 1793 1885 1795  18 14  —  1749  1783  1801 1802 1796  1753 1753 1746  1786 1787 1779  1754 ( 1 7 3 8 ) 1808 (1771)(1717)(1755) ( 1 7 0 9 ) 1748 ( 1 7 6 3 ) (1816 1758 1793 ( 1 7 6 7 ) ( 171 1 ) ( 1 7 5 3 ) 1799 1750 1785 1801 1748 1787 1803 1752 1786 1752 1782 1798 1751 1786 1802 ( 1 8 1 1 ) 1758 1790 1800 1751 1782 — 1785  18 25 1817 1818 1821  1803  17 46  1782  1801  1752  1785  de v i a t i o n : 6.34  4.20  6.70  5.64  3. 5 0  6.63  i n brackets  and were  differed  not Included  substantially  in determining  d e v i a t i o n s . Some o f t h e s e  by c o n t a m i n a t i o n or bubbles.  (figure  1884  1799  1821  and standard  caused  1787 1815 1789 18 15 1791 18 16 1792 1818 1784 1811 1790 1823 1802 1831 1796 1826 1793 ( 1837) 1796 1826 ( 1 8 1 8 ) 1832 1794 1832  1793  constants  expected  s m a l l 'e 1 e c t r . KI K2 K3  1885  eel 1 constants:  w i th standard The  constants  Temp. (°C)  Sal (PSS)  1 1 8 5 - 1 2 -1 1 1 1 12- 1 1 12 12- 12 13 12- 13 13 12- 1 3 20 12- 20 28 12- 28 34 8 6 - 1 - 3 34 1 -3 34 1- 3 37 1- 6 1 -20 51 53 1- 22 53 1 -22 54 1- 23 55 1- 24 55 1- 24 62 1- 31 66 2- 4 81 2- 19 81 2- 19 86 2- 24 89 2- 27 99 3- 9 106 3- 16 143 4- 22 159 5- 8 165 5- 14 196 6- 27  calibration  of the e l e c t r o d e s  A time-series plot  B-3) shows  t h a t any d r i f t  87  from  the  the average  differences could Inside a c e l l  by  of the c e l l  constant  I s much l e s s  than the  variability the alter cell  field the  In  the  observations.  distribution cell  constant  and  constant.  versus  The  current  conductivity  path  In  Some d e p e n d e n c e  salinity  during  88  the  cell  i s seen  calibration  may  affect and  in a  (figure  thus  plot  of  B-4).  1900 - l 17  G  Q  •  o • X  1800 -  X  CO  — I. Xa  X  (0  -p c 0  Q  a  Q  Q  Q  X  X  X  y—_a-  -p  (0  c o 0  X  A  Xxv  X-X-  a  01  x 1700  0  30  60  —r 90  T  r 120  Time-series o f m i c r o - c e l l  calibration  OG11#1  X  cell#2  0  cel103  r  i  T  150 days  F i g u r e B~3  I  after  constants  T  1  180 85-12-1  F i g u r e E>-4\Cell  Salinity calibration  (PSS) constants  vs.  Salinity  B.5  Micro-cell  time  The r e s p o n s e been  ty at  of the c e l l  investigated  required  response  to determine  at a selected  reaches  depends  point,  t h e volume r e q u i r e d  to determine  the  AM/CT d a t a l o g g e r ,  and  the output  before the calculated  After  a step-change  System  to respond  characteristics  of the c e l l .  In  response  t h e minimum  s a m p l i n g was a b o u t caused  i s shown  4  by  circuit.  s a m p l i n g , an HP-3497A  The a r r a n g e m e n t  initial  of the m i c r o - c e l l  showed e x c e s s i v e v a r i a b i l i t y  was u s e d .  i n the s a l i n i t y  f o rthe c e l l  the time  data and f a s t e r  salini-  of time  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  accurate  has  ( o r the time  rate)  the length  on t h e f l u s h i n g  attempts  with  flow  t h e new v a l u e .  the intake  t o an abrupt change i n s a l i n i t y  Data  with  seconds problems  To g e t more Acquisition  i n f i g u r e B-5.  •T-TOP CELL OUTLET SYPHON TUBE  HP-7225A PLOTTER  MICRO-CELL ELECTRONICS T-BOTTOM  HP-9825 VALVE  COMPUTER  JAR HP-3497A  S-l  Figure The a  B-5. Time R e s p o n s e  intake  valve  -PAIL  which  - Experimental  of the m i c r o - c e l l could  switch  •CH9 -  Arrangement  was c o n n e c t e d t o  the flow  91  DATA ACQUISITION SYSTEM  from  a j a r o f one  salinity  to  a pall  of a n o t h e r .  The  minimize  temperature  differences  drop  h e i g h t between  in  The  gravity-driven  constant during over  time  from  about  drops  and  the  0.5  i n 50  Each  r u n were  at  through  measured  per  was  connected powered  switching.  The  micro-cell  thermistors  were  which  for  this  from  both  the  calculated  on  the  At  to  by  Actual  c o u n t i n g the  second.  nearly rates  number of  drops  settings.  These  C o u n t i n g showed  to a  micro-cell  ranged  about  a run,  output  of  conductivity  which this  circuit  then connected  controlled  by  an  avoids  to the  825  salinity  each  r u n and  i n number the  i n a change were to  effect  on  the  difference in flow and  change the  The  computed  observed  of drops  counted  this  tape.  counted ln fluid  flow per  for both  i s unknown but  response  of  A  the  program  temperature and  to  store  salinities were  stopwatch of p a i l  between  believed  were marked  seconds. and  jar  salinities.  heights. to  The  time  have  a  time.  first  time-series  at constant s a l i n i t y  overall  variability  of  92  and  rates  levels  when s w i t c h i n g marked  transients  HP-9825 c o m p u t e r .  the  v a l u e s on  circuit  HP-Datalogger  for calculating  the  outlet.  flow  thermistors  negligible  to  constant  remain  average  flows,  the  did  the  adjust  that  the c e l l  pall  the c e l l  m o d i f i e d t o use  rates  From  and  was  plots  resulted Flow  was  system  during  low  levels  larger  a nearly  salinities.  during  by  plotted  l n the  to get  for different  to 4 drops  continuously  System,  and  fluid  between  outlet  floated  ml.  cell  caused  the  flow  when s w i t c h i n g each  j a r was  this  system  was  i t was  about  0.01  found S.  The of  next the  used of  series  response  steady  steps are  of  The  0.5  to  steep  an The the  was  these  marked were  as  the 95%  of  the  of  the  appears  less  than by  linear  about  as  a  within  the  time  switch  the  different and  for plots  90%  from  or  this  start  of  rapid  change  the  calculated  in s a l i n i t y . over  per  the  density to take i n which  The  p a r t of  the  2 seconds  calculated along  In  salinity  as  rapid  value the  flow  profiles  i n the  s e t of  plots:  tc;  switched  was  t 9 0 and  t95  changed  by  90%  starting  at  except  at  flows  ml/sec). This approaches  time  w i t h the  final  change  change,  intake,  the  was  had  the  of  first  value  (.03  at  95%  intake  intake,  salinity  in s a l i n i t y  to reach  of:  the  final  the  multiplying  i s needed  plots  time-series  consist  change  which  by  rate  rapid  at  to  obtaining  at  of  second,  switching  time  D i s t a n c e s measured  For  per  curves  approaching  salinity. volume  of  determined  1 drop  a curve  consists  These  part after  salinity  at which step  at flowrates  three c e l l s  4 drops  response  after  the the  runs  salinity.  section  required  times  t=tc  lowed  the  to  characteristics  v a l u e s and  of  0.5  the  appendix.  linear  and  salinity  f o r each  i n the  graphically  tO  look at  these  horizontal  plots,  of  to  of  from  S  shape  calculated  done  output  exponential t a i l time  value,  The  in this  nearly  a  for  4.0  was  range  salinity  typical a  or  for a  flow rates  included  On  runs  in experiments.  calculated  but  of  axis  were  the  folfinal  converted  rate.  tank  a reasonable  successive readings at different larger  is  of  p a t t e r n s In the  flow depths  convection  tatik  change.  A steady  disturbance  at the  rapid  change  tube  through  on  the flow  (tO-tc)  show  that  The  a  and  of  has  been  switch  volume Into  switching  plots.  Several  and  At  their  over  of  2 and  7 ml  of  curve  The  curves  A plot shows  f o r each  is  Intake.  The  explains  the  plotted  data  takes  30  to  the flow  90  that  change  required  rates.  segment  plots  and each from  salinity  the response  flow  rate.  conductivity  time-series  of normalized  of computed  were  i n time  at d i f f e r e n t flow  for salinity  time-series  respectively  The  changes with  recorded.  at higher  relative  which  and  flow  a t the  value  the  the c e l l  the c a l c u l a t e d t e m p e r a t u r e s , were  of  the c e l l  ml.  the  fluid.  i n terms of volume  time  fluid  t o 0.66  the  before  but the  salinity  t o 95% of the f i n a l  normalized  the higher  2 t o 3 ml  flow,  0.28  conductivity ratios  check  entering  from  a s i n g l e curve end  reaching  volume  f i g . 2-5)  and  fluid  of time  and d i a m e t e r  are approximate  in salinity.  start  the l e n g t h  rate  replotted  (text  length  f o r steady  of the response  been  The  flow  salinities  have  the m i c r o - c e l l minimizes  moves b e f o r e  s e r i e s of c a l c u l a t e d s a l i n i t y  These  a  while  s e t of runs  and  on  volume  constant  between  shape  a next  ratios  The  f o r a change  and  point.  the f l u i d  be  in initial  seconds  In  point  through  depends  Interrupted  starting range  which rate.  flow  intake  (tO-tc)  should  briefly  slow  The  are also  section of  change  vs.  collapse  rate  marked  salinities,  p l o t t e d a t t h e same  rates.  the time  curves  flow  show  and  the  on  the  temperatures time-scale  to  effect.  flow  rates  ( 4 0 / 1 5 d r / s o r 0.16  f o r a change 12 t o  of 90%  19 s e c o n d s .  94  To  ml/s)  It  t o 9 5 % o f t h e new get a density  takes value  profile  of  fluid ting  i n the experimental the drop  i n h e i g h t between  the  cell  20  seconds  the  calculated  in  outlet.  the flow rate the f l u i d  I f the Datalogger  after  salinity  tank,  the intake  salinity  <Sc) w i l l  o r , assuming  level  multiplexer  i s moved  be c l o s e  the rate  mixed  layer  c a n be  smaller  used  and s l o w e r  since than  is started  height,  then  t o 95% of the change  yields:  S2  i t at a fixed  point,  the average  changes  those  observed  95  +  0.95CS2-S1)  = (Sc -  m o n i t o r i n g of the s a l i n i t y below  cycle  and  S i < S2:  which continuous  adjus-  i n the tank  to the next  Sc=Sl  For  i s s e t by  .05SD/.95  i n the tray a much over  slower  time  i n the test  or  are  in flow much  profiles.  96  ,  SALINITY (PSS)  iFO I —I  1  0.100/DIV  1  H H  1  1  1  2B 500  1  1  1  1  1  1  1  1  1  1  29 r 00  , — —  S a l i n i t y (PSS) CD  c  i  fD  o m  CO 1  CD  0  ;.  ro  0  ;•  .  0  <  I  fD  1  co  ca ro  3  fD  -J n>  ( /  ®  '••  •-+>  cT *  ^3  a,  0  w fD  cn  •  4>  ca ca 0- D_  \  1—• :  V  ui  ©  (D  0  (0 ID O  a.  \  >—•  cn  03 ft) 0  L6  SALINITY (PSS) &RL* I  CD. C  "5  0.100/DIV  f-rH  1  2D.  m  29.SB0 H  1  o  fD  m  00 !  ro  O  "5 0  I O fD  r o c n i  *—* i  00 c n  OJ M-  3  fD CO  TJ 0  (0  fD  o  c n ra  D_  T  r o  co o  E3 CO  m n *^  CJ  rx. UJ  cr>-  0 OJ  co  0 a>'  0) CO  ©  cn  -~i  L  f.  -si-  %r  c o  —• OJ \ V.  Q_ CO CU L CU  GO  e  o  CU O I 0 L 0  00  LO CD I C3 «—i I LO  •I-I  CO I CD  CU L D Ul  ro LU  my EI  H  h  >  1  005"BZ  1  1  1  1  h^-H  Aia/001-0  f—  h—I  i ring  (SSd) A1INI1VS  98  F i a u r e B-9.  M I C R O - C E L L TIME RESPONSE CELL01 2 5 - 1 0 / 0 . 4  F i g u r e B-10.  S 1 - S 2  =  MICRO-CELL TIME RESPONSE CELL#2 25-10-85/1. 1 - 1 . 2  2 7 . 8 5 - 2 9 . 0 2  1  2  3 Vol ume (ml)  4  5  6  F i g u r e B—11.  M I C R O - C E L L TIME RESPONSE CELL#3 2 5 - 1 0 /  FILES F1.7-F1. 10  S1-S2 = 27.97-29.13  1  2  3 Volume(ml)  4  5  6  B.6  Spatial A  resolution  t w o - l a y e r system  sharp  step  salinity  of was  in salinity  profile  from  the  micro-cells  used at  to check  the  how  interface  micro-cells  well  an  apparently  is represented  in  data taken at c l o s e l y  a  spaced  po i n t s . The  lighter  container bottom. image due by  fluid  and The  as  the  a narrow  withdrawing  3  was  drops  per  fluid  from  second  at a  (30  salinities spread can  0.5 8  over  runs  while  the  with  depth  between  either  a  3 mm mm  o b t a i n e d by  (figures the  lack  which  profile  s t e p s o f 0.4  were  showed dated  long  102  to  next  of c o n s t a n t or  period  i n which  each.  intake  the  sharpened  in  through  the  to a  depth  flush  the  depth. calculated plots  show  salinity.  the a c t u a l  oscillations interface salinity  2 to  steps  the  ). S e v e r a l  15-4-86 a s h a r p  thickness,  broadened  a t about  fluid  plotting  of r e s o l u t i o n  shadowgraph  I t was  time  to the  B-6,7  layers  the  slowly  syphoning  intake  at  different  enough  the  added  micro-cell  allowing  moving  the  line.  a reading after  ln depth  PSS  which  filling.  the  in  i n the  the c e l l  against  In the  visible  below  placed  slowly  lowering  interface  case.  first  then  light  through  were  was  rate,  profiles  indicate  the  fixed  s e c ) , then  Salinity  of  in several  micro-cell  cell  was  a point  syphoned  Measurements  taking  line  was  t u r b u l e n c e from  salinity.  and  salinity  interface  bright  and  then  lower  heavier fluid  density  to d i f f u s i o n  Fluid  of  a  This  shape  of  ln  one  i s seen  of  increases  in  SALINITY PROFILE 11-4-86 CELL SPATIAL RESOLUTION 30.0  103  SALINITY PROFILE 15-4-86 MICRO-CELL SPATIAL RESOLUTION 0  9. J  10  .  20  _  30  _  40  _  2  | f  0  SALINITY (PSS) i 1 1 i  2 G  .  30.0  5  I  1  I  50 60  .  70  J  CL.  UJ Q  1  80 90 100  .  110  -  120  _  130  _  140  .  150  _  flow  through  abt.  3  •*  e-  oell  dr/8ec  Figure B*I3. Resolution i n 2-layer system.  104  L  1  Therm i s t o r s  A P P E N D I X  1C5  APPENDIX  C l  C  THERMISTORS  T h e r m i s t o r use Thermistors  inside  each  accurate The  type  small in  were  micro-cell  calculation  bead  mounted  outlet  between  cell  b y some a m o u n t  of  outlet  error (some  to differ which  A.l).  of which  point  Figure  C-1  below  of a  shows  cell.  glass  the value  that  was  to  with  the  through  difference.  of  installed  i n the c a l c u l a t i o n  to determine  The  determined  of flow  develop  of the temperatures  combined  tee.  a t the centre of  on t h e r a t e  found  i n the flow at  i n the experimental  on t h e o u t p u t  were  T h i s was t h e n  (see appendix  a small  caused  thermistor  was u s e d  e x p e r i m e n t a l tank  intake  to enable  consisted  of the temperature  and t o check  The a v e r a g e  of the c e l l  fluid  of the f l u i d .  inserted  of f l u i d  from  depends  of each  was  through  temperature  time) a second  cell.  appendix the  thermistor  a n d on t h e magnitude  over  each  room  thermistor  thermistors leaks  and o u t l e t  the temperature  this  this  and d e n s i t y  i n these experiments  of the m i c r o - c e l l s  from  reduce  used  a single  and ambient  cell  of  i n the t i p of a h o l l o w n e e d l e , and p l a c e d i n  tank  the  the temperature  and i n the experimental tank,  and a t the i n l e t  Initially,  difference  to determine  of the s a l i n i t y  of thermistor  the tank  the  used  these  older  electrical a t the  inlet  at the inlet  and  of s a l i n i t y (see  the temperature  the d e n s i t y  To  of f l u i d a t  in the  A.2).  the micro-cell  106  with  t h e two  thermistors.  Figure  C-1 . T h e r m i s t o r s a t m i c r o - c e l l  Temperatures  are calculated  calibrated  thermistors.  resistance  RT  then  computed  T ( I n °C>  fora  of  given  from:  initial  cell,  between  + B*ln(RT)  tests with  significant  the c a l c u l a t e d  Electrical form  The t e m p e r a t u r e  resistance  + C*(ln(RT>> ] 3  -  273.15  Leaks In  each  the measured  ( i n o h m s ) a n d c a l i b r a t i o n c o n s t a n t s A, B a n d C i s  T = 1/1A  I.1  from  I n l e t and o u t l e t .  leaks  an e x t e r n a l  were  the thermistors  differences temperatures found  current  I n some  path  were  found  above  in several  and below  thermistors.  parallel  107  a t t o p and bottom  to the  the  of  cases cell.  These  leaks  Internal  path,  with  a resistance  fluid  or with  which  the  resistance  corresponds  to a higher  a leak  the  apparent  the  calculated  = 1/Rtrue  resistance  close  found  thermistors  were  thermistors  thermistors.  are  listed  output  from  the curve i s included  date,  used  and  20.281  reduced  20.338  leaks.  c a l i b r a t e d at temperatures  at temperatures  bath against  constants  of the needle  calibrated  was u s e d  to generate  f o rthese  thermistors,  Some t y p i c a l  examples of  program f o r the  a t the end of t h i s  and standard  108  error  u p t o 25 °C  recently  appendix.  of the  which the  re-calibrated  f o r the f i t , generated c a l i b r a t i o n  t h e maximum e r r o r  to  #31  by r e p l a c i n g t h e  use, the r e s i s t a n c e  fitting  ohm,  range  C.1 b e l o w .  thermistors data  t o have  o f 2000  For thermistor  from  T h e HP u t i l i t y - p r o g r a m F I T T E R  i n table  resistance,  c h a n g e by 0.3-0.4 P S S .  were  was d e t e r m i n e d  a new s e t o f c a l i b r a t i o n  leak  temperature:  change  originally  a c o n t r o l l e d temperature  Any c u r r e n t  resistance  PSS w o u l d  f o rextended  t o 0 °C. F o r l a b o r a t o r y  mounted in  were  the  c a n change the  parallel  1 9 9 6 ohm.  i n temperatures  which  of  1/Rleak  would  a t 20-30  Re-calibration The  as a  apparent  +  which  cracks.  value  becomes  temperature  discrepancies  thermistors  the c o n d u c t i v i t y  o f 1 megohm a n d a t r u e  °C a n d t h e s a l i n i t y  C.2  i n minute  true  For  with  i n temperature,  resistance  1/Rapparent  The  may v a r y  variations  contact-surface lowers  which  This  lists  constants,  estimate.  Table  C l Thermistor  Therm#  A =  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  1/CA  with  laboratory (used to  input  conversion  +  Bxln(RT) +  C*(ln(RT))» ]  -  273.15  calibration correction  voltmeter  datalogger  done  C =  3 .216646e-4  Recalibration  The  B =  0.928120e-3  Datalogger  digital  Constants  17  T (<*C> =  C.3  Calibration  d i d c o r r e c t the e r r o r was u s e d  still  from  a linear  an e l e c t r i c a l  but temperatures  d i d not agree  datalogger  determined  fordifferent  temperatures  returned  at the exit  of the f i r s t  leak).  linear  This  RT = 2 5 2 6 - N T * 0 . 2 5 3 7 3  when a  from the  thermistors.  N-number t o r e s i s t a n c e v a l u e  f i t f o r the r e s i s t a n c e values  operating  initially  in observations  where  #41,  b u t r e p l a c e d due  f i t was g i v e n b y :  RT = r e s i s t a n c e v a l u e NT  109  f o r a range of  by t h e r m i s t o r  cell  was  = datalogger  (ohm)  N-number  Many values. yields  of the t h e r m i s t o r s A second  a  order  better  RT  with  the range  resistance  of  u s i n g the c o e f f i c i e n t s  of  second  order  1 8 1 8 . 4 ohms.  #40,  After  with  Using  of  this  be  expected  from  :  N-number  t o an  of the l i n e a r  fit,  (2861) y i e l d s  a  the c a l i b r a t i o n  N-number but  with  resistance  constants f o r thermistor  to a temperature  o f 2 3 . 7 2 °C  while  2 3 . 4 4 °C.  implementing  observed  of  NT-numbers  values  o f 0.854221  1 8 0 0 ohms c o r r e s p o n d s  1 8 0 0 ohms c o r r e s p o n d s  1 8 1 8 ohms w o u l d  the  f i t  range  NT*4.771296E-6>  A thermistor  the  lower  of r e s i s t a n c e  a standard error  = 2527.62 + NT*(-0.261192 +  2 8 6 1 when  a slightly  f i t to the datalogger output  f i t over  1600 t o 2 5 0 0 ohms,  cover  the above c o r r e c t i o n s ,  temperatures  were  values f o r f l u i d  found  t o be  i n the tank  temperatures.  110 4  in  the values good  of  agreement  and f o r ambient a i r  T i t l e : T H E R M * 31 X-Variable: R C r e a t e d 07-04-85 O b s e r v a 11 o n Observa tion Ubservation O b s e r v a 11 o n Obse r v a t i o n O b s e r v a 11 o n Observa t i o n Observa t ion Observa 11on  ! :  9 •  •  3: 4: 5: 6: 7: 3: 9:  Y-Variabie:  T  x/ A  Y  \/  Y y Y Y Y Y Y Y  * = X == V A *  3 9 6 1 . 72 3 8 5 4 .75 3 5 8 0 . 44 3 1 0 1 .18 V = /\ 2 6 9 2 . o_>-> ._ \/ " ) 0 ' ' Q .38 A X *= 2 1 5 5 .63 X =•• 1 9 4 3 .39 \/ 1G91 .93 A "A  s  F I NHL  -== == == === === =-  1.953 2.B48 4.539 8.282 12.053 1b.009 18.157 21.097 25. 1  RESULT  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+ A 2 * 1 n  The  estimated  AM J= AI2]= A13 J =  parameter  values  after  OF  CURVE  (X)+A3*ln  7  FIT  (X)*3)-273.15  iterations'.  1 .03541 /e-03 3.033537e-04 1.520697e-07  Maximum e r r o r i s 1 . 2 2 0 3 0 9 e - 0 3 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  111  i s 8.155511e-04  Tjtie: IHE.RMI::. FOR* X Variable: R C r e a t e d 08- 1 3 86 Gbserva Observa Observa Gbserva Gbserva Gbserva Gbserva Gbserva Gbserva Gbserva  t ion t ion t Iori tion t ion 11on t ion t ion t i on 11on  i •  1 . '}  •  j •  4: IS: 7: 8: 9: 1 ii:  37 T  Y~\> r i ;b i e : a  X == 3694 . •' ii V /\ = 3 3 0 9 .9; X =* 3IIU6 . 2 \/ A "= 2 6 4 6 i V A "- 2 4 15 . 6 5 X =- 2 3 2 2 .26 X = 2 1 1 1 . <X -- 1 9 8 6 . 76 X == 1 9 1 3 .41 X ==• 1 8 6 4  T v  11  r  i  v  I-  i  /  Y  V1  V V 1 t  iiirii  9.96 12.612 16.971 18.483 19.682 22.27 24.022 26.091 == 2 6 . 0 0 2 ••  •• < =^  ••:! t ii i nf  b a t a s e t t i t l . ? : THth'M I S TOR* 37 Model used: 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  fh>- e s t i m a t e d  parameter  values  a t U-r 6  (' IJRVL  (XMHJ'ln  611  ( X ) ' 3 > -273. 15  it o r a t ions :  fH i J= 1 . U 1 6 6 8 7 e - 0 3 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  112  i s 8 . U 1623lle-U4  Dataloggers  A P P E N D I X  D  APPENDIX  In  D  this  used  DATALOGGERS series  at different  of experiments, times.  two t y p e s  The f i r s t  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 for  i n p u t from  an  HP-3497A  conductivity cases  D.l  Data  Acquisition  circuits  was d i r e c t e d  cells The  System  t o a n HP-9825  C/T  was u s e d  be u s e d  manually  with  individual in  both  a l l o w s a number  to designated  electronics  in  of  channels. this  of conditions  AM/CT  expected  experiments.  o r a t some p r e - s e t c l o c k  input  channels.  Analog  input signals  are converted  into  contains serial  number, t i m e ,  and numbers f o r temperature  conductivity.  converter The ting the D.l  and entered  sampling pin  This  cycle  line  into  t h e HP-9825  frequency  switching  f o r each  on t h e d a t a l o g g e r ,  by an  rate  A.M.  on t h e S e q u e n c e r  board  edge  the sampling  line  serial  interface.  i s s e t by connecboard  connector.  p i n of the Clock  115  output  v i a an RS-232  or clock  #32 o f t h e e d g e - c o n n e c t o r  the function  a digital  Is t r a n s l a t e d  a p p r o p r i a t e p i n on t h e C l o c k lists  of  the m u l t i -  cycles  and  the pre-set pattern  rate,  plexer  which  through  available,  ( S / N 1 7 0 ) was a d a p t e d f o r  were m o d i f i e d f o r t h e r a n g e  Triggered  When  i n range  The o u t p u t  an input panel  and c o n d u c t i v i t y  i n laboratory  output  Datalogger  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 temperature  Microsystems  computer.  Datalogger  the micro-cells:  Datalogger to  the d i g i t i z e d  f o rthe micro-cells.  An A p p l i e d M i c r o s y s t e m s with  was a n A p p l i e d  the t h e r m i s t o r s and m i c r o - c e l l s .  Applied Microsystems  use  o f d a t a l o g g e r were  cycles  board.  to  Table After  are initiated  automatically manually  by p r e s s i n g  The through four  pattern  different  added  on a ROM-chip  micro-cells  a n d up t o f o u r  D.2  triggered  "start".  which  the sequencer  cycles  i n the Datalogger.  additional  i n table  (MUX) b o a r d  o r c a n be  c a n be s e l e c t e d ,  the temperature  are listed  multiplexer  marked  of C and T channels  to determine  patterns  s e t on t h e c l o c k  the button  was p r o g r a m m e d  thermistors,  the  a t the rate  each  thermistor  at points  Up  with  inputs  to two  c a n be  i n the tank.  These  . D i p - s w i t c h e s S 1 - S 5 o f SW1 o n  are pre-set  to the desired  pattern  number: MUX# = 1 +S1 +S2 +S3 +S4 +S5 Here and be  and i n the f o l l o w i n g d i p - s w i t c h  S i = 2 -" closed  f o r 12-bit  Datalogger of  i f closed.  <1  SW1  in  The number o f c h a n n e l s i s s e t with  on on t h e S t o r a g e  Formatter  (FMT) b o a r d :  requires  are instrument  ( a p p r o x 1 mate 1 y ) , a n d  an a d d i t i o n a l  number  of c e l l s  MUX-SW  and  that  each  channel.  and e x t r a  FMT-SW1.  number o f t i m e s  i f open should  output  by t h e  switches  S1-S5  1 +S1 +S2 +S3 +S4 +S5  two c h a n n e l s  seconds  open).  data.  Converter  first  Si=0  D i p - s w i t c h e s S 6 - S 8 o f MUX-SW1  to the Serial  #CHNLS = The  patterns,  serial  temperature  time  and  conductance  The HP-9825 p r o g r a m s  prompt f o r  thermistors  and d i s p l a y  D i p - s w i t c h e s S6-S8 o f the data  number a n d  words a r e output  settingsf o r  FMT-SW1  s e t the  (once  i f a l l are  D i p s w i t c h e s S 1 - S 6 o f FMT-SW2 s e t t h e d a t a  output  rate i n  mi 1 1 i seconds: Time/bit For  12-bit  word  output  = 5.15*(1  S 7 o f FMT-SW2 116  +S1 +S2 +S3 +S4 + S 5 ) i sclosed  (10-bit  I f open).  Table Pin#  1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17  Table MUX# =  D . l . Clock Board  Edge  Connector  Function  Pin# 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  o/p 2 5 6 h o u r s o/p 128 h o u r s p a r a l l e l transfer pulse s e r i a l data output o/p 32 h o u r s o/p 16 h o u r s o/p 8 h o u r s o/p 6 4 h o u r s o/p 2 7 . 4 6 6 m i c r o s e c o n d s o/p 1 h o u r shift clock o/p 2 h o u r s o/p 4 h o u r s o/p 15 m i n u t e s o/p 2 2 5 s e c o n d s o/p 7.5 m i n u t e s t i m e c o d e I n c r e m e n t o/p  D.2. M u l t i p l e x e r  Pin Functions  Function o/p 3 0 m i n u t e s o/p 5 6 . 2 5 s e c o n d s o/p 2 8 . 1 2 5 s e c o n d s s e r i a l data Input o/p 1 1 2 . 5 s e c o n d s o/p 1.75 s e c o n d s o/p 3.51 s e c o n d s o/p 7 . 0 3 o/p 1 4 . 0 6 2 5 o/p 4 2 9 . 1 5 3 5 2 2 m i c r o s e c o/p 6 . 8 6 m s e c o/p 3 . 4 3 m s e c cl'ock r e s e t p u l s e o u t clock reset parallel transfer Vss Vdd Vss  Input Channel  Cycling  Pattern  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2 0  CHANNELS: T1-C1-T6  x x x x x x x  x  T2-C2-T7  x x x  x x x  T3-C3-T8  x x  x x  T4-C4-T9  x  x  x  x  x x  x  x  x  x x  x  x x  x  x x  X X X X X X  T12  x  X  x  T13  X  x  x  x  x x x  X  x  X X  x  x x  X X  x x  x x x x  x x  x  x  x  x  x  x  x  x  x  x  x  x  x  x  x  117  x  x  x  T14  x  x  x  Til  x  The  datalogger  collection during the  of  the  slope  were the  made  to a to  cell  on  still  became  HP-3497A The  used  HP-3497A in  micro-cells last  two  slope  micro-cell circuit. cells  on  was This  but  eliminated Small  relative  as  the  to each  only time  any  0.1  the  response  after syphon  PSS.  units, Several  between  which efforts  switching  in a  conductivity readings  known  cause.  on  occasion.  characteristics  for simultaneous When u s i n g by  transients  the  more  The  r e p l a c i n g components  available  some c r o s s - t a l k  shifting  found  some  System  c o n t i n u o u s l y powered  when t h e  a  of  the  profiles  this  caused  by  the  in  system,  the each  switching cells  operating  collecting  experimental  outlets  the  of  was  separate c o n d u c t i v i t y  between  individual  It  the  which  was  frequencies. data  micro-cells  were  were  seen moved  other.  HP-datalogger  well  as  averaging  further  was  or  delay  but  experiments.  The  which  output,  obtain data  caused  shifts  occur  the  10  by  i n c r e a s i n g the  reduced  by  to  reliability  Acquisition  flow  were  conductivity circuit.  o c c a s i o n a l l y without  to  from  the  System  and  data  from  the  determining  the  output  almost  Data  while  stable output,there  of  noisy  conductivity cells  very  variability  reading  simultaneous  gave  up  by  nearly  However,  by  and  the  a l l t h e r m i s t o r s and  times  improve  and  simplified  experiments.  jump a t  datalogger  D.2  flow  i n the  did  corresponds  from  circuit  jumps  N-numbers  to  data  temperature  spurious  greatly  reduced  allowed of  rapid  the  much h i g h e r  sampling  multiple readings  noise  118  i n the  data.  of  frequencies each  sensor,  Membrane Salt Flux Calibration  A P P E N D I X  119  APPENDIX  E  E.l  and  Salt The  MEMBRANE F L U X  volume  surface salt  simulated  in  a porous  between  two  tray. the of  The  water  The and in  was  method  salt the  of  c e n t e r of  since is  the  the  flow  the  the  was tank  layer  was  flux  a l o n g and  the  partly  the  filled  water mounted  of  about  across  s u r f a c e of with  magnitude  is detailed  calibration  t a k e n as  unit  sea  of  the  fluid  in  a  mixture  the  volume  in section  runs,  to  average  the  reduced  time  and  f o r the  bottom. by  The  the  unit  low  2.6  i n which  hor1zontal,the salinity  inflow  per  of  was  water.  extends  high s a l i n i t y tray,  was  water  perforations  cm  with  membrane  kept  with  4 per  level  of  sea  T h i s m e m b r a n e was  board,  tap  of  a percolation  for estimating  through  tank  by  tray.  which  filtered  mixed  to the  in a  suspended  In a s e r i e s  the  freezing  uniformly at  used  flux  text.  bottom the  and  to the  of c i r c u i t  experimental tank, sea  pressure  experiments  spaced  tray  driving  due  membrane  layers  diameter  and  flux  these  through  1 mm  flux  CALIBRATION  of  fluid  whole  net  at  tank  salt  salinity  a r e a . I t was  the  flux  return  expressed  as : Bn Bn=  net  Vw=  volume  Si=  salinity  Di=  density  Vl=  volume  A  = area  salt  of  flux  flux  = Vw.(S2.D2-S1.Dl) = dlSl.Dl1.VI 1000 d t 1000 A (g/cm /s) 2  (cm /cm /s) 3  2  in tray(2) in tray(2)  of  fluid  the  tray  and and  i n the bottom  tank(l)  (g/kg  tank(l)  (g/cm )  tank  3  (cm )  (cm ) 2  120  3  or  PSS)  (E-l)  The  flux  density  i s driven between  rather,  the f l u i d  the weight  a column  by t h e p r e s s u r e caused i n the tank  o f a column  o f t h e same h e i g h t  by t h e d i f f e r e n c e  and that  of f l u i d  i n t h e edge  i n the tray  In t h e t r a y between  = pressure  Di=  density  tank  and  3  = effective  = 981  fluid  formed  space  slowly  salinity  a surface well  layer  E.2  Flux To  of tray  slope.  flux).  2 mm  in  The  salinities  salt  tray from  The  i n the  the tray  fluid  the  mixed saline  tray,  which  the surface i n the tray systems  became  less  (and thus and i n the  with  and the e f f e c t i v e  the  same  height  height reduced  by 2  used mm.  experiments of the s a l t were  of c a l i b r a t i o n flux  and depths  and  rises  2 mm  as 2-layer  and temperature  a series  which  Fluid  layer,  e s t i m a t e the magnitude  conductivity  tank  without disturbing  p r e s s u r e s was  calibration  flow  of about  were a p p r o x i m a t e d  i n the upper  compute  between  Increases i n s a l i n i t y .  p r e s s u r e and a s s o c i a t e d space  (cm)  as the r e t u r n  n o t be m i x e d  edge  to  height of f l u i d  stratified i n the tank  the  (cm/s*)  i n t h e edge  layer  can  (E-2)  <g/cm )  h  stably  tray:  2  = gravity  fluid  of  (g/cm/s )  g  The  or  and that  P = (D2-D1).g.h P  in  was v a r i e d of f l u i d  flux,  collected  experiments by u s i n g  In the t r a y .  121  time-series from  tank  without a  different The m e n i s c u s  data and  bottom starting i n the  edge the  space fluid.  made  It d i f f i c u l t  Shadowgraph  uniform  distribution  near  tank  the  triangular small  downflow  of c o n v e c t i v e motions where  widening  under  the  slow  upward  motion  i n the  side  walls  cannot  be  integrates show any  over  salt  flux  edge  space  Vertical  calibration between  salinity  of  of  tank  be  may  fluid taken  a  along  tank  and  to the  sampled a  the  tank  except  appear  reduced  Is caused and  The  the  of  dye  the  taken  to  due  of  in  E-1  possibly  estimate  image  the E-3).  membrane to  incom-  indicate centre  the  not  several  and  the  the  the  tank.  below  at a p o i n t near  at  did  during  profiles  the very  shadowgraph  injected  just  in a  by  effect  centerline  bottom,  reasonable  i n the  tray,(figures  found  spill.  nearly  the  data  of  show a  similar  but  height  runs  tray  in a cross-section  local  as  the  since  from  exact  This  Any  tank,  plotted  the  of  space.  the  runs,  close  mixing after  salinity  the  edge  g r a d i e n t s were  i n some c a s e s  plete  were  motions  with depth.  distinguished  width  profiles  these  end-walls  mean c i r c u l a t i o n  Salinity  and  the  the  p a t t e r n s d u r i n g these  end-walls  section  to determine  that  of  average  the for  tank. The  initial  similarity  l n the  salinities. the  ces  method:  of  the  values  by  the by  the  are  rate  the time  taken  runs  d i d show  time-series f o r volume  e x p r e s s i o n s formulated above,  approximated  density  of c a l i b r a t i o n  shape  Estimated  with  divided  series  of change  fluxes  using a  in salinity  difference  between  interval.  Interpolated  as  the  average  122  plots  of  general  calculated  were  obtained  finite  differen-  and  in density  successive  of each  a  time, pair.  was  observations salinity The  and  volume  fluxes the  and p r e s s u r e s  above  obtain a  expressions  a single  doubling  too  high  results single tray  found  flux  i n one s t e p a  bottom  will  first  by u s i n g  curve  be c l o g g e d  A new  ventilation membrane  successive  method  of experiments flux  to inspect  versus  This  precipitation,  5 micron  pore  size  was  through  After  adjusting  and a d d i n g  before  a 0.8 each  the s a l i n i t i e s , biological  or 5 micron  activity,  filter  calibration run.  into  were  combined i n a s i n g l e  shows  with  some  estimates  were  calibrations  flow  experiment  E-2, a l s o The and the  following  were done  was  used  before through  not  of  values,  form  a The  which  filtering  be c a u s e d  by  from the  flux  and  filter.  amount  E-3) .  volume  flux  print-out  This  for salt  flux  volume  first  the combined p l o t s salt  these  Membrane the  of  pumped  from  (figure  results  the  reservoirs  plots  and a f t e r  the time-series  123  micron  a small  of fluxes.  a typical  o f membrane  a 0.45  graph  t o compute  pages c o n t a i n  calibration plots  plotted  installed in  the tank  repeatable  f o r a range  and a curve  in text)  calculated  scatter,  obtained  flux  point  t h e f l u i d s were  The s a l t  experiments that,  The  and by d u s t  a n d a l l f l u i d s were pumped  through  a  system.  with  to control  There i s  membrane,  could  tray,  bleach  to  pressure.  in spite  cartridges.  into  runs  since  did  the  and d i s c o l o r e d  a c t i v i t y or mineral  laboratory  values  f o r the system.  this  o f volume  was d i s a s s e m b l e d  to  for  these  be t o o l o w i n t h e n e x t .  series  water-purifying  organic  plotted  c a l i b r a t i o n graph  characteristic  through  were  of v a r i a b i l i t y  from  appeared  by s u b s t i t u t i n g  slope (figure  estimates. of the  plot  of s a l i n i t i e s  flux  versus  data and  pressure.  F i g u r e E - l . MICRO-CELL  TIME SERIES  PLOT  Membrane f l ux c a 11 brat. 1 on:  26-2-86  55.0-1  CO  s a l i n i t y i n the tray  -P  c ro  o CO  30. 0 i  s a l i n i t y i n the tank  5.0 30  —r—  90  150  —r :I0  Time (min) 1  270  F i g u r e 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 l o p e flow experiment.  126  D E S C R I P T I O N OF  EXPERIMENTS  A P P E N D I  127  ZXi  TT  APPENDIX  This slope  F  append IK c o n t a i n s  flow  salinities during  experiments. of f l u i d  measured  from from  membrane  determined,  a brief Included  i n tank  the i n d i v i d u a l  salinities  the  D E S C R I P T I O N OF  experiment,  salt  features flux  values  from  the  starting  features  observed  values  of  tray  collected  data,  velocity  i n the slope  flow,  the estimates  time-series plots  and the l i n e p r l n t e r  special  individual  angle,  the t a b u l a t e d  a t the times  ments  of the  are the slope  and t r a y ,  the manually  dye  description  EXPERIMENTS  that  flow  of s a l i n i t i e s  output  datalogger.  1.7.8  maxima  velocities  during  o f t h e raw d a t a  the  and  of  were  expericomputed  F. 1  In was  the 3.3  mm  at  first  slope  degrees  and  the  filled  r a i s e d end  mm  at  to a  of  fluid  of  15  ppt  was  on  shadowgraph before  Velocity  color slide  Salinity  sequences were  t=ll-38min  obtained  mixed  profile  a  dye  adjusted to  17  mm,  salinity  slope  a  data  i n the  the  tray  points  (figure  tray  34  and  mm,  while  flow  became was  determined  streaks. m i c r o - c e l l data  taken  F-2 ) . ' Q u a s i - i n s t a n t a n e ou s '  second  tank  levelling were  7 was  between  slope  flow  t r a y was  The  edge  angle  order  curve  F-3)  and  through  at  profiles  the  profile  s u b t r a c t i n g the  f i t  points:  with  under  the  slope  the  about  filling  p l o t t e d from  layer (figure  profiles  Micro-cell  of  to  S(instant)= The  under  A bottom  i n the  of  (fig.  fitting  i n the  equal.  maxima  profiles  over  the  added  bottom  deep end.  height  the  the  levels  tank  the  to keep  completed.  from  63  ppt  visible  points  and  the  i n the  59  tray  were  depth  of  and  port#6  the  experiment,  fluid  ml  from  flow  with  800  14  #1  S L O P E FLOW E X P E R I M E N T  (figure  rise were  tank  F-6)  show a  in s a l i n i t y also  along  (figure  F-4)  taken the  F-5),  gives  S(profile)-  of  to  a  0.6-0.7  check  bottom but  slope  the  slope  and  S(fit)+ S(tl) flow  detail  of  PSS. distribution along  time-series plot  insufficient  depth  about  the of  the  of top  these lateral  distribution. Table and  driving  were as  Fl  lists  pressures  measured,  described  the  and  i n the  the  computed  values  at  times  those  volume  text  and  (section 1Z9  of that  salt 2.6).  salinities, slope  flow  fluxes derived  densities velocities from  them  Table From  F1. S a l t f 1 u x e s  dye  taken  seen  in siide#  flow  velocities  12-13  -  sloperun#l  17-19,20-21  (min)  t == 25  30  velocity  (cm/s)  v  0.401-0. 519  salinity-tray  (g/kg)  S 2 == 5 7 . 9 2 6  57.676  from  C#3  salinity-mixed  layer  S I == 2 0 . 5 4 1  21.395  from  printer  max.  a t time  and  temperature tray  =  layer  driving volume  density  pressure flux  flux  0.510  T - t a n k = 21 .67  CO  d e n s i t y ( s i g m a - t ) D2 ==  mixed  salt  :  (cm/sec) (g/cm /s) 2  Dl  :=  P ==  B =  21.64  41.867  41 . 6 8 3  13.357  14.010  89.50  86 .87  Vw := 2 . 9 5 e - 4 1.780e-5  130  (lineprinter  2.82e-4 1 .694e-5  time)  data f i t  thermistor Unesco M  C#2  #526  Eq.of  State n  g*h*(D2-Dl)/1000 from  f ig.2-15  F i g u r e F - l . MICRO-CELL TIME SERIES SLOPE FLOW EXPERIMENT  PLOT #1  60.01 : : « z  co  salinity  in tray tit  i i  t  II  HI  CO  a co 35.0-  salinity  i n tank  (includes p r o f i l e s )  Time (min) 1  10.0 20  "60"  100  140  180  F  17.0  SALINITY PROFILE S L O P E FLOW E X P # 1  -2  Salinity 1  I  (PSS) 1  1  1  Q  5  I  2  I  I  I  2  .  I  PROFILES IN PORT #6 t l l - 2 7 min g o i n g down- 2 min i n t e r v a l e e  t=30-38 g o i n g up- 1 min i n t e r v a l e  132  0  1  time  (min)  Figure F-3. Time-series plot of profile points.  SALINITY PROFILE S L O P E FLOW E X P # 1  Figure F~4.  16.90 4 -J 0  Salinity 1  CPSS)^  3  17. 7 0  0  L  J  I  • P r o f i l e a i n port #8 t = l l - 2 7 going down (o) t 30-38 going up e  (x)  S <profile)-S (actual) - S ( t ) + S(t0) S(t) = 14.1185 +U.2S736 -t*.0021194) (2nd order f i t t o mixed l a y e r data) (S(t0)- S ( t - l l )  134  32.01  Xs5 s a l i n i t y at 2 mm above bottom o= s a l i n i t y at 4 mm below tray samplinq interval 3 minutes  SLOPE FLOW EXP#1  &=r using 2nd order f i t (fig. F~6).' 'quasi^inetantanous' points  near tr<  near bott om slope PORT  0  #8  ~ i —  #7  n—  20  #6  i—•  Figure F~5. Distribution.  #5  n—  40  Distance  §A n— along  #3  n—  80  60  tank  (cm)  31.5  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  29. 5ON  co CO CL  •rt  c 1 (  o  LO  X #8  27.5 80  S(t) =34. 2406+t (-0. 23219+t*l. 87359e-3) — r  90  100  Figure F~6. Time-series plot of distribution data  110  time (min)  F. 2  S L O P E FLOW E X P E R I M E N T #2  In and  slope  flow experiment  the f l u i d  and  below  the tray  6 5 mm a t t h e d e e p e n d .  micro-cells Profile and  #1  data  taken  linear  l n port  micro-cell was  used  maxima mixed  at fixed  depth  f o rf l u i d  #6 a t t = 3 9 - 5 6  F - l l ) after  taken  the  flow  i n the mixed  were  was u s e d in  layer  the  min  F2.  dye  F-9)  start.  least  (figure  A  t h e second F-8,F-10)  profiles.  0.4 t o 0.5 p p t a b o v e  velocities  from  photos  :  Salinity  those  start  (clock  time):  on photo(mm/1Osec):  velocity  Tray  fluid  max. ( c m / s e c )  data  were  S a l i n i t i e s at other  volume  only times  - sloperun  7-10  : ports(cm)/photo(mm):  moved  flow  Flow  #  after  scale  i n the  :  taken were  #2  14-17  55 ( 1 5 : 2 5 )  125 ( 1 6 : 3 5 )  20/74  30/81.8  16  8.5  0.43  0.312  at the start estimated  and end ofthe  from  conservation  and s a l t : V1*S1(t)*Dl(t)+V2*S2(t)*D2(t>=  the  tank.  layer.  Photos  ln  with  min ( f i g u r e  simultaneously with  to obtain the quasi-instantaneous  i n the slope  Table  run.  f i t to data  was 3.8 d e g r e e s  was 7 mm a t t h e s h a l l o w e n d  a n d #2 t o o b t a i n d a t a  were  angle  T h e AM/CT d a t a l o g g e r  a t t =112-130 min ( f i g u r e  squares  of  depth  #2, t h e s l o p e  which  V I a n d V2 w e r e  salinity  corresponding  the tank  i n the mixed densities.  layer  and tray  and i n the tray  The a r b i t r a r y  137  volumes,  function  G(t)  SI and  S2  a n d DI a n d  D2  G(t)  represents  the  salt  loss  t o the bottom  over  the p r o f i l i n g  from  data  Table and  F4  time.  of m i c r o - c e l l lists  Table #3,  F3  was  shows  salinities,  fluxes  linearly  proportioned  the s a l i n i t i e s and V2=26.5 densities  a t the times  that  computed liters.  and  flow  pressures velocities  determined.  Table  F3.  Salinity  of tray  -VC#3  fluid  #2  - sloperun  RT#22  RT#40  1950  1883  T(deg.C)  S(ppt)  start  2.217  t = 55  ( e s t i m.)  55.21  t=125  ( e s t i m.)  52 . 42  end  Table At  arid  w i t h Vl=7.08  the computed  the d e r i v e d s a l t  were  flow,  F4.  time  2.026  1956  Saltfluxes  (min)  Sal.-mixed  and  ttprtl=  layer  1889  slope  55  flow  2 2 . 37  125  from:  25.006  C#2  S2  =  55.21  52.04  estim.(table  T-tnk  =  21.286  21.585  t h e r m i s t o r #526 Unesco  D2  =  39.890  37.652  dens  mix.layer  Dl =  9.794  16.754  pressure flux  sloperun#2  -  15.694  dens(sigma-t)  volume  52 . 04  velocities  tray  driving  57.64  SI =  Sal in1ty-tray temp(deg.C)  2 2 . 45  (cm/s)  membrane  salt  flux  max.flow  velocity  print-out F3)  polynom.  P =  94.48  65.60  Vw=  3.17e-4  2.00e-4  from  B = F * S 2 * ( D2 +1) 1000 1000 (cm/sec)  B =  1.820e-5  1.712e-5  v =  0.43  0.312  13B  (D2-D1)/1000*g*h figure  2-15  Figure F-7. MICRO-CELL TIME SERIES PLOT SLOPE FLOW EXPERIMENT #2  Figure F~B. Time-seriee and lineor f i t  time (min)  Figure F-9. y  SALINITY PROFILE 6-3-86 SLOPERUN §2  141  25. 80  24. 70-  23. 60  Figure F _ 10. Time-series and linear f i t  Figure a  F-ll.  SALINITY PROFILE 6-3-86 SLOPERUN #2  23.60 SALINITY (PSS) * t ' ' ' ' ' ' i  10  2  f  4  <  7  J  E E  dl O  20  J  30  J  40  J  0  2  5  Q  0  i i i t t » t i • ' • •„ "  143  F. 3  SLOPE FLOW EXPERIMENT  In The at  slope depth  flow  below  experiment  T h e AM/CT D a t a l o g g e r  #1 f o r p r o f i l e s , w i t h salinities  temperatures from  briefly been  i n the tank.  re-established from in  itself  the shallow  the previous  from  this  point  Sketches  cells  are included  taken  depth  (figure  F-14>.  the  bottom.  the  distance  flow  flow  were  A linear  F - 1 3 ) was u s e d  rise  These  computed  moved flow  the tank  which  might  The s l o p e  starting  cell,  slowly  when  towards  patterns  was have flow  a t about also  i n the shadowgraph  disappeared  taken  to obtain show  30cm found  upslope  the s t a r t i n g the  shallow  and the double  flow  #8 a t t = 1 0 5 - 1 2 9 m i n computed  layer during  the c o n v e c t i v e l y mixed  o f 0.8 P S S s t a r t i n g  i n photo  velocity  sequences. 144  from  profiles  l a y e r and  a t 1 2 - 1 8 mm were  data  the p r o f i l i n g  'quasI-instantaneous'  i n the slopeflow  d y e moved  i n port  f i t to salinities  i n t h e mixed  lnsalinity Maxima  the f i l l i n g .  was s e e n  uphill  data  (figure  sharp  for  i n the text.  profile  at a fixed  patterns  A c o u n t e r - r o t a t i n g flow  of the t y p i c a l  the s t a r t .  the tray  #526  i n t h e t r a y were  w i t h i n one m i n u t e ,  of the down-slope  end.  after  during  experiment, This  thermistor  the experiment,  circulation  flux  end.  point.  Salinity  to start  t o remove  by uneven  with micro-cell  o f m i c r o - c e l l #3.  the tray  stirred  e n d a n d 51 mm  a t 15mm b e l o w  l a y e r and with Salinities  readings  filling  formed  was 2.2 d e g r e e s .  was u s e d  m i c r o - c e l l #2 f i x e d  In t h e mixed  volt-meter  After  angle  t h e t r a y w a s 2 0 mm a t t h e s h a l l o w  t h e deep e n d .  for  #3 t h e s l o p e  #3  measured  a  above from  Table min  F5.  after  dist. time  dye  Flow start  (clock  from  moved on p h o t o  Table  velocity  F6.  mixed  =  t ime  60  (mm): :  (cm/sec) :  Saltflux  1inepr inter  photos  time):  between photos  slopeflow  tray  velocities  and s l o p e f l o w 60  #3  - sloperun  (10:30)  135 ( 1 1 : 4 5 )  11-11.5  10.5-11.0  11.5  12.5  0.259-0.270  0.227-0.238  velocity  #3  - sloperun  135  min.  after  start  layer  SI  = 21 .561  29.106  (PSS)time-series f i t  salinity  S2  =  54.583  52.695  (PSS)tIme-serles  T- t n k  =  21.420  21.877  CO  (sigma-t)Unesco  temperature tray  density  D2  =  39.366  37.775  tank  dens i t y  DI  =  14.192  19.781  pressure volume  P = 81 .50 flux  Vw  =  membr.salt  flux  B =  slopeflow  max .  V  thermistor  M  (gr/ct/s )  2.50e-4  1.67e-4  (cm/s) f l u x  1.418e-5  0. 9 4 6 e - 5  gr/cm2/s  145  0.2 27-0.2 38  #526 eqn.  M  58.25  = 0.259-0.270  f i t  2  cm/s  from  cal.plot  photos  SALINITY PROFILE igure F-14. 1 1 - 3 - 8 6 SLOPERUN #3  PORT #8 >5.80  SALINITY  (PSS)  2 6  .  8 0  27. 80 i  f tual  profile*  adjusted p r o f i l e s by linear f i t t o data from f i x e d  depth  148  F.4  S L O P E FLOW E X P E R I M E N T  In  slope  The  depth  at  the  flow below  deep  micro-cells voltmeters of  fluid  the tray end.  #4, t h e s l o p e  were  T h e AM/CT D a t a l o g g e r  used  was 5.2  with  t h e tank  micro-cell  e n d a n d 10 cm  was a g a i n  used  #3 t o m o n i t o r  the s a l i n i t y  F7.  Salinities  mi n  —  VC#3  i n the tray  - sloperun  RT#22 -->  TO°C>  #4  SCppt)  30  2 .012  2000  21 .746  52.381  15:23  53  1 .982  2006  21 .662  51 . 5 8 5  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 . 5 5 0  49.480  16:55  205  1 .899  2013  21 .564  49.226  17: 25  235  1. 880  2007  21 .648  48.566  Salinity  profiles min a f t e r  the mixed  layer  were  plotted  the start, (figure  F-16).  bottom  o f t h e tank  at port  #7.  Three  data  were  a t about  points  2 mm a b o v e  averages  were  from d a t a  corrected  the  corrected  with  thermistor, and d i g i t a l  15:00  t=97-131  degrees.  i n the tray.  t i me  port  angle  w a s 2 cm a t t h e s h a l l o w  #1 a n d #2 a n d w i t h  Table  in  experiment  #4  Data  were  in rapid  the bottom, (figure  149  i n port  #5  f o r the s a l i n i t y  #8 t h r o u g h  taken  plotted  taken  also  over  change  taken  along  #2 a n d b a c k  to  port  succession  in  each  and the pointwise F-17>.  time-  The dye of the  slopeflow velocities  carried sampling average  units  At  ports  i n the tray  of v e r t i c a l  F8.  clock  measured  a l o n g by t h e b o t t o m  on a s c a l e  Table  were  along  lines  =  f o r scale  1 4: 5 0  video  footage of  u s i n g t h e 10 cm where  a t the back  the front  Flow v e l o c i t i e s  time  flow,  from  visible  (spaced  spacing  or  taking  5 cm) a n d t h e  of the tank.  and  saltfluxes -  s l o p e r u n #4  15:21  16:12  16: 48  1 i n e p r i n t e r t = 20  50  102  138  min  tray  51 .585  50.175  49.3445  ppt  9.557  12.720  14.847  fluid  mixed  S2= 5 2 . 7 0 8  l a y e r S l = 7.011  hr:m i n  j ppt  tank  temp.  T = 21 . 0 5 3  21.392  2 1 .639  21.715  tray  dens.  D2 = 3 8 . 0 3 3  37.068  35.911  35.252  s i gma-1  tank  dens.  D l = 3. 2 9 5  5. 138  7 . 464  9 .049  s i gma-1  103. 4  92.09  84.83  °C  pressure  P =  volume  Vw= 4 . 0 0 e - 4  3.50e-4  3.00e-4  2.67e-4  cm/s  B = 2. 1 9 e - 5  1 .87e-5  1 .56e-5  1 .36e-5  g r /cm / s  salt  flux  flux  max.f1owspeed  112.5  = 0. 45-0,49 0. 45-0.49 0. 39-0.41 0. 33-0.36  150  gr/cm/s  2  2  cm/s  Figure F-15. S A L I N I T Y P R O F I L E SLOPE RUN #4 Port #5 t= 97-111 min  K-AS=0- 2 4 — ^  151  FiqureF-16. S A L I N I T Y PROFILE SLOPE RUN #4 Port #5 3 <  4  SJa l i n iLt y  t-ll1-126 min  (PSS) • • • i 3 . 9  1  1  L  14. 4 I  Q= actual C#l data Cueing 1 therm)  10  X= linear f i t to mixed lay«r data 20  —= adjusted p r o f i l e  30  40  50  h=16mm 60 >k  Sm=13. 593 152  1 3 - 6 - 8 6 SLOPE RUN #4:  S A L I N I T I E S ALONG BOTTOM S L O P E pointwiee  time-adjusted  Figure 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.  t=148-173  F.5  S L O P E FLOW E X P E R I M E N T In  the  t h i s experiment  depth  new  2 cm  at the shallow  m e m b r a n e was  were  connected  the slope  tray  and  Starting  13 p p t  i n the  F9.  Salinities min  —  again  10 cm  5.2  degrees  and  a t the deep end.  Micro-cells and c e l l  salinities  were  #1  #3  and  was  52 p p t  tank.  i n the tray  VC3  during  sloperun  RT#44  RT#23  T- a v g  #5  S ( K = 178:  1 .9961  2497  2059  2 1 .644  52. 030  12: 40  40  1. 9659  2496  2058  21 . 6 5 6  51 . 1 10  12: 5 0  50  1 .9336  2496  2058  21 .656  5 0 . 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 . 9 4 8  13: 30  90  1 .8610  2494  2056  21 . 6 7 9  47 . 9 6 7  13: 40  100  1 .8449  2494  2056  21 .679  4 7 . 492  14: 0 3  123  1 .8160  2496  2057  21 . 6 6 3  46. 663  14: 20  1 40  1 .7971  2496  2058  21 .656  46 . 1 16  14: 5 0  170  1 .771 1  2496  2058  21 . 6 5 6  4 5 . 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 . 6 0 1  43. 934  17: 0 0  300  1 .7111  2500  2063  21 . 6 0 0  43. 668  p r o f i l e s from and  #2  i n the  30  F-19)  A  used  12: 30  Salinity (figure  end and  t o t h e AM/CT d a t a l o g g e r  t h e DVM's f o r t r a y .  t i me  was  i n s t a l l e d i n the tray.  with  Table  angle  #5  in port  data #3  taken  in port  #5  a t t=80-97  a t t= 125-141 min a f t e r  154  the  min start  (figure in  F-20) were  simultaneously  well  Another  where  profile  between  tank  the  videotape  flow  (figure  part  footage, layer  clock  formed  time  upslope  a  o f 9 t o 15 0.3 P S S .  i n t h e edge  space  were  the place  measured  and s a l i n i t y  Flow v e l o c i t i e s  includes  recorded  footage o f where  the  itself.  i nthe flow  t = 13:11  This from  times  of the time-series data  Table F 1 0 .  by about  taken  run.  i n t h e t r a y a t those  interpolation  region  show  o f i n j e c t e d d y e were  of this  and thetemperature  and  data  They  2-12 i n t e x t ) .  established  maxima  flow  increases  images a n d m o t i o n s  first  Velocity  layer salinities.  was p l o t t e d f r o m  during  by s u b t r a c t i n g the change  layer and a slope  c o u n t e r - c e l l which  bottom  mixed  thes a l i n i t y  and tray  Shadowgraph  instantaneous  taken  mixed c o n v e c t i v e  mm t h i c k n e s s  on  made  from  of fluid  were  i n t h e mixed  obtained  of calculated  and s a l t f1uxes -  200(15:20)16:21  videotape  by  linear  values.  s l o p e r u n #5  16:42  hr :min  p r i n t e r t ( p ) = 71  200  261  282  min  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-tnk =  21.568  2 1 .843  21 . 8 6 3  21 .872  deg. C  tray  d e n s D2 =  34.991  31.707  31.112  30.982  s i gma-1  tank  d e n s D l = 9.831  16.510  17.740  18.123  s i gma-1  81.45  49. 20  43.29  41 .63  2.50e-4  1.35e-4  1.25e-4  1 . 22e-4  1.267e-5  0.623e-5  0.567e-5  0.551e-5  pressure  P =  vol.f1ux  Vw =  membr.flux B = s1 o p e f l o w  g/cm/s  cm/rain gr/cm /s 2  v = 0.47 4-0.665 0.269-0.279 0.248-9.312 0.259-0.27 3 c m / s i  155  2  Figure F-18. MICRO-CELL TIMESERIES 18-3-86 SLOPERUN #5 d=2-10 Kl 2=1878, 1793 new membr f  24.0n CO CO Q-  Ln  o  CO  14. H  4.0  30  120  Time (min)  210  300  Fi  0  aure f _ i g :  1 6 > 5  SALINITY PROFILE 1 8 - 3 - 8 6 SLOPERUN #5  SALINITY (PSS)  17.5  18.5 i  i  POUT  iS  t»80-97 (13.20-13i 37) x " actual p r o f i l e data o - f i x e d depth backgnd £ - oorreoted p r o f i l e (pointwiee d i f f . )  10 _  n.  UJ  o  30 _  40 _  50 _  60 _  1  5  7  Figure F -20  : SALINITY PROFILE .18-3-86 SLOPERUN #5  158  F.6  S L O P E FLOW E X P E R I M E N T In  and 57  slope  flow  the depth  experiment  below  was s e e n  This  convergence  slope  flow  during  in  Any  fluid  centerline, port  mm tank  about  During was just  higher below  the u p h i l l  flow  along  height  experiments.  where  the  cell  experiment  or a slight  was u s e d  a t port  fluid  t<printer)=  the point  of this  with  part  1 cm b e l o w  down-  which  formed  was t o c h e c k f o r the length  ofthe  bow i n t h e s i d e s of the heavier  o f the mixed  #2 a t p o r t  #7 n e a r  of  fluid  t(vldeo)+  the f i r s t  along  #2 n e a r  to the  the shallow end, occasionally  there.  11:10 t o 11:20 t o a h e i g h t  timer  are printed  layer  t h e deep end b u t  o f 10 P S S w a s a d d e d  data  micro-cells  m i c r o - c e l l #1 was u s e d  the s a l i n i t y  between  The v i d e o  a l l three  the tray:  to determine  t r a y was f i l l e d  time-series  near  the local  the center,  to the tray  and tray.  t h e t o p o f t h e mixed  of the previous  layer salinity  i n the upper  #5 n e a r  while  near  end and  the s a l t f l u x .  #3 was u s e d  The  from  increase  AM/CT d a t a l o g g e r  sample  moved  was c e n t e r e d  sag i n the bottom  and thus  The  and  i n several  the mixed  t r a y would  column  at  to occur  s t a r t - u p . The o b j e c t  tank. the  A convergence  was s e p a r a t e d  variations  a n g l e was 2.3 d e g r e e s  t h e t r a y was 20 mm a t t h e s h a l l o w  mm a t t h e d e e p e n d .  layer  #6, t h e s l o p e  #6  t o t h e edge  space  o f 34 between  was s t a r t e d a t 1 1 : 2 3 : 3 0 b u t t h e  i n minutes  after  11:00 and  thus:  23.5 m i n .  40 m i n u t e s  i n the time-series, the s a l i n i t y  b y 0.2 t o 0.5 P S S n e a r t h e t r a y was v i s i b l e  the center,  and a  l n t h e shadowgraph.  159  convergence A t t=29 o r  t(vldeo)=5 during a  filling.  short  time  confirmed was  min,  Into  shadowgraph but by  depth.  salt  The  flux  recorded  on v i d e o  determined  Table  from  F l l .  dist (cm)  at points  below  along  the r u n .  I t might  near  tape  centerline  layer  salinity  by m i x i n g was  the end w a l l  of  visible  10 cm  have  formed  re-formed i n  the  the mixed  end, explained  l n the  of the tank  been due  salt  sustained  to the  area  dye  were  the end of the t r a y .  images and s t r e a k s  this  patterns  to the shallowest  In s a l t f l u x  shadowgraph  flow  The c o u n t e r - c e l l w h i c h  Image d e c r e a s e d  the d i f f e r e n c e  t o remove p a t t e r n s  measurements,  the shallow  p e r s i s t e d throughout  without  stirred  injected  In later  towards  a smaller  was  The d o w n s 1 o p e / u p h i 1 1  and dye  this.  higher  the tank  during  injected  much o f t h e r u n .  are tabulated  Slopeflow  from  dt (s)  - sloperun tCprtl (min)  #6  velocity (mm/s)  2  1:36:49 -  1:37:21  =  32  1 2 0 .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  velocities  below:  velocities  video t i m e - i n t e r v a l (h:min:sec)  Flow  A third  order  polynomial  fluid  and  from  cell  times  that  flow  velocities  obtain  saltflux  Table  F12.  S2  #1  f i t was  done  to determine were  to data  the s a l i n i t y  measured,  which  Salinities  values were  tray a t the  used  in tray  and tank  - sloperun  t(prt)  S-C#3  t(prt)  S-C#l  51  30.173  40  17.039  53  30.251  51  17.411  122  29.613  100  18.871  123  29.601  147  19.669  240  28.919  210  20.913  267  28.832  240  21.621  270  28.810  280  22.115  274  28.906  339  22.682  467  28.398  468  23.674  468  28.325  470  23.635  469  28.348  = 30.779  =  the  estimates.  +t(-0.1197  +t<2.3288E-5 (rms  SI  from  15.8225  +t(0.03325  #6  -t*1.4454E-8)) diff.=  0.0265)  +t(-4.4859E-5 +t*2.03725E-8)> (rms  161  diff.=  0.0867)  to  Table F13.  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  video timer  t(v)  pr i n t - o u t  t ( p ) = 1 38  S-tray S-mixed tank  2:01:30  3:11:30  hr:min:sec  145  216  min  29.495  29.447  29.041  PSS  =  19.610  19.763  2 1.117  PSS  T - tnk =  22.291  22.325  22.574  °C  fluid  S2 =  l a y e r SI  temp  = 1:54:35  - s l o p e r u n #6  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 igma-t  23.68  19 . 37  g/cm/s2  6.50e-5  5.50e-5  cm/s  P = 24.18  pressure volume  membr.salt flow  Vw = 7 . 3 3 e - 5  flux  =  flux  velocity  V  2 . 2 0 5 e - 6 1 . 952e-6 1 .628e-6 gr /cm2/s  = Q.123  0.1 1-0.1 3  162  0.09-0.1 1  cm / s  F i g u r e F~2 1  8-5-86  MICRO-CELL TIMESERIES SLOPERUN #6 d = 2 0 - 5 7 h=34 K=1892, 1 7 9 5 , 1817  Time (min)  S L O P E FLOW E X P E R I M E N T #7  F.7 In  t h i s experiment  rested end  o n the b o t t o m  was 7 8 mm.  and  Salinity figure  The s t a r t i n g  of micro-cell  profiles  mixed  in  salinity  in  both  seen  layer  data  extends  along  even  The  tray  at the deep  7 PSS i n t h e tank used  with a l l  continues  were  up v e r y  t h e tank  a rise  over This  time, c a n be  F-25).  one h o u r a n d no  the  mixed  convective  Dye i n t h e s l o p e the bottom,  f l o w was the other  into  the mixed  .  recorded  close  of convection on v i d e o t a p e .  and the s t a r t The v i d e o  The s l o p e  to the shallow  curtain  except  with  As t h e s a l i n i t y  (figure  i t i sentrained  t h e membrane became  descending  region  increases  the tray  along  images o f t h e onset  through  along  from  (see  F - 2 4 ) show a  stratified.  after  t h i s depth.  shear  flow  t=40-59  (figure  8 mm.  t=87-100  that  t=0 a t 14:00.  #5 o v e r  slopeflow  stably  where  with  a t 1 3 : 4 8 s o t [ v i d e o l = t t p r t ] - 12.  to start  a slowly  shows  the interface  by t h e v e l o c i t y  saltflux  a t port  #7 o v e r  3 cm d o w n  one p a r t  of the slopeflow  seen  taken  t=109-121  becomes  i s seen below  to split:  started  taken  and the slope  image  about  Shadowgraph  was  were  and the bottom  layer  shadowgraph  penetration  layer  data  #4 o v e r  i n a p r o f i l e at port  flows  were  was a g a i n  o f 0.2-0.4 PSS i n t h e l o w e s t  t h e mixed  The  as  from  deep end o f t h e tank  seen  the d e p t h  salinities  The d a t a l o g g e r  F-23) and a t p o r t  typical  layer  was 5.5 d e g r e e s .  micro-cells.  Time-series  the  angle  a t the shallow end,  28 P S S i n t h e t r a y .  three  up  the slope  end soon  visible  164  faster  f l o w was  after  the  on t h e shadowgraph  o f l i n e s . The d e s c e n t  slightly  timer  was n e a r l y  i n the area  where  a  counter-rotating cell  was  layer  near  sharp this  seen  cell  this  time.  velocity  dye  lifted was  Table  A cloud  into  flow  t i me  16:14  of dye,  injected  from  I t was  footage  and s a l t f l u x  movement:  #7  and :  d t = 2: 26 : 3 7 - 2 : 2 7 : 2 6  =49s  138  minutes  S2 =  26.552  PSS  l a y e r SI =  16.871  PSS  24.179  °C  t [ p r 1=  temp  T-tnk =  tray  density  D2 =  17.2106  s i gma-1  tank  density  DI =  9.930  s igma-t  23.569  g/cm/s  6.33e-5  cm/s  1.710e-6  gr/cm /s  pressure  P = Vw = flux  B=  J  165  2  after  start  the  above  slope  =42s  cm/s  membr.salt  The  - sloperun  0.102-0.119  flux  entrained  o f dye  tank  volume  i n the s t a b l e  d t ( v i d e o ) = 2: 25 : 5 5 - 2 : 2 6 : 3 7  v=  such  s l o w l y d i f f u s e d below  layer.  video  No  in:  max.  fluid  S-mixed  experiments.  the r e t u r n c i r c u l a t i o n .  Flow v e l o c i t y  m o v e d 5 cm  slope  the mixed  determined  F14.  S-tray  in previous  the deep end of the tank,  interface with and  formed  flow  >2 MICRO-CELL TIMESERIES 9 - 5 - 8 6 SLOPERUN #1 d=0-78mm h=34 K=1892, 1795, 1817 30.0H  Time (min)  Figure F-23. SALINITY PROFILE 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. SALINITY PROFILE 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=1892,1795,1817  169  F.8  S L O P E FLOW E X P E R I M E N T  In and  experiment  #8,  the bottom  a t the s h a l l o w end the depth  HP-3497A and  Data  Acquisition  f o r the output  which  powered  from  computer  the  calculated  v a l u e s from  data  of c a l c u l a t e d  Simultaneous  ports  the middle  bottom.  salinity  the above  Figure  which  the tray used  5.1  was  degrees,  12 mm.  for a l l  system  The  thermistors  conductivity  The  stored  each  was  circuits controlled  a l l d a t a on t a p e ,  s e n s o r and p l o t t e d  profiles  of the tank  were  printed  time-series  intakes  C#l,  d a t a were  C#2  a n d C#3  of  were  together  F-26).  micro-cells  170  data side.  lowered  taken at successive  (see figure  F-26. Arrangement  to either  and s e t t o touch  of the m i c r o - c e l l  the bottom  o b t a i n e d from  a n d a t 20 cm  a n d #3 r e s p e c t i v e l y ,  Simultaneous  raising height  #5  was  was  salinities.  of m i c r o - c e l l s  #7,  system  the three m i c r o - c e l l s .  an HP-9825  intakes  under  the i n d i v i d u a l  with  near  slope angle  #8  The  through  the sloped  depths to  taken  the  after same  In 20  the f i r s t  minutes,  mixed  layer  again. data  of p r o f i l e were  lowered  and the s l o p e  flow  region  o r d e r c u r v e s were  each  cell  F-28) appeared  which  t o be p a r t  the  convectively  to the bottom  f i tthrough  of  those  and  raised  sequences  time-series  of  (figure  layer:  = A + Bt + Ct2 coefficients A=  B=  o f 2nd o r d e r  fit:  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(corr)  quasi-instantaneous profiles  = S(actual)  i n the p r o f i l e s  each the  through  of the mixed  d a t a - f i l e number from t o and t o F# F# F# F#  Simultaneous  and  taken over a period  i n an expanded  S(t) Micro -cell  data,  the intakes  Second from  series  individual profile  profiles, shows  that  (figures  i n the bottom  i n the mixed  later  profile  from  shows  a  from  nearly  done  after  this  tance  may  tubes  of those  #2  #1  as  salinities  from  a shift  micro-cells  that  which  171  syphon  heavy  F-31)  set.  fluid of  that  The end  profiles Tests  i n conduc-  of the  t h e same  as  which  time.  shift  position into  salinity  the deep  i n t h e shape  in relative  of  does not r i s e  near  a sudden  of  end  (figure  i n the e a r l i e r  a n d #3 d i d n o t c h a n g e o v e r show  and  s e t of  later,  i n port#7  Differences  experiment  occur with  layer  current  stratification  i n the bottom.  micro-cells  layer  micro-cell  linear  the mixed  85 m i n u t e s  from:  start)  F-29,30).A second  data taken about  the s a l i n i t y  at  obtained  a r e t h e same a t t h e s t a r t  much a b o v e t h a t  collected  + S(fit  so o b t a i n e d ,  station  sequence  from  - S(fit)  were  outlet  bottle.  ta ta ca  DATA  10-31-86  HP-DATALOGGER  L  •  i  11  0 E L OJ-P QJ4-  e <H to  I—  ta ca ca  09  ca 0)  CT) II  6^ •rt  4- +r  C -P CD  o  Figure F~27. Time-series slope flow exp#8 300  i  i  SEC/DIV  t  i  t  MICRO-CELL  SALINITY  TIME  SERIES  PLOT  Fiqure F-Z9,  SALINITY PROFILE S L O P E RUN m  3  9. 55 40  Salinity I  (PSS)  g  >  g  /  /  Cl : port#7 C2 i port#5 C3 t portl?3  o _u V  >  0  _Q  0  ID  i  t = l l : 58-12: 06 ' quasi-instantaneous' profiles, using 2nd order f i t .  / E E  10. 15  5  l  l  20  •rt  a;  10 -  0  174  FIGURE F-30. 9. 90 40  SALINITY PROFILE S L O P E RUN #8  Salinity I  (PSS)  1 0 -  2  I  0  L_  _L  t - 12:06™12t 17  profilea  ueing aeoond order f i t through  E E E  I  F#i 110-132  'quaoi-inetantaneoue'  0  10. 50  mixed l a y e r data  30 Cl C2 C3  -P 0 -0  port#7 port#5 port#3  > 0  J)  C2 C l  0  •rt  X  10 "  h=13mm, AS=0.38-0.46  0  175  SALINITY PROFILE FIGURE F-31. S L O P E RUN #8 0  Salinity 1  <PSS) I  quasi-inetantaneoue change i n s a l i n i t y profiling).  i g >  3  13. 6  L_  1  profilee  (correotedf o r  i n t h e mixed l a y e r  Simultaneous  during  p o i n t s a t equal  height© above t h e e l c p i n g bottom*, s p a c e d  20  cm:  i n port#7  (deep)  cell#2  i n port#5  (middle)  oell#3  i n port#3  (shallow)  t=13:42-13t 56  AS = 0.31-0.37 176  ( d a t a F6-46)  

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
China 13 8
United States 9 0
Ukraine 5 0
Germany 3 1
France 2 0
Canada 1 1
City Views Downloads
Unknown 10 1
Beijing 6 0
Guangzhou 4 0
Ashburn 3 0
Hangzhou 2 0
Fort Worth 2 0
Redmond 1 0
Mountain View 1 0
Shenzhen 1 8
Sunnyvale 1 0
Nanaimo 1 1
San Mateo 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0053226/manifest

Comment

Related Items