Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Salinity intrusion in the Fraser River, British Columbia Hodgins, Donald Ormond 1974

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-UBC_1974_A1 H63.pdf [ 8.62MB ]
JSON: 831-1.0064165.json
JSON-LD: 831-1.0064165-ld.json
RDF/XML (Pretty): 831-1.0064165-rdf.xml
RDF/JSON: 831-1.0064165-rdf.json
Turtle: 831-1.0064165-turtle.txt
N-Triples: 831-1.0064165-rdf-ntriples.txt
Original Record: 831-1.0064165-source.json
Full Text

Full Text

SALINITY  INTRUSION  IN  THE  FRASER  RIVER,  BRITISH  by  DONALD B.A.Sc. M.A.Sc.  A  thesis the  ORHOND  University University  submitted  in  requirements Doctor  in  of  the  C i v i l  of of  Waterloo, Waterloo,  partial for  the  1969 1970  fulfilment degree  of  of  Philosophy  Department of Engineering  We a c c e p t t h i s t h e s i s reguired standard:  THE  HODGINS  UNIVERSITY AUGUST  OF  as  conforming  BRITISH 1974  to  COLUMBIA  the  COLUMBIA  In  presenting  an  advanced  this  thesis  d e g r e e at  t h e L i b r a r y s h a l l make I further for  scholarly  by h i s of  agree  this  written  it  of  23  British  available  for  that permission for extensive  p u r p o s e s may be g r a n t e d  for  It  financial  Civil  gain  August  1974  Columbia  the requirements  Columbia, reference  copying of  I agree and this  for  that:  study. thesis  by t h e Head o f my Department: o r  is understood shall  Engineering  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  Date  freely  permission.  Department  fulfilment of  the U n i v e r s i t y of  representatives. thesis  in p a r t i a l  that  not  copying or  publication  be a l l o w e d w i t h o u t my  i  ABSTRACT  estuary the  The  dynamics  was  studied  use  series  of  of by  numerical  conductivity  kilometers  above  winter  tides  the  observed  f a i r l y  in  velocity  data  by  80  60  to  A  minutes  agreement  of  comparable  to  velocity stress  as  and was  stresses in  the  were the  minutes  interface  KiyoD|U|Fi  Fi  i s  an  included found flows.  to  the  at  where  as be  sufficient  not  2  ebb  and  3  in  a  gradients  were  mixing  took  conductivity  lagged  to  was  and  two-way  predicted total  15  high  cm/sec.  and water  0  Froude  Kb^'u'lu'l  where  s i g n i f i c a n t ^  in  i s  salt  and  water  a  phase  Velocities  The  the  Ki=0.0075,  the  depth  intrusion.  included  i n t e r f a c i a l  low  mouth.  maximum  but  15  inequality.  between  s a l i n i t y  intrusion  cycles  despite  flood  Both  Time  estimated  column  ebb  to  that  the  within  t i d a l  an  water  and  motion.  Mixing  typically  model  of  of  river  3  Fraser  measurements  diurnal  the  appeared  river  cent  measurements  across  formulated  energy  ±40  of  periods.  two-layer per  large  m /sec.  maximum  the  f i e l d  tidal  several  Longitudinal  that  near  10  of  out  1100  ebb  the  equations  indicating  and  revealed  within  tides  wedge  in  exceeding  currents  salt  layer,  flood  the  of  spanning  water  layer.  numerical  thickness  mixing  the  each  of  throughout  surface  and  during  for  salt  water  well-defined  detectable  programme  averaging  although  meters/second,  place  washed  salt  intrusion  penetrations  Steveston  discharges  disperse  a  measurements  significant  ebb  both  water  solutions  indicated  Large  salt  model  were  neglected  Reynold's the  relative  number.  The  Kb=0.0055, the  stress layer bottom and  dissipation  both of  i i TABLE  OF  CONTENTS PAGE  ABSTRACT TABLE  i  OF  CONTENTS  LIST  OF  TABLES  LIST  OF  FIGURES  i i iv . ,  NOTATION  i x  ACKNOWLEDGEMENTS CHAPTER  1 The  2  1  Fraser  3  Estuary  Work  6  INSTRUMENTATION  Location  of  10  Instruments  11  Conductivity Profilers Operating Principles I n s t a l l a t i o n and S e r v i c i n g Calibration  12 15 16 20  Data  23  Processing  Current CHAPTER  x i i  INTRODUCTION  Previous CHAPTER  V  3  and  Accuracy  Metering  29  OBSERVATIONS  Conductivity Salinity  Temperature  Profiles  Conductivity Current  and  34  Charts  Structure  Parameterization  34 36 41 47 49  i i i CHAPTER  4  THEORETICAL  CONSIDERATIONS  The  Equations  The  Characteristic  A Steady The CHAPTER  5  of  Flow  Boundary SOLVING  Motion  -  THE  The  Barotropic  I n i t i a l  Control and  Two-layer  Conditions  66  MODEL  '  Equations  and  Boundary  Conditions  . . . . . .  Wash-Out with  Observations  106 107  Comparisons  112 118  Alternate  Interfacial  Stress  Essential  Features  the  of  Forms  121  Model  123  AND C O N C L U S I O N S  130  Remarks for  133 Future  Research  135  BIBLIOGRAPHY APPENDIX  A  100 105  analysis  Recommendations  87 88  Results  Qualitative  Concluding  62  95  Predictions  SUMMARY  Conditions  Model  I n i t i a l i z a t i o n  6  Boundary  78  TWO-LAYER  Difference  Computational  CHAPTER  and  Stresses  Finite  Sensitivity  59  Structure  Model  The  Comparing  56  138 e E E Rf If N eG c t sA S PoEf C TMS i x O i nF g T H an E N TGhI N E d S TSUt Dr Ya t i f i c a t i o n  ....  114471  >  iv LIST  OF  TABLES  TABLE 1  PAGE Comparison for  2  3  4  of  station  Summary of instruments project.  derived on  2  March  s a l i n i t i e s  1973.  28 with River 33  Comparison  of  River  Salt wedge estuaries of  29,  measured  accuracies associated used for the Fraser  from  Fraser  and  Richardson data  and  numbers Taylor  obtained  (1931).  intrusion characteristics various depths.  82 for 143  V  LIST  OF  FIGURES  FIGURE  PAGE  1  Map o f Fraser  2  Fraser R i v e r h y d r o g r a p h f o r 1973 a t Agassiz, British Columbia. T h e Hope d i s c h a r g e reading i s adjusted f o r i n f l o w s above Agassiz.  3  Lower the  4  south-western B r i t i s h Columbia River and S t r a i t o f Georgia.  Fraser  various  estuary  showing  measuring  the  showing  locations  2  4  of  instruments.  13  Cross-sectional profiles and probe line locations at the three measuring s t a t i o n s i n the Lower Fraser e s t u a r y .  14  5  Diagram general  of the timber pile platforms showing arrangement of instrumentation.  18  6  (a) I n d u c t i v e c o n d u c t i v i t y probe and sensing line. Guide wire and c o u p l i n g shackle appear to the l e f t . (b) F r o m l e f t to right: lead acid storage batteries, Rustrak recorder, and instrument electronics. (c) Timber pile p l a t f o r m a t s t a t i o n 2.  19  Timber pile platform damage. Skirt logs p i l e clamp on f u r t h e s t The current speed meters/second.  at station 1 after are m i s s i n g and upper pile i s ineffective. i s approximately 1.5  21  Comparison of measured different instruments predicted temperatures March 29, 1973.  c o n d u c t i v i t i e s by two (a,b) and measured and (c,d) f o r two t i m e s on  7  8  9  10  (a) O p e r a t i n g t h e portable salinometer off the s k i f f . (b) H y d r o P r o d u c t s c u r r e n t meter and t r o l l e y r u n n i n g a l o n g a guide w i r e . (c) O p e r a t i n g the c u r r e n t meter a t s t a t i o n 2.  31  Typical s a l i n i t y data from the on a strongly ebbing tide. d i s c h a r g e i s 960 m /sec.  35  Fraser The  estuary Agassiz  3  11  24  C o n d u c t i v i t y and temperature data obtained with ' a n RS5 s a l i n o m e t e r on f o u r o c c a s i o n s i n the Fraser estuary.  37  vi 12  13  Salinity-depth February 1 0 , 1973 stations 1, 2 a n d greatest sounding  profiles obtained and March 18, 1973 3. Channel bottom is a t s t a t i o n 1.  Contour maps of conductivit s t a t i o n s i n the Fraser estuary. marked relative to the p r o f i l e r surface l i n e s are indicated usi data at stations 1 and 3. d i s c h a r g e i s 1130 m / s e c . Times P a c i f i c Standard Time. 3  14  on at the  at three Bottom is and the free ng measured The Agassiz are noted in  38  y  43  Contour maps of conductivity at three stations in the Fraser estuary. Bottom is marked r e l a t i v e t o the p r o f i l e r and the free surface lines are indicated using measured data at stations 1 and 3. The Agassiz d i s c h a r g e i s 1060 m / s e c . Times are noted in P a c i f i c Standard Time.  44  Current stations March 30,  48  3  15  16  17  18  speed in 1973.  measurements the Fraser  made at estuary  Comparison of h c a l c u l a t e d from and the measured conductivity M a r c h 1 8 , 1973 a t s t a t i o n 1. 1  equation structure  two on (4) on  51  Two-layer parameterization of the conductivity data obtained in February 1973. Bottom l i n e s r e p r e s e n t the r i v e r bed at the platform sites. Free surface lines are p l o t t e d from measured data at s t a t i o n s 1 and 3.  53  Two-layer conductivity Bottom lines platform site plotted from 3.  54  parameterization of the data obtained in March 1973. r e p r e s e n t t h e r i v e r bed a t the s. Free surface lines are measured data at s t a t i o n s 1 and  19  V i s u a l i z a t i o n of Fraser estuary.  s a l i n i t y  20  Notation  mathematical  21  Possible flow states for the two-layer s t r a t i f i e d computation. The r e q u i r e d number of boundary c o n d i t i o n s i s i n d i c a t e d .  used  in  intrusion  into  the  modelling.  58 58  65  v i i 22  Notation  used  in  steady  flow  solution.  23  Stage-discharge estuary.  24  Measured and p r e d i c t e d s u r f a c e three stations on the Main estuary.  relationship  an  Fraser  elevations at Arm o f Fraser  arrested  wedge.  74  26  Typical i n t e r f a c i a l stress curves for arrested salt wedges asuming a uniform surface slope.  77  Profiles of °~t and March 2 9 , 1973 at s t a t i o n 2. of the Brunt-Vaisala frequency R i c h a r d s o n number are shown.  83  velocity on Distributions and gradient  28  Finite  29  I l l u s t r a t i o n of relationship between continuum and f i n i t e difference domains of dependence for a stable e x p l i c i t difference scheme..  30 31  Schematization  of  the  hydraulic  34  35  of of  at  of on  at  molecules.  Fraser  River  used  and  surface  stations  5  93  in 96  surface 3  75  90  model.  stations  predicted  observations  Comparison observations and 2.  Lower  predicted  observations  Comparison with  33  barotropic  Comparison with  32  computation  salt  69  Typical  difference  for  for  25  27  solutions  69  and  elevations 4.  98  elevations 6.  99  predicted velocities with March 3 0 , 1973 at s t a t i o n s 1  Relationship between the e s t u a r y and parameters. Conductivity p r o f i l e r s stations 1, 2 and 3 a r e shown i n t h e i r configuration.  model at March  Comparison of t y p i c a l i n t e r f a c i a l positions predicted by the s t r a t i f i e d f l o w model with two-layer parameterization of observations at s t a t i o n s 1, 2 a n d 3 .  101  103  108  v i i i 36  37  38  39  40  41  42  Comparison of predicted and measured layer velocities at stations 1 and March 29 a n d 3 0 , 1 9 7 3 .  upper 2 for  111  Interfacial solutions from the s t r a t i f i e d flow model a r e shown s u p e r i m p o s e d on c o u t o u r c h a r t s of c o n s t a n t d e n s i t y ( °~t) for three days in February 1973. The periods of s u p e r c r i t i c a l o u t f l o w a r e i n d i c a t e d by c f <0 on t h e s t a t i o n 1 c o n t o u r c h a r t .  113  Interfacial solutions from the s t r a t i f i e d f l o w model s u p e r i m p o s e d on c o u t o u r c h a r t s of constant density ( °~t) for three days in March 1973. The periods of s u p e r c r i t i c a l o u t f l o w a r e i n d i c a t e d b y c 7 <0 o n t h e station 1 contour chart. Supercritical inflow by cf >0.  114  Interfacial solutions for the t i d a l cycle on February 10, 1973. Isohalines interpolated f r o m t h e d a t a i n F i g u r e 12 a r e s h o w n i n each section.  116  Tidal variations in the i n t e r f a c i a l and b o t t o m s t r e s s e s and t h e mean layer velocity shear at station 2 for March 17, 1973 (upper). Six l o n g i t u d i n a l sections are shown f o r f l o o d and ebb phases (lower).  126  Comparison of the measured boundary c o n d i t i o n f o r h' at station 1 with the theoretical condition of Vreugdenhil (1970) (upper). Comparison of u' calculated from the s t r a t i f i e d flow model and the theoretical r e l a t i o n of vreugdenhil (lower).  128  Advection paths of into the M a i n Arm s m a l l numbers along time in hours follow  145  four particles released of the Fraser R i v e r . The each path indicate the ing release.  ix Notation The following notation has been used in O c c a s i o n a l l y symbols have been used more than subsequently l i s t e d with each meaning. a  = salt  a-,  water  depth  = coefficients  = square  b  = storage  b; B  width  = multiple = column  c = x plane,  area  coefficient  = dx/dt  =  least  squares  dimension  analysis,  2n  x  2n,  river, coefficients,  dependent  inverse  variable  slopes  cf of  = celerity comparable  o f i n t e r n a l waves on i n t e r f a c e between but d i f f e r e n t d e n s i t y ; e.g. water over  C,Cs  on  a  free  curves  of  of  waves  characteristic  dimension  = celerity  = constant  gravity  of  derivatives,  c*  C  long  a  river,  matrix,  regression of  from  of  across  vector  = conductivity  in  vector  of  force  terms,  dimension  n,  f  = column  vector  of  force  terms,  dimension  n,  F (V) = column dimension n,  F;  U  /J  = M/J  £ gh  vector  =  g e 77 h * / h  = acceleration  h  •= t o t a l  water  = thickness  i  -  time  j  = space  line line  of  densimetric  g  h«  x-t  surface, two salt  fluids water,  millimhos/centimeter,  = column  =  in  n,  integration,  C  FA  thesis. and are  x=0,  obtained  A = cross-sectional A  at  this once  to  column  in in  Froude  = i n t e r f a c i a l  due  of  functions  salt the the  gravity depth water  x-t x-t  in  plane.  dependent  number,  Froude  number,  = 9.800  m/sec ,  river,  layer,  plane,  of  2  variables,  X  K  = dimensionless  Ki  =  Kb  = bottom  Kc  = inductive  L,L  i n t e r f a c i a l  m = number n  stress  of  = integer  N (z)  = mean  P  = solution  length,  characteristics  di)/  point  = solution  g  = discharge  per  Q  = discharge  in  Q = solution  point  € gh  = N(z)/(  Req  =  gch/u  / V  3  2  flow  at  a  given  boundary,  layers,  Brunt-Vaisala  frequency,  the  = equivalent  x-t  width or  salt  =  plane,  x-t  plane, (m /sec), 2  m /sec, 2  plane, water  x-t  thickness,  plane,  densimetric = gradient  2  = overall  Reynolds  number,  Richardson  Richardson  S  = s a l i n i t y  in  in  x-t  parts  per  = characteristic  t  =  number,  T  = temperature  u  = instantaneous  plane, thousand  s a l i n i t y  of  Strait  ), of  time,  = time  mean  number,  resistance,  point  h  x-t  in  du/ dz)  = solution  u  in  in  point  S  Sg  =  in  point  = solution  0  p  3  R  R i  discrete  m /sec  = non-dimensional  Ri  of  unit  R  = J  entering  pressure,  P  R^  constant,  number  p  coefficient,  coefficient,  c e l l  (-g dp /  =  coefficient,  stress  = intrusion  0  stress  in  degrees velocity  barotropic  Celcius, in  x  direction,  velocity,  Georgia  water  (%«, ) ,  xi u  = observed layer  0  velocity,  u = t i m e mean v e l o c i t y u*  = fluctuating  U = u-u  1  i n x direction,  o r t u r b u l e n t v e l o c i t y component i n x d i r e c t i o n ,  = mean l a y e r  velocity  shear,  V = column v e c t o r o f dependent v a r i a b l e s , w = instantaneous velocity w = t i m e mean v e l o c i t y  dimension n  i n z direction,  i n z direction,  w* = t u r b u l e n t v e l o c i t y c o m p o n e n t i n z d i r e c t i o n , x,y,z  = r i g h t hand C a r t e s i a n c o - o r d i n a t e  y = Rustrak recorder = p~\ = s p e c i f i c  d 8x  = spatial  St  = time  ordinate, volume,  increment,  increment,  = p' - p /p  €  1  =Ap/p*  77 = h-h* = f r e s h  - density  water l a y e r  X =p / p* = d e n s i t y  contrast,  thichness,  ratio,  V  = kinematic v i s c o s i t y of water,  P  = fresh  p  %  i  T  w a t e r d e n s i t y i n gm/cm  - s a l t w a t e r d e n s i t y i n gm/cm (p-1  . 0 0 0 0 ) x10  = interfacial = bottom  <z =  v  axes,  3  3  o r Kg/m ,  3  o r Kg/m ,  3  3  = sigma-t,  stress,  stress,  (du/dz)/-<u*w*> = k i n e m a t i c e d d y  viscosity  x i i  ACKNOWLEDGEMENTS The Fraser  has  proven  area  and  undeniably,  persons  have  particular  I  i n t u i t i o n  provided  research.  would  Leblond,  and  equation and  the  also  studies  l i k e  to  by  in  a  s a l i n i t y  very  also me  a  interesting  the  acknowledge  f i e l d  M.  work  and  Oceanography,  advised steady  am  most  wish  to  express  at  grateful  much for  me  and  to  help  in  valuable the  gave in  me  converting  Professor  during  both  and  supervised  use.  flow  the  times.  points  (Oceanography)  p r o f i l e r s  I  who  in  challenging  one  guidance  Quick,  conductivity  the  and  d i f f i c u l t  the  Osborn  the  intrusion  frustrating  by  Professor  integrated  (31).  the  be  T.  during  preparing  to  helped  Professor  encouragement and  into  River  research Many  investigation  the  P.  theoretical  equations  to  yield  for  their  assistance  the  Westwater  guidance. I  also  Research  Centre  monitoring making  available boats  Limited  and  success  of  help.  The  helpful  and  the  the  valuable  were  f i e l d  of  in  the  to  Institute  the  instruments.  and  I  the  of  Canada  I  gratefully  would  l i k e  things f i e l d  to  done"  Canada  both  Engineering  the  f i e l d for  organizations Rice  contributed  M i l l s to  acknowledge Department  thank around  programme  of  Oceanography Both  used.  of  C i v i l  to  expenses  the  Survey  "getting  contribution  the  extensively  work  particular  experience  to of  Water  staff in  and  most  which  appreciation  underwriting  programme,  provided  whose  for  my  on  Mr. the more  the their  were  most  Geoff  Sharp,  river  made  than  one  a  x i i i occassion.  Mr.  platforms  for  appears  the  as  The were  excellent  the  figures  on of  the  services  C i v i l  National  in  fine  job  R.  Brun,  Mr.  this  thesis  is  IBM  computer  and  370  Columbia f a c i l i t i e s  support  of  a  along  Research  Engineering  did  modelling  British  Financial the  also  river.  numerical  done  University  Sharp  the  in  whose  also  with  during  the  Council  of  University  the  excellent  work  thanked.  the  data  available  Computing are  fabricating  reduction  through  Centre  and  the their  acknowledged.  study Canada of  period and  British  was  the  provided  by  Department  of  Columbia.  1 Chapter  1.  INTRODUCTION  The Columbia, water 1).  Fraser discharges  passage The  water  River, into  connected  confluence  above  respects  c i r c u l a t i o n  established while  river  layer. salt  in  a  study  73,  can flows  into  are  these  reported The  nature  of  and  problems  had  description different  programme  the  1973 salt  of  to  to  for  The  of  seawater  plain  period  the  the  P a c i f i c  large  Ocean  Georgia  results  bottom  extending  in  salt  (Figure a  salt  several  shown  that  salt  wedge  estuaries  landward  along  of  a  relatively  the in  a  where  very  each  large  layer.  carried  many is  the  bottom  fresh  surface  well  defined  tides  produce  The  out  in  results  during  of  1972  and  examine  the  thesis. of  Strait  tackled stress  the and of  structure.  be  Georgia,  estuaries  circulations  intrusion  the  of  British  have  in  maintained,  this  density  flows  seaward  objective  between  currents  of  in  of  typical  water  t i d a l  to  river  pattern  t i d a l  main  the  relation  of  S t r a i t  Strait  coastal  be  south-western  Observations  flows  other  in  ends  the  salt  water  wedges  the  mouth.  which  Unlike  intensified  the  the both  along  kilometers a  at  with  intrusion  located  along  arrive  Georgia  This  along an  project  was at  tides  to a  quantitative  and  the  observed related  meant  that  several  way,  such  as  the  interface  arriving  between  two  at  a  fluids  density.  study  proceeded  f i e l d  measurements  collect  wedge  suitable  movements  on  along  data a  was to  two  main  directions.  undertaken provide  sub-tidal  a  scale.  during detailed To  F i r s t ,  the  a  winter  picture  complement,  of  •  3  and  help  explain  s t r a t i f i e d  The  t i d a l  Fraser  Hope  flows  lower to  l i t t l e  t i d a l  over  as  Since  the  the of  of  number  Strait  2,  percent  resulting  extensive derived The  in  during  watershed  from  annual  define  (Figure  of  discharge  and  the  low  s t r a t i f i e d  estuary  conditions  as  extending  1),  undergoes  flows  low and  snowmelt,  typical  lower  estuary  lesser  the of  only  main  of  The  probably  accentuated  high of  the  It  i s  to arm  is  the  a  are  significant  curve  which  that  discharges.  there  winter  is  are  a  large  for  flows  1973,  result  the  in  subject  and  the  of  the  9  connected  carries  deepest  dredged  meters,  a  to  the  has  been  approximately  channel  throughout  and  with  an  the  seaward  30  to  provide  a  feature  which  has  intrusion.  t i d a l  water  are  channels  investigation  which  continuously  importance.  sedimentation  which  meters  depth  principal  This  river also  two  of  tide.  s a l i n i t y  of  into  some  15  channel  understanding  fundamental  concerns:  arm  main  shipping  An  at  10  minimum  divides  branches,  the,flow.  depth  kilometers.  of  Georgia  is  Georgia to  average  is  may  kilometers  an i s  we  elevation  110  flow  which  of  in  variation.  of  of  confined 80  models  study.  The a  as has  the  Figure  density this  mathematical  developed.  Strait  much  flow  in  observations,  River,  change  river  proportion  shown  were  Fraser  the  relatively  seasonal  f i e l d  Estuary  The from  the  hydraulics  There quality.  are,  in  the  perhaps,  Preserving  estuary two the  main  4  F i g u r e 2. Fraser River hydrograph for 1973 at Agassiz, British Columbia. The Hope discharge reading i s adjusted for inflows above Agassiz.  5  shipping large  channel  public  wedges;  of  that  Vancouver result,  and  a  the  a  be  lower  the of  f i r s t the  2.,  discussion In  wedge  of  together  the  effort  study  i s  a  or  to  in  for  the  s t r a t i f i e d  one  side  by  on  the  a  part  of  river  city  of  other.  As  concern  is  a  for  domestic  either  on  salt  principally  produced  monitoring  relies  the  and  quality,  of  studies.  river,  recently  f i e l d  a  forming  gather  the  the  comparison ^concluded  and  techniques of  and about  by  using  complicated  knowledge  by  of  the  features  project,  was  flow  in  description  and  6  tidal  problems along  presented  model  observed Chapter  a  models  developed of  the  data  is  this  on  and  the  mathematical  steady are  data  river  examples  basic  for  v i c i n i t y  storage  water  and  s i g n i f i c a n t  procedures with  has  commonly  the  the  and  is  in  communities of  continuous  patterns.  of  the  4  use  on  consuming  by  It  sedimentation  flanked  smaller  models  typical  solution  numerical  The  Some  the  movement  motion  some  Chapter  analytic  is  of  capacity  in  investigation  intensive  instruments, Chapter  value  intrusion  f i e l d  salt  accentuated  Assessing  c i r c u l a t i o n  The  i s  disposal,  water  principal  load.  predictive  dispersion  salt  s i l t  timber  quality.  the  water-borne  concentrated  the  numerical  necessary  estuary  waste  operation,  made  of  i n d u s t r i a l  dredging  and  number  transportation,  water's  round  deposition  would  The  year  the  therefore,  hydraulics  a  expenditures,  sedimentation observed  is  are is  with  of  i s  with in  a  Chapter  3.  and  an The  Chapter  predicted a  in  brief  presented. in  the  given  derived,  applied  and  variations  discussion  5  results. of  some  6  important  aspects  of  s a l i n i t y  intrusion  Considerable  research  effort  Previous  sedimentation  twenty  years.  model  constructed  Professor  Notable  E.  schemes  made  and  (1952,1953).  the  flow  confined made  the  penetration.  Although indicated  relate  water of  conditions  to  were  s a l i n i t y  Markert and  were  Branch valuable  of in  made  in  density  and  structure made.  temperature 1971  (1967).  profiles by  A.  Environment  Canada  i l l u s t r a t i n g  s t r a t i f i e d  H.  at  Ages  (unpublished)  D.  and  and  no to  long  physical  various  t i d a l  series  of  reported  by  series  of  was Several  conditions  this  have  estuary,  and  low  during  piling  the  can  Baines  sedimentation  various of  which  conditions  for  by  stage  flow  research  One  measurements Meickle  by  timber the  scale  of  discharge  and  last  controlling  series  river  the  Columbia  tide-low  However,  in  rarely  during  high  hydraulics  presence  salinity/temperature/depth Waldichuk,  for  1952.  borers  the  of  toward  physical  channel  discussed  made  over  B r i t i s h  extensive  are  the  the  of  unstratified  marine  salt  measurements  in  to  was  calculations  were  directed  Fraser  various  Two  data,  conditions  were  salt  regard  which  cubature  attempts  delta  estuary.  been  lower  University  on  series  has  the  this  the  these The  was  at  in  developed.  from  tide-high  in  Pretious  were  measurements  period  the  Work  controlling  be  in  locations Marine these for  in  the  Sciences data  high  were tides  7  during  the  winter  months,  and  aided  in  the  design  of  the  instrumentation.  The  Water  continuously River at  at  of  semi-annual P i t t  estuary  River.  " t i d e l e s s " Keulegan  t i d a l l y  numerical have and  In  made  between  are  only  physical  the  arrested in  salt  Fraser motions  are  modelling,  offered  published  by  far  varying a  the  good  Vreugdenhil  the  Fraser  theoretically  Mississippi  from  lengths  data. a  From  was  chance  of  and  River  achieved.  flow  i t  a i s  and  the  standpoint  of  are  required  success.  behaviour  (1970)  applied  However,  the  in by  between  steady  equations  unsteady  Georgia  the  flume  important.  time  describing  i s  of  penetration  comparisons  experimental estuary  for  salt  The  detailed  Keulegan  to  good  Georgia.  Strait  data  Fraser  elevation  (1953).  penetration  obtained and  Morgan  the  very  the  studied  wedges  predicting  model  models  and  of  publishes  been  Farmer  solution  Marvaud  surveys  have  and  the  been  also  controlling  induced  numerical  Works  in  Canada  surface  Strait  mechanisms  Morgan  mathematical  the  hydraulic  for  that  of  river  basis.  "steady-state" clear  the  discharge  continuous  (1966)  and  and  Environment  a  success  Farmer  on  estuaries  results  where  These  available  1),  upstream  Public  of  freshwater  (Figure  sounding  The  his  B.C.  Branch  the  locations  Department  and  monitors  Hope,  eight  Survey  of  salt  Boulot,  and Two  wedges  Braconnot  (1967).  both  conservation  of  analyses mass  and  a  two  layer  momentum  model  equations  was for  assumed  each  layer  and were  8  numerically  integrated  et  did  not  include  their  model  and  i t  They  presented  a l .  distance  of  resulted  from  using  can  salt be  results  less  water  showing one  small  The  model  of  but  unfortunately  and  physical  predictions  was  Vreugdenhil*s salt  and  water  discussed  in  Rotterdam same  Waterway  equations  reproducing i s  the  -  The  distances  on to  the  model  give  salt  a  in  a l . ,  water  slope  ranges  in  between  the  and  salt and  the  i n t e r f a c i a l  states  good  the 9  that  from  he  was  2  stress able  to  correspondence  with  calculation  the  their  model  of  model  are  from  the  essentially  the  the  method  features.  succeeds Of  times  from  in  3x10~  shown)  the  has  a  calibrate  the  t i d a l to  suggesting  a  Penetration 1.6  coefficient  term  in  interest  (ebb)  4  velocity. for  empirical  downstream  measurements Using  data  Km  in  mixing  from  several  water  meters  neglects  Vreugdenhil's  for  a  discussed.  prototype  shown  over  distance  0.14  between  results  intrusion  in  analysis.  Grand-Rhone  also  and  layers  short  averaged  were  Boulot  o s c i l l a t i n g  This  correlations  model  (estimated  variation  front  the  the  no-mixing  Netherlands.  shape  concludes  analysis  The  i n t e r f a c i a l  vary  Vreugdenhil  no  to  layers,  et  a  which  observed  Boulot  (flood)  4  salt  schemes.  between  kilometer.  layer  the to  wedge  as  measurements  in  main  mean  considerable  the  as  the  salt  cycle. 8x10  relation  the  applied  two  between  exchange  tides  amplitude. Aries,  difference  c l a s s i f i e d  than  the  f i n i t e  meter  tide.  which  enters  dominant  effect  the  observations  predictions using  this  coefficient.  By  using  a  for  horizontal  tide,  that  is  9  the  barotropic  or  u n s t r a t i f i e d v e l o c i t y f i e l d as a f u n c t i o n  time and p o s i t i o n i n t h e e s t u a r y , V r e u g d e n h i l reduced  the  of  total  number o f e q u a t i o n s r e q u i r e d f o r t h e s i m u l a t i o n from f o u r t o two. As a r e s u l t he found t h a t the o v e r a l l b e h a v i o u r of the s a l t wedge was l a r g e l y dependent on t h e h o r i z o n t a l  tide  prediction.  10 Chapter  2.  INSTRUMENTATION  Previous indicate winter  the  presence  months.  penetration Strait  of  f i e l d  measurements  of  salt  However,  and  tides  are  data.  Tidal  amplitudes  percent  of  depth  for  several  Under i s  and  kilometers  these  River  river  bottom  during  salt  water  the  extent  between  the  s a l i n i t y  to  determine  the  river  of  to  reverse  the  of  seawater  the  region  value  of  structure  entrance  s u f f i c i e n t  above  conditions,  was  clear  that  adequately  describe  measurements  in  conductivity 1972/73. were  the  Three  installed  to  over  point  and  from can  the  these  exceed river  40  flow  penetration.  measurements  in  time  of  would  f i e l d  and  the  and  as  i n s t a l l a t i o n  by  of  column  to  programme  of  the  and  which  every  15  February  of  the  winter  of  Osborn  1973  "conductivity were:  reguired  records  during Farmer  March  water  a  continuous  undertaken  described  be  (1973)  provided  minutes,"and  p r o f i l e r s " . 01  to  13  The  and  March  30.  are  parameters Canada  was  described of  data  emphasizing  February  most  series  density  r i v e r ,  during  periods  The River  the  instruments  subsequently  actual  time  structure,  conductivity  16  are  Fraser  in  d i f f i c u l t at  the  the  limited.  It  are  along  variations  correlations  Georgia  the  water  from  two  most  important  the  tide  and  are  continuously  (Environment  calibrated  the  gauging  forcing  freshwater monitored  Canada).  staff  at  Hope,  The  functions  discharge. by  the  discharge  B.C.  for  on  an  the Both  Water i s  Fraser of  Survey  computed  average  these  daily  from  of a  basis.  -  11  This  figure  upstream used  is  then  point  of  the  f i n a l  carried  out  provided  comparable  during were  the  made  sensing and  using  The  B.C.,  the  Agassiz  large  wire  abandoned  for  d i f f i c u l t y  in  during well  to  In many  furthest  figure  while  not  current  w i l l  was  of  depth the  of  a  readings  be  20  the  °)  with  ebb  exceeding  boat.  30  °.  measurements  explain  why  of  water  slack  in  the  most  periods  the -  pound  real  The weight  used  currents  produced  equipment  i l l u s t r a t e s the  available  over  when  were salt  were  the  Fraser  data  was  limitation  measurements  in  occasions  times  measurements  winch  light  and This  This  other  25  The  Ebb  this  phase  a  the  speed.  was  salinometer.  above  but  At (STD)  RS5  line  small  current  (exceeding  angles  winch  metering  measurements.  data.  physical  main River,  obtained water  was  river.  Instruments  any  factors  protecting  s a l i n i t y  Instruments a  stern  portion  established  of  March,  conductivity  and  to  accurate  making  high  Location  the  depths  considerable  helps  attached  angles  of  with  Industrial  off  very  days  salinity/temperature/depth  an  was  operated of  two  velocity  winter,  accurate  and  Agassiz,  influence.  simultaneously  head  capable  a  t i d a l  for  throughout.  During  to  adjusted  the  scheme  to  influence  in  the  time  instrument  conductivity  interfering  considerations  collect  with  Fraser  p r o f i l e r s  series  from  disposition. in  navigation River.  data  .It  the  large  f a c i l i t i e s , was  also  estuaries  Securing ebb were  and  currents, the  important  main to  12  monitor  as  p r o f i l e r s Figure part  much  adjacent  3 shows of  the  1 2  Timber the  system  protection tides, The  a  3  for  thickness  4  two  were  river  t r a f f i c  of  meters  located  separate of  the  in  the  for  on  covering  indicating  the  of  column.  extent  of  coverage  stations  1,  2  and  gauges,  river This  and  of  provided  a  was  low  monitored. Rice  made  each  of  At  to  M i l l s obtain  cross-sectional for  a  degree  Canada  were  and  beside  currents.  water  pier  The  tide  2.  the  Conductivity  the  and  installations  water  and  from  temperature the  properties  periods  found.  was  s a l i n i t y  characteristic  to  erected  6.1  chart,  shape  p r o f i l e r ,  are  3.  P r o f i l e r s  months  25  were  lines  Figure  from  two.  sensing  and  established  these  the  the  river  t i d a l  to  mooring  of  winter  between  adjacent  the  gauges.  instruments.  1 and  coverage  The  located  enlarged  locate  tide  penetration,  permanent  platforms  p r o f i l e r  Conductivity  the  water  and  maintained  profilers  improved  in  possible,  for  where  shown  with  salt  debris,  minimum  as  channel  Limited,  the  were  pile  from  third  River  of  placed  navigation  rigid  Fraser  column  government  various  and  was  water  the  region  of  p r o f i l e r s  the  to  the  the  locations  p r o f i l e r  of  when  along 29 The  the  parts fresh  of  Fraser the  two  salt  water  river  bottom,  per  had  collected  River water  from  thousand,  water  data  the  and  Strait  some  During of  those  Georgia  typically  temperatures  temperatures  the  i l l u s t r a t e  masses.  s a l i n i t i e s  during  ranging  of  6  from  was  ranged to 2  8° to  C  Figure 3. Lower Fraser measuring instruments.  estuary  showing  the  locations  of the  various  14  G.D. LOW WATER  LEVEL  J  STATION  12 LOW  WATER  G.D.  LEVEL  STATION  2  G. D. |0  \  2  4 6 8 10 M E T E R S  STATION  3  100  F i g u r e 4. C r o s s - s e c t i o n a l p r o f i l e s and probe l o c a t i o n s at the three measuring stations in Lower F r a s e r estuary.  200  line the  METERS  15  5°  C  throughout  For  these  the  temperature  profiles  are  Thus  a  measure  infer  the  primarily  both  however,  these  temperature  Operating  inductive  and  the  conductivity  of  be  the  STD  and  can  be  used  to  structure.  should  by  density  structure.  density  temperature  the  s a l i n i t y .  s a l i n i t y  distribution  improved  from  detectable  the  hence  and  can  be  recorded;  incorporating  the  measurements.  sensing  located  probe by  by  cycle  to  e l e c t r i c a l  conductivity  successively  l i n e  inside  i s  current c o i l current  water  Each  secured  the  act  as  of  two  in  interrogating  the  water  instrument  housing,  a  any  check  on  of  column. is  d r i f t  also  in  the  c o i l s  applied in  in  i t s the  acts  of  to  core. sea  in  a  mu-metal insulated  one This  water  c o i l , current  path  proportional  to  the  copper which in  linking  complementary  annular  the  e l e c t r i c a l  wire.  induces  turn  fashion  cores  induces two  to  the  A an an  c o i l s . f i r s t ,  conductivity  of  path.  probe a  consists  torroidal  current  second  on  a  depths  the  response.  e l e c t r i c a l  a  on  every  voltage  e l e c t r i c a l  measure  fourteen  in  surrounded  recorded  no  conductivity  available  probe,  Each  sea  the  profile  probes  e l e c t r i c a l  the  both  function  estimates  at  interrogated  carrying  a  instruments  fifteenth  The  ranges  and  Principles  water  constant  period  conductivity  data  The  A  of  s a l i n i t y  Ideally,  sea  measuring  was  Rustrak  interrogated chart  for  recorder.  one  minute  The  and  sensing  the line  output was  16  interrogated  from  occupying  fifteenth  the  completed hour,  a  every  bottom  to  position.  fifteen  frequency  top, In  minutes,  considered  with  the  this  way,  producing  satisfactory  calibration a four  for  probe  sequence  was  cycles  the  to  examining  tidal  phenomena.  Timing small  hobbyist's  inside ±4  the  minutes  per a  batteries,  Ebb  A could would be  in  the  be  also  in  by  near  was  with  an  outdoor  constant  power  accuracy of  lead  supply  replacement  once  by  a  supply exceeding  the  operating  volt  6  controlled  independent  independent  four  line  Rustrak  conditions.  acid  storage  voltage each  the  seemed  to  of  conjunction  had  to  be  a l l  logging in  for  two  week.  real  be  free  with of  addition, types,  the  and  the  river  floating  Holding  under  2  and  constraint  challenge.  the  types  exceeding  industry.  place,  best  purposes.  other  In  of  securely a  currents  River.  t r a f f i c  provided  and  produce  Fraser  boat  variety  possible,  operated  platform  cost,  a  for  required  from  sensing  platform  serve  an  timing  feature  a  on  clocks,  regularly  primarily  reasonable  the  interval  Servicing  tides  a  These  provided  considerable  protecting  operating  powered  charts  and  meters/second  of  were  which  Installation  debris  interrogation  made  desirable  Rustrak  carries  clock,  week,  instruments  weeks.  the  instrument.  behaviour, The  of  Servicing  of  the  solution from  measuring conductivity  strong  because a  small  equipment profilers.  o s c i l l a t i o n s  which  i t boat could Any would  17  affect  the  Rustrak  operation  and  could  lead  to  structural  deterioration.  A  f i n a l  equilateral three and  feet  the  apart  5  station the  2.  piles,  a  deck.  The  of  and  protection  crossbraced sketch  in  of  the  i n s t a l l a t i o n  at  floating  for  an  spaced  arrangement  actual  logs,  in  frames  were  dimensions the  tube  frames  working  triangle  arranged  steel  These  shows  some  The  by  guide  at the  was  by  a  probe  brass  The  wire  line  stressed  rigging.  on  Two  piles.  6 (c)  perimeter  sensing  5).  wire  weight  the  piles  the  just  outside  probe  line  by  secured  to  debris.  platform,  guide  chosen.  pertinent  provided  The  (Figure  the  timber  supported  Figure  The  deflecting  the  triangle  and  three  was  ^joined  gives  instrument  of  triangle  lower  Figure  design  down  weight  was  probe  are  shown  line  kept  i n s t a l l e d ,  the  i t  a  guide  and in  wire  resting  coupled  snap-shackles,  l e f t ,  probe  heavy line  inductive the  lowered  in  often  on  five  the  bottom  places  to  used  in  sensing  line,  coupled  Figure  6 (a).  the  s a i l  A  boat to  30  the  pound  extended.  s  Once The  platform  the  probe  without  This  cover plywood  large  lines  and  box  As  shown  Rustrak  meant  during  enough  that  bad  also  for  conveniently,  d i f f i c u l t y .  instrument box.  was  instruments  were  Rustrak  weather,  provided  a  some  in  one and  were  person  to  batteries  Figure  arranged charts frequent security  in  easy raise  could  6 (b), a  could  to  the  service.  and be  exchanged batteries,  weather-tight be  plywood  replaced  occurrence against  lower  in  winter.  vandalism.  under The  18  FLOOD GUIDE  CURRENT  WIREN  PROBE  LINE. EBB CURRENT  P L A N VIEW HIGH  WATER  C C C C LOW  WATER  C O PROBES GUIDE  -SLIDING  (14)  WIRE  WEIGHT  -PERMANENT  ELEVATION Figure showing  WEIGHT  VIEW  5. Diagram of the timber pile platforms general arrangement of instrumentation.  19  Fijure 6. (a) Inductive c o n d u c t i v i t y p r o b e and sensing line. Guide wire and coupling shackle appear to the l e f t , (b) From l e f t t o r i g h t : lead acid storage batteries, Rustrak recorder and instrument electronics. (c) T i m b e r p i l e p l a t f o r m at s t a t i o n 2.  20  Two so the  strong  the  that  f i r s t  problem  d i f f i c u l t i e s  two  total  significant week  more  period  weights  encountered.  probe of  added  weight  of  this  the  last  line  The  to  to  type  the  currents  occurred  To  guide  185  a  ebb  deflections  i n s t a l l a t i o n .  were  submerged  i n s t a l l a t i o n s  were  during  alleviate wires,  pounds.  minimum  were  figure  this  increasing  For of  300  future pounds  is  recommended.  During was  damaged.  causing  the  entire  v e r t i c a l . broken  A  and  the  s k i r t  logs  were  structure  to  on  resulting to  progressive next  February  weld  susceptible  the  of  The  the  upper  loss  in  deterioration two  weeks,  o s c i l l a t i o n ,  the  to  1  sustaining 1.5  one  this  design's  platform  smashed  triangle  (station  free 5  pile  made  of  remaining third  of  clamp  the  the  remained  damage.  The in  also more  occurred  securing  Figure  over  clamps  were  amplitude  of  operative  to  the  7 shows  current  the  was  off  Consequently,  increased  effectiveness.  1)  piles,  platform  welds  the  the  degrees  o s c i l l a t i o n s .  and  meters/second  1  approximately  r i g i d i t y  the  platform  attesting  approximately  of  u n t i l  Despite  the  go  flow-induced  ineffective.  after  week  is  end,  platform  ebbing  at  photograph.  Calibration  Following (1973), stages. of  the  the  procedure  calibration  First probe  the  a  c e l l  casing,  of  each  constant was  found.  developed  probe Kc,  was  by  carried  depending  The  value  Farmer  of  only this  and  out  on  the  Osborn in  two  geometry  constant  21  Figure  7. Timber p i l e p l a t f o r m a t s t a t i o n 1 a f t e r d a i a a g e . Skirt logs are missing and upper pile clamp on f u r t h e s t p i l e i s i n e f f e c t i v e . The c u r r e n t s p e e d i s approximately 1.5 meters/second.  22 varies of  s l i g h t l y  the  solution  instrument the  output  voltage  probes  were  sea  was  in  a  Reg,  found  sea  water  c e l l  constant  from  which  probe  solution. i s  find  Kc  the  about  11  and  selected  ranging  the  were  each  water  function  known  the  calibrating conductivity.  immersing  after  each The  which  the  A conducting  loop  box  was  the  "equivalent  passed  voltage  solution  of  conductivity.  dried.  output  the  of  by  solution,  and  same  of  and  to In  from  increasing value  in  mean  the  of  through  the  resistance",  obtained  conductivity,  be  in  the  Cs,  the  sequence  practice, to  was  process  were  used  used  for  was  to each  typically  value.  measured  100  three  averaging  constants  a  conductivity  these  were  calibrated  through  output.  of  c e l l  conductivities  recorder  a  response  involved  determined  resistance  average  of  the  box  as  stage  independent  by:  scatter  electronics  resistance the  worst  percent  Once  the  always  (1)  solutions  The  for  i s  Cs  separate  probe.  f i n a l  Knowing  Three  and  The  i t  e l e c t r i c a l  solutions  the  defined  = Reg.  the  casing,  yielded  but  and  were  water  variable  each  probe  recorder  recorded  removed  with  Kc  chart  constants  several  series  opening  and  c e l l  in  to  recorder.  electronics  probe  probe  conductivity  and  The  in  from  1000  by of in  known,  the  simply resistances  the  nine ohms.  f i e l d  chart  adjusting compatible and  resistance A least  recorder  noting values  squares  the with the were  analysis  23  was  used  output chart  to  find  and  the  record  a  functional  resistances.  has  the  a-,  are  recorder  Data  mmhos/cm  and  on  one  the  to  least  a  a  and  and  relative  range  l i e  within  to  the  results  from  two  =  Kc  2  of  the  the  quote  an  of  mmho/cm  +2  individual  mmho/cm  discussed  ±1  conductivity  conductivities of  different  (1973)  accuracy  of  nearly  station  2  on  conductivity  from  in  of  0  RS5  mmho/cm. another  on  and  y  is  figure  and  subsequent  p r o f i l e r s .  The for  the  of  the  one  best.  the  These  values  I  this  value  Figures  conductivity for  found  calibration  applied  plotted  ±2  probes  during  In  of  the  mmhos/cm.  sections.  are  two  8 (a)  obtained times  at  j  March  an  29, line  In  of  are  f i e l d  The  ±2  the  comparison  the'latter  the  with  recorded and  shaded  mmhos/cm.  shown  were  comparison  worst  1973.  represents  accuracy  profiles  each  35  have  instruments  accuracy  between  measurements  profiles  salinometer  i l l u s t r a t e of  the  (2)  absolute  to  simultaneous  profiler  based  the  reducing  3  coefficients  i  values  for  a, + a y + a y :  squares  Osborn  line  to  8(b)  equation  recorder  Accuracy,  repeatability  and  f i n a l  the  output.  Farmer  apply  (mmhos/cm)  the  Processing  any  The  between  form:  conductivity  where  approximation  case  band  range The  of  an  error  within  15  obtained,  and  accuracy  obtained  bar  minutes  in  of  each  possible  values  results  the  on  of  ±1  of  one  Figure those ±2  in  8  (a) 8(b)  mmhos/cm  24  CONDUCTIVITY ( MMHOS/CM )  STATION • CONDUCTIVITY  2  PROFILER  MARCH  T E M P E R A T U R E (°C )  29,1973 K H RS5  SALINOMETER  F i g u r e 8. Comparison of measured conductivities by two- d i f f e r e n t instruments (a,b) and measured and p r e d i c t e d t e m p e r a t u r e s (c,d) f o r two t i m e s on March 29, 1973.  25  seems two  very  deep  side  probes  of  the  magnitude, a  small  results due  reasonable, in  Figure  line  in  suggesting ebb  from  to  measurements  or  of  a  i t  does  8(a). 8 (a)  a  tide. those  either  as  for  The are  almost that  Therefore,  the  salinometer  s h i f t  in  calibration  the  i s  near  identical quite  between  that  surface  results  cn in  of  2 and  and  either  shape  stable  departure  water  factors  the  profiler  structure  the  both  and  following  the 5  profiler  meters  is  column  structure  between  are  in  error  certain  and  a  for  j probes. be  The  second  observed  differences profiler their  are  error),  instrument  to  outdoor effects become cases  a  on  within  the  flooded,  f a i l  laboratory  but  In  these  practice  of the  probes,  were  found  period  and  their  and  was  and  . A more  serious  probe  heads.  were  appearance  for  heads,  three  data  were  values  RS5  considered the  problem Often  as  probes  of  apparent the  was  deep  Rustrak  charts  retained  in  the the  f i n a l  was  from  and in  under  moisture  probes  removal  distinguishable during  the  but  done  detected.  after  on  humidity  concerned  easily  values  condensation  determined  the  the  (including  effects and  not  the.  applicable.  calibration  were  of  was  on  calibration  effect  can  although  the  seepage  influence  moisture  8 (b)  temperature  electronics  and  Figure  trend  accuracy  exact  entirely  similar  mmho/cm  influence  The  the  "moist"  ±2  moisture  their  conditions.  beads  to  heads.  minimize  few  figure  humidity  changes  the  in  overlapped  seemed  probe  l i k e l y  probes  Since  accuracy  electronics  temperature order  this  most  same  always  probe:  the  is  smaller.  factors  each  inside  the  results  Two for  for  cause  In to  would other the  normal. flooded  i n s t a l l a t i o n  analyses.  The  data  26 presented charts  in  subsequent  using  i n s t a l l a t i o n induced  calibration and  no  changes.  positively  sections  factors  attempt  Probe  were  was  made  eliminated  and  density  data  were  used  in  the  A  estimate  of  s a l i n i t y  reasonable  temperature  effects  improved  the  computed  for  salinometer  but  if  Rustrak prior  for  to  moisture  failure  each  of  of  and  representative  of  Knowing from  b, C  for  measured  8(c)  following  S  =  + b T  S  = s a l i n i t y  C  = conductivity  T  = temperature  2  on  data  where  derived  from  could  be  made  and  without  including  temperature  data  Temperatures  linear  relations from  accuracy  of  between RS5  periods.  are ±0.5  were  the  i n s t a l l a t i o n  shown °C  would  in be  way.  temperature,  the  s a l i n i t y  was  relation:  + bjCT,  (parts  measured results.  accumulated  this  the the  temperatures  an in  of  background  based  derived  conductivity  the  be  particular  and  (d) , data  can  estimates.  temperature  surveys  Comparisons  the  conductivity  and  derived  parameterization  incorporating  accuracy  conductivity  where  account  were  and  computed  to  the  immediately  heads  conductivities  Figures  obtained  from  determined.  Salinity  the  reduced  per  (3)  thousand),  (mmhos/cm), (°C),  as  derived  from  the  conductivity  data. The  coefficients  bj  were  obtained  from  a  multiple  regression  27 analysis  performed  from  Lafond»s  from  Figures  compared  in  s a l i n i t y ranges  calculated root  mean  then,  that  are  Table  the  1.  quantities  in  accuracy  of  Sigma-t  is  (P  closer  represents  of of  given  results,  is  listed  and  tho  each  previously  in  differences column  6  from  the  conductivity  values  indicate.  maximum  l i m i t  temperature  In if  data  fact  profiles computed  error  range  inaccuracies  combined  a  appears,  the  the  a l l  have  It  than  error between  and  thousand.  are  computed  quoted  per  actual  profiles  s a l i n i t i e s  for  The  obtained  f i e l d  parts  the  would  computed  terms  of  ± 0.01  for  related  fresh sea  to  an  of  combined  used  The for  in  of  properly taken  often  as  written  or  3  for  and  the  maximum the  specific  is  Kg/m ) 3  O" t  range  accuracy.  way  was  can  in  gravity  the  in worst  be  by  and  of  1.0000 in  sea  and  this  data and  (7)  the  been  from  evaluated  their in  one-half  Table  an  1 l i s t s  ,  by the  specific (that  done  the  including  of  Since  density  has  and  p  water,  3  of  to  temperature.  gm/cm ,  terms  Lafond  calculated  diroensionless.  established  Column  given  s a l i n i t y  calculated  temperature worst  relation  which  the  gm/cm  accuracy  °~t,  values  water i s  the  given  and  3  water  using  sigma-t,  conductivity  equation. figure  was  units  estimate  were  to  the  and  -1.0000) x10  density  i s  0.53  the  measured  appear  derived  ±3. 1 % o  and  temperature.  of  parameters  way.  (1951)  gravity  value  s a l i n i t i e s  Density  =  (3)  and  conductivity  °~t  accuracy  and  square  three Using  computed  equation  measured  the  (1951)).  (d),  An  of  conductivity  the  %o  possible  To  and  on  averaging  ±3.1  values  (Lafond  8(b)  considerably  error of  Tables  based  for  on  here.  p r o f i l e r errors Lafond's of a  this  Table  1  Comparison o f d e r i v e d and measured s a l i n i t i e s f o r s t a t i o n 2 on M a r c h 29-, 1 9 7 3 ( 1 5 5 2 h o u r s ) . * i n d i c a t e s i n t e r p o l a t e d values.  DEPTH (meters) ( D  0.3  0.8 1.3 1.8 2.8 3.3 3.8 4.3 7.3  .  COND. (mmhos/cm) (2) 4.47±2.0 3.89 4.61 5.01 6.65 9.06 12.09 1 4 . 18 26.34  TEMP. (°C) (3) 5.89±0.5 5.86 5.89 5.91 6.00 6.12 6.27 6. 38 6.99  SALINITY CALCULATED MEASURED*  (7oc)  (%o) (5)  C O  3.83±2.9 3.24±2.9 3.97±3.0 4.37±3.0 6.02+3.0 8.42+3.1 11.43±3.1 13.49±3.2 25.28±3.4  3.00±0.5 3.25 3.60 4.30 6.75 9.00 11.20 14.15 RMS  -  value  DIFFERENCE  (%o)  ( 4 ) - (5) = (6) +0.83 -0.01 + 0.37 +0.07 -0.73 -0.58 +0.23 -0.66  -  0.53  SIGMA-T (7) 3.04±2.3 2.58±2.3 3.16±2.3 3.47±2.3 4.77±2.3 6.66±2.4 9.02±2.4 10.63±2.5 19.8U2.7  NJ CO  29  sequence  of  together  with  and  as  in  °"t • s the  the  calculated errors.  case  of  from  An  the  average  s a l i n i t y  this  profile value  figure  of  in  Figure  ± 2.4  was  represents  8(b)  obtained  the  maximum  range.  C«££gnt  Metering  One  aspect  measurements tide.  is  Due  the  to  measurements  from  v e l o c i t i e s  motion  i t s e l f  exceed  However,  once  current The speed  years.  A  March our  siumlataneous  and  two  at  located record  at  the  of At  these  station  The suspend  the  2  platform current  meter  is  a  Canada  impossible  on  station  and  time  the  boat  particularly  in  the  i t  both  from  became  The  a  catamaran  River  was  object  three  to  for  with  several  undertaken station  was  as  a  conductivity  however,  vessel.  angle.  occupying  density  the  feasible  wire  Fraser  programme  2.  the  addition,  In  operated  boat  f i e l d  the  constant  the  by  once  suspended  has  Survey  velocity  to  1  on and  obtain  function profilers  probes  at  a of  were  station  1  lost.  station  meter.  current  at  stations;  at  reliable  flow  Water  were  making  installed  measuring  this  to  were  of  at  relation  errors,  equipment  velocity  tide.  functioning  the  Survey  1973 with  and  in  its  meter/second.  the  measuring  equipment  depth  meter  joint  30,  i f  examined  v i r t u a l l y  large  platforms  Water  current  one  is  seldom  and  angles,  boat  induce  direction,  River  structure  wire  small  can  the  Fraser  current  a  current  a  the  large  river  hold  of  To  2  was  used  eliminate  as the  a  fixed  problem  point of  to  changing  30  wire  angles  the  platform  constant meter  using  stable  platform  meter  of  equipped and  in  300 10  this  rope  for  each  i n s t a l l a t i o n  operating  the  RS5  sensor, a  and  magnetic  and In  ± 5  a  s o l i d  compass. degrees  general,  the  when  minimum  clearance in  vane An  i n  the  a  of  1  give  the  manner  to  and  the  was  reading.  Figure  9 (c)  shows  and  in is  was  Figure  guide  9 (a)  hand  To  tied  obtain off  the  the  wire  by  depth.  a  current  lowered  required  gave  The  on  from  This  rope  to  current  method  of  shown.  a  Hydro  Products  rotor  ±  3  is  quoted  were  became  small. from  minimize  by  the  platform  the  to  speed  manufacturer. each  guide  nearest  speed  relative  for  The  speed  the  for  stable  the  series  readings  percent  values  meters  400  activates  direction  of  direction  1/2  running  raised  provides  speeds  i n s t a l l e d . currents.  was  accuracy  the  a l l  Savonius  direction  except  located  A  in  running  hauling  meter  meter.  was  wire  the  salinometer  current  direction  to  guide  trolley  configuration,  the  and  a  system  a  anchor  degrees  and  The  current,  pound  with  calibrated  most  the  a  angle  9(b)) a  changes  to  wire  was  (Figure  the  with  depth  wire  pile  had  and  interference  of  a  was the  flow.  The primarily current pound but  the  channel  Water for  meter  estimating is  weight.  suspended The  direction at  Survey  station  of  Canada  discharges on  a  magnitude  relative 1 is  to  f a i r l y  in  single of  the  the  eguipment  was  unstratified line  just  current  river  is  straight  and  the  rivers. above  vector  not  designed  is  a  150  obtained  measured. principal  The  flow  The  31  F i g u r e 9. (a) O p e r a t i n g t h e p o r t a b l e salinometer the skiff. (b) Hydro Products c u r r e n t meter and trolley running along a guide wire. (c) O p e r a t i n g t h e c u r r e n t m e t e r a t s t a t i o n 2.  ofr  32 directions at  station  desired is  are  more  2.  Although  direction  reasonable  represent  to  flows  29,  minutes,  on  A instrument presented  in  be  be  parallel  actual  current  aligned  with  the  2  was  Velocity  March  the  Table  also  the  from  the  speeds  shoreline  component station  exceeding  than in  a  1 data,  i t  20  cm/sec  banks.  occupied profiles  during were  daylight  measured  hours every  on 45  30.  of derived 2.  to  velocity  computed  that  summary and  the  cannot  1973.  as  to  assume  Station March  l i k e l y  the data  accuracies for  the  associated  Fraser  River  with project  each is  33  Table  2  Summary o f a c c u r a c i e s a s s o c i a t e d w i t h the Fraser River project. * indicates explained i n the t e x t . CONDUCTIVITY PROFILER  (D  instruments used for derived values as  RS5 SALINOMETER (2)  HYDRO PRODUCTS CURRENT METER (3)  CONDUCTIVITY (mmhos/cm)  ±2.0  ±0.5  -  TEMPERATURE (°C)  ±0.5*  ±0.5  -  ± 3 . 1*  ±0.3  -  SALINITY  < %o> °t SPEED (cm/sec) DIRECTION (° of arc)  ±2.a*  -  —  -  -  -  ±  3 ±5.0  PERCENT  34  Chapter  OBSERVATIONS  3.  On  five  occasions  salinity/temperature/depth collected  primarily  p r o f i l e r s  and  temperature once  the  water  short  space  in  the  of  conductivity straddle deepest These  60  On  data  water buoy  the  are  f a i r l y  was  done  well be  decreases  in  the  downward  Conductivity  The  to  and  Figure  feature the  the  upstream dilute  the  of  ebb  s a l i n i t y  of  river  the  over  were  a  sampled  with  locations  located  in  the  found.  longitudinal  section  depths shape  the  -  of  at  each  the  salt  p r o f i l i n g  s t r a t i f i c a t i o n  stations in  indicating  water  quick  coincide  currents  between  f a i r l y  were  like  -  the  approximately  water  isohaline  direction salt  a  wedge  on  upstream  salt  and  angles  average  stations  station, of  10  the  especially  the  the  strong  wire  in  were  conductivity  examination  and  the  is  was  stations  traces  period  data  the  two  fourth  for  an  distance  the  limiting  that  a  At  in  on  profiles  four  1973  2  no  These  locations  and  maintained, seen  8,  study  information  allowed  1  Despite at  check  f i r s t  channel,  obvious  f i e l d  spanning  by' i n t e r p o l a t i n g One  also  March  profiled  intrusion. 28  mixes  of  made.  various  The  3.  were  these  and  at  p r o f i l e r s  part  plotted  Making  minutes,  station  station.  can  time.  a  the  background  station  kilometers.  10.5  i s  on  structure  space  as  provide  was  of  surveys  act  structure.  boat  salt  to  to  during  1 and  at is  2.  It  the  salt  wedge  that  fresh  water  below.  Temperature  measured  conductivities  reflect  the  extent  of  mixing  35  SALINITY  (%o)  SALINITY  (%o)  (d) 2  0  2  BUOY 27  4 DISTANCE  (KM)  6  BUOY 28  8  (e) F i g u r e 10. T y p i c a l s a l i n i t y data f r o i n the F r a s e r estuary on a s t r o n g l y e b b i n g t i d e . The A g a s s i z d i s c h a r g e i s 1 6 0 m /sec. 3  36  of  salt  between  approximation, in  a  like  the  manner  temperature  data  in  11  Figure  and  relation  between  of  as  overall  Salinity  in  inequality  of  predecessor  produces in  the  stations  be  last  in  summarized  for  and  is the  Figure  from  the  two  week  2.  This  considering  profilers and  group  from  Chapter  estimate  linear  during  particular of  groups  a  each  density  section  The  three  relation  and  s a l i n i t y  are  warmed  temperature  a  rough  distributed  intervals,  masses  reasonable  on  day  for  a  conductivity.  conductivity  conductivity  range  a  the when  to  of  very a  1,  derived  2  Fraser  the  the  effect  of  density.  from  3  which  below  data.  t i d a l  Figure  plotted  which  each  tide  high-high  intrusion  extreme  conductivity  in  the  amplitudes,  produces  In  for  the  variation  succeeding  different  been and  estuary  large,  meter  markedly  have  considerable  each  conductivity  profiles  were  this  is  zero  fraction  the  a  30  water  the  to  to  considered  s a l i n i t y  in  gives  of  is  results  described  assumed  as  Profiles  There  nearly  and  and  measurements  roughly  pertinent  calculate  accuracy  temperatures  by  the  calculation  STD  data  both  p r o f i l e r  i n s t a l l a t i o n type  the  be  related  Since  to  conductivity  i f  masses  can  during  another  period, used  linearly  temperature  reasonable.  was  11  one  water  temperatures  collected  from  measuring  two  and  separated  very  the  looks a  ranging  much  high-low  water.  This  two  series  i l l u s t r a t e tide  type.  profiler  data  the  as of  from  as  water  characteristics 12  diurnal  i t s only  variation revealed s a l i n i t y  behaviour  The using  a  at  s a l i n i t i e s equation  37  8  STATION  I  A JAN. 30 0925 O JAN. 30 I 3 0 0 O MAR. 8 1 0 3 9  © + • 0 9  STATION 2  J A N . 29 0920 J A N . 29 1 2 5 0 MAR. 8 I I 0 I MAR. 29 0 8 5 3 MAR. 29 I 5 5 2 ~0"  o  BOTTOM WATER  SURFACE WATER  ± 10 15 CONDUCTIVITY (  0 Figure  11  obtained occassions  20  MMHOS/CM)  Conductivity and temperature with an RS5 salinometer on in the Fraser estuary.  25 da t a four  30  Salinity  [%o  10  Station I  >{k  River discharge M 3 0 m V s e c .  a>  °"'»  0355 H  l'  20 2  4  E • Station 1 • Station 2 * Station 3 20  22  0  2  4  6  B  10  February •0  20  10  10  -  12  14 *  16  18  20  22  0 Hour*  10, 1973 Salinity  K  20  IQ  •/  (%o)  2Q 6  VI  ^  0856  \  0933  \ V  \  \ \\ • Station 1  \  * StOtion 2 * StoNttn  3  •'Deepest Channel bottom at Station  Station I  I  River discharge l 0 6 0 m V s e c .  22  0  6  2  8  10  12  14  16  20  March 18, 1973  22  0 rtoun  Salinity  *.  u  *\ *  0258Hou't  • S'01'On 1  *  * Siot.on 2  |  • SiO'.on J  I  \  \  \f  f  0456  } \  0358  ff  >  j | * t  tt ' " X  •U .6  10 r :  \  ZD  HJ  0658  "'V  \  (%„) 10  Y\  V\  20  *  ;•0  07 SB  \ i  !  \  \ V  10  56  20  iV  \ \  •  \  "  i  io  20  \ "V ' ^  09S9  {  3B  O  1 \  \ >  \  3  ' *  1  i \ »  i  \  Deepest Channel bottom ot Station I  Figure 12. 18, 1973 a t station 1.  20  Salinity-depth p r o f i l e s o b t a i n e d on February 1 0 , 1973 and March s t a t i o n s 1, 2 and 3 . C h a n n e l b o t t o m i s t h e g r e a t e s t s o u n d i n g a t  CO CO  39  (3)  and  the  profile  is  plotted  particular could  the  less  nearer  to  meant  that  any  for  the  not  of  the  fresh  This  water  layer  u n t i l  the  station  shallowest  with  respect  i s  the  at  Despite  upstream  these  station and  water  The  that  we  are  has  2. to  any  centimeters  error  would  profile can  be  position  has  monitored  at  as  i s  probe  s l i g h t l y  has  the  f a i l e d  behaviour  actual  salt  least  five  at  station  station  be  occur  each  is  the  Furthermore, of  this  1 and  watching  reached  datum  estimate  situation  additional  of  the  platform  column  l i t t l e  at  50  below  an  intrusion  above  at  Each  measurements  line  series.  seeing  I  The  where  means and  3.  11.  surface  and  the  probes  the  f i r s t  kilometers  worse  of  datum,  since  bottom  lost  Figure  free  1 and  channel  series  1.  stations  of  of  approximately  s o l i d  the  March  of  The  percent  for  the  station  70  the  horizontal  series  water.  relations to  error  each  deepest  only  a  for  combination  at  motion  respect  maximum  most  station  worse  a  high  represents the  with  profiles  for  seen,  temperature  station,  introduce  between much  linear  so  1  wedge or  six  is  this  of  the  problem  positions.  limitations  there  i s  much  to  be  gained  by  series  the  s  examining long  high  the water  penetration, The  at  duration  and  at  a l l  station  been  recorded March  at  three  this has  manner. resulted  exceeding  associated  tide  the  in  probably  p r o f i l e r  halocline  by  data  3  has  with  maximum series,  a  February  very  long  kilometers  s a l i n i t i e s  the  the  shorter  pattern  high  water  wedge  station  the  interface  exceeding  This  salt  above  measured  salt-fresh  penetration. where  in  clearly  the  stations  15  In  distinct  around 25  is  1.  %•>  high have  contrasted  duration  has  40  produced to  be  a  s i g n i f i c a n t l y  measuring  improved gain  nearly  3  The  by  the  after  typically  between  halocline  has  the 2  depth March  at  suggest  layer.  a  These  local  mixing  surface  10  %o.  In  lost  to  an  almost  1 and  the  back these  previous  ebb  v i c i n i t y  . of  river  and  Strait  These does with  not  produce  a  measurable  the  salt  more  tide,  the  wedges  upstream  -  i s  18).  show  a  maximum,  any  distinct  of  s a l i n i t y  preserved  instruments the  result  flooding flood  strong of  tide,  far  as  (near  the  f i n a l  salty or  a  duration  formed  as  and  water  from  tide  in  1  salt  convection  waters,  water  by  stations  is  mixing 1 and  confluence  2 of  ).  show  localized  dispersed  longitudinal  surface  certainly  high  data  to  d i s t i n c t  series  reach  over  the  The  Sandheads  Georgia  profiles  have  arrested  of  brackish  or  the  series  and  both  for  could  masses by  17  (17  seems  fresh  increase  flowing  mechanisms.  during  the  convect  1 for  halocline  s a l i n i t i e s water  tide  uniform  layer  and  3 of  less  salt  February  through  upstream  to  from  14  a  s a l i n i t i e s  the  The  surface  surface  s u f f i c i e n t the  2.  profiles  between  of  surface  15  mixed  high  waters  combination  water,  high  station  to  and  well  following  of  spite  between  column)  mixing  profiler  In  relocated  water  at  and  l i m i t .  was  two-way  recorded  stations  series  of  and  high  been  3  profiles  p r o f i l e s  just  with  meters  evident  penetration  intrusion  (profiler  more  is  suggested  that  the  coverage  halocline is  near  shorter  t i d a l  the  s a l i n i t y mixing  density  s a l i n i t y  that  gradients  is  structure  gradient  Fraser  in  strong and the  estuary associated  enough there surface  to is  a  and  41 bottom  waters  estuary  can  be  discernable The  near  in  particular  these  If  salt-fresh  coupled  w i l l  small.  data  the  maximum  two  hours  to  seaward  water  at  confirms to of  the  these  occur velocity  quantify  penetration  of  approximately  Conductivity  The two  week  1 and (and  three  two  to  be  w i l l  layer, mass  2.  the  and  the  in  water  tide  at  station  gradients  water  being  forces.  flow  where  water three  the  lags  but  occurs 3,  10  are  maximum high  i t  high  and  w i l l  be  the  the  flows  relative  the  just show  February one  to  after  two  that  the  increased  during  downstream that  The  the  a  due salt  March  series  penetration  seems  tide. i t  In  is  appears tide  the  the  about  and  phase.  across  of  In  upstream.  measurements  relationships  time.  suggests  following  these  small  are  to  motions  accelerated  This  to  is  the  pressure  momentum  and  density) is  of  separation  exchange  9  t i d a l  response  layer  phase  Profiles  a  of  which  the  comprised  salt  hours  during  salt  layer  of  observations,  phase  of  separation  continues  data  the  high  pressure  about  most  relative  large  surface  depth  throughout  then  i f  behaviour  layers  of  large  of  the  two  the  penetration  s a l i n i t y  when  the  a  following  period  in  the  have  stations  v e r t i c a l  each  Conversely  w i l l  at  i s  and  motions  hours  in  However,  terms  exchange  interface  highly  in  balances the  tide.  data  motion  force  f r i c t i o n .  be  viewed  in  changes  high  absence  d i f f i c u l t  that  at  the  the  station  to  maximum 1  by  hours.  Charts  conductivity  periods,  since  by  p r o f i l e r s  were  the  13  end  of  or  operated 14  days  basically in  the  for river  42  sufficient  damage  to  removal  warrant  these  time  constant the  values  two  where  of  vertical  axes  meters  time.  stations  this  1 and  datum  surface from  is  based  probe  the  bottom  the  platform  As during  the  known.  on  t i d a l  was  1  lines  assumption  was  would  to  be  the  of  a  the  these  previously period.  examining applied  and  map  line  The  anchor  also  directly  relative  to  indicates  the  depth  the  the  are  dimensions  represent  14  horizontal  used  position  1.  data and  13  lines were  broken  t i d a l  the  of  between  represent  and  datum  level  contours  of  datura  of  the  to  bottom  and  unlike  river  bed  at  of  f a i l  failure  charts  and  reduced  data.  within  the  error  were  plotted,  at  time only  general  probes  any  could  in  which  at  the  bounds were  the  water of  the  operative  appropriate  section.  surface (G.D.)  would  data:  indicate  zeros  time  Rustrak  stable  To  the  probes The  the  to  s t a t i c a l l y  left  Records . geodetic  2  from  measurements.  section  depths,  station  contour  maps  one,  line  presenting  Figures  surface  estimated  i n s t a l l a t i o n  One  a  free  station  explained  by  for  in  2  locations.  determined  individual  number  probe  12,  a  of  1 and  interpolating  contour  from  Figure  of  plotted  Sandheads  the  At  by  stations  method  form  data  in  be  column  above  since  3  the  and  at  Conductivity  are  probe  bottom  heads  obtained  tide  for  heights  the  cycle.  above  The  Tidal  in  conductivity  types  probe  A convenient  is  different  plotted. for  data  values  in  the  repair.  each  the  is  of  to  for  distance axis  and  series  measured  for  occurred  height are  also  at  station  plotted  in  1 relative  to  Figures  and  13  the  '1  STN.I  FEBRUARY  Figure 13. Contour estuary. Bottom i l i n e s are indicated d i s c h a r g e i s 1130 m  3  1973  maps o f c o n d u c t i v i t y a t t h r e e s t a t i o n s , i n s marked r e l a t i v e to t h e p r o f i l e r and t h e u s i n g measured data a t S t a t i o n s 1 a n d 3. /sec. Times are noted i n P a c i f i c Standard  the Fraser free surface The Agassiz Time.  O J  STN.I  MARCH  1973  Figure 14. Contour maps of c o n d u c t i v i t y at. three s t a t i o n s i n the Fraser e s t u a r y . Bottom i s marked r e l a t i v e to the p r o f i l e r and the free surface lines are indicated u s i n g measured d a t a a t s t a t i o n s 1 and 3. The A g a s s i z d i s c h a r g e i s 1060 m V s e c . Times a r e n o t e d i n P a c i f i c S t a n d a r d Time.  45  14.  Chart  datum  for  representing  the  of  Geodetic  position.  such  a  more  contour  recorded  pronounced occurred  lowest  diurnal  inequality  height  is  8 and  produced  to  the  and  therefore  Figure  inequality. 16  is  is a  a  sloping  level  a  line  function  plane  and  as  obtained  from  the  datum.  in  February  River  considered  reference  March  and  t i d a l  charts  between  from  Fraser  datum  convenient  The data  the  11,  In  20,  13  were  1973  for  contrast  1973  the  have  conductivity  data  tides  a  having  tides  small  contoured  a  which diurnal  in  Figure  14.  Care data. wire 2  As  must  mentioned  angle  during  of  excessive and  f i r s t  during  wire  the  angles  did  this  into  account a  approximately  2.5  of  on  this  error  data)  periods  than data  is i s  of to  the  probe  not  for I  estimate  measurement 3.0  meters  contours  to  indicate  the  case.  This  wire  angles  where  an  during  scale  attempt absence  problem were  at  of  been  was  water  to  and  ebb  The  the of  effect  to  adjust  for  longer  corrected  confined  that  reading  made  and  stations  large a  a  ebb.  period,  shown.  salt  daily  both  the to  has  1  indicate  recording  that  giving  large  one  February  stations  phases  Probe  the  at  the  correspond  on (no  on  t i d a l  entire  the  deflections  occurred  period  occur.  the  interpreting  line  degrees  remaining  function  points  20  when  i n s t a l l a t i o n  not  lowest  March  previously,  2 did  taking  the  exercised  approximately  the  Observations  1  be  for  less  than  the 10  degrees.  The  conductivity  profiler  at  station  3  produced  data  for  46  only  one  t i d a l  operative  for  The  the salt  at  If  and  water  true  entire  period  in  Figure  feature  in  both  scale  cycle.  salt  in  predominant  horizontal tidal  the  cycle  of we  is  2  station  1 due  the  (Figure  13)  and  However,  the  flood  indicate  a  water  were  degree  an  The  vertical  of  mixing  the  data;  March  p r o f i l e r  was  penetration. show end  that of  layer  ebb has  is  the  the  water  appreciable taken  of  and  place.  only  mixing  15  most  of  both true  station to  i s  is  figures  probe  line  the  salt  of  however, 10  the  certainly  indicative  the the  of  measured ebb  the  cycles  and  flood  for  stations  1 and  3  indicate  that  the  of  the  following  fresh  both  14).  kilometers.  contours  very  at  February  (Figure  study;  upstream  of  acertain  tides  the  removed  when  certainly  in  on  February  contours  on  from  i s  on  during  This to  each  separate  periods  flood  this  large  time  March 1  was  during to  measurements in  3  the  is  of  in  exceeding  close  steepness  salt  station  wedge  d i f f i c u l t  On  made  the  contour  station  were  is  deflections  water.  comparable  located  is  direct  This  water  long  but  probes).  figures  probes at  distance  results  i t  probes),  (10  instrument.  No  spacing  tide.  The  at  present  s t r a t i f i c a t i o n the  salt  length  14  are  line  of  large.  intrusion  of  probe  records  not  (seven  salt  there  although  tide of  the  each  loss  detected  portions  3,  13  millimho/cm  the  penetration  indicates  15  at  large  return  s t r a t i f i c a t i o n  the  and  of  masses,  present  stations  deflections  the  water  not  to  motion  use  fresh  Figure  rapidly  water  down  l i m i t the and into  ebb toward the  2  in  tide the salt  47  The water  did  not  result,  move  the  profiler The  conductivity  contour  both  toward  predominantly water turn  the  become  Current  the  two-way,  furthest  (except  on for  times  15(a).  not  The for  March  surface  is  suffer to  the  the  further  cf  each  3  and  mixing  processes  since  greatest  a  at  1 to  rate  reasonable  as  interface.  station  mixing  salt  and  the  and  are  the  dilution  salt and  in  mixing.  In upstream  and  station  2  bend.  1973.  Profiles  made  plotted  in  15  are  indicated  are  current  are  from  general  An  to  the  the  the  15(b)) the .  mean  of  90  for  the  ebbing  tide  from  speeds  apart 2.  in  Figure  the  f i e l d  directions  period  two  1 and  relative  and  at  minutes  30  flow  the  out  stations  directly  since  was  carried  March  Throughout  were  to  the  occupied  its  at  direction  value.  directions  examination  the  component  current  location  to  plotted  current  downstream due  2  plotted  surface  ±15°  are  (Figure  station  Figure  relative  speeds  1  At  this  only  was  30,  station  2  metering  6)  current  station  sharp  trend  If  that  present  from  current  no.  measured.  varied  flood  along  completion  show  Structure  stations  data  14  each  increases  toe.  would  3 on  mixing  wedge  susceptible  Simultaneous  The  in  of  this  Figure  s t r a t i f i c a t i o n  degree  upstream  more  in  generally  the  in  station  variation  spacing  that  increase  past  differences  reflect  suggests  much  records  of the  speeds at  are  station  station river  2 -  bed  greater 1  than  on  the  in  both  those inside  topography  near  at of  a  STATION 1  k  6  CL"  < I  < Q 0 1 0  1 6  12 MARCH  (a) -150  1  1  18  24  1  CURRENT -100  3 0 , 1973  SPEED -50  ( CM  SEC.) 0  downstream -150  CURRENT -100  SPEED -50  upstream  (CM/SEC.) 0  F i g u r e 1 5 . C u r r e n t s p e e d m e a s u r e m e n t s made a t t w s t a t i o n s i n t h e F r a s e r e s t u a r y on March 3 0 , 1973.  49 station the  shows  2  bend  located  (Figure  on  that  One the  4  salt and  as  on  the  have also  5).  can  increases  than  trend  return  near  can  to  the the  be  ebb  flows.  After  continues  to  increase  at  station  the  seen  station  bewteen  in data  2  profiles the  t i d a l  5  of  the  increasing  p r o f i l e although and  flows  the  induced  the  be  behaviour  of  the  transport  trend  velocity data  in  surface  profiles  velocity a  shear  is  not  shear  also  each  of  to  (compare  1 the  These  6.  stream  upstream  Such  5.  outside  shore.  2  in  ebb,  effect  flow  observed  in  the  the  station  increase  has  on  main  to  between  lag  suggests  rather  readily  in  removal  started  This be  apparent  phase  side  sediment  and  4)  s i g n i f i c a n t  p r o f i l e s  currents of  considerable  so  also  indicate  a  layer.  Parameterization  The  conductivity  the  behaviour  and  use  in  of  the  the  the  height  of  salt  the  water  column the  layer  of  fresh  egual  to  that  Thus  the  two  water  provide masses,  mathematical,modelling  parameterize  decompose  charts  lower  data  in  terms  water. came  from  measured water  and  a  lower  characteristic layer  depth,  a  a l l  the  water  of h*,  detailed  but  for  procedures,  of  Since  a  length the  Strait  column layer the i s  is  scale  associated  Georgia,  to with  found we  =  VSg  / o  S(z)  dz  in can  two  layers:  an  an  average  s a l i n i t y  having Strait  of  Georgia  upper  water.  by:  h h»  of  analysis  convenient  o r i g i n a l l y  of  into  defined  further i t  salt  description  (4)  50  where  Sg  water,  S (z)  total  depth  salt  in  layer  is  is  the  of  the  characteristic  the of  measured  water  o r i g i n a l  thickness  There  are  gives and  part  a  salt  not  of  problem data  when  the  reliable  calculated  and  used  depth  to  contours  salt  chart  for  a  the water are  loss  probe  below  at  and  this  way  of  Georgia  h  is  a l l  into  of  the  of  probes  of  the  of  the  the  salt  The  meters constant  of  the  this  way  station the  error  the  it to  of  not  +50  included  (Figure  4).  The  which in  plagued  this  line,  way and  intrusion.  superimposed tide  in  the  s a l i n i t y  Figure  represents the  conductivity,  river not  30.5 %  the  s a l i n i t y ;  16 does  wedge c  Strait  mouth.  the  onto  salt  of  is  The  parameterization once  is  the  probe  18  here  at  maximum  March  total  expected  probes  been  of  to  each  column  be  have  reference  adjacent  at  percent  the  features  since  defined  1  introduced  2  kind  extend  location  on  the  this  parameterization  near  1 and  intrusion  80  deep  low  1  h  bottom  to  error  station  the  water  is  in  not  maximum  line  i s  do  so  the  obtained  analyses 10  of  The  level  line.  f i n a l  lines  In  least  loss  portion  of  essential  to  z  involved  the  error  the  are  to  probe  1.  water  h'  reached  Georgia  station  and  estimated  the  from  estimates  the  Strait  redistributed  1 and  portion  to  arises  the  depth  lines  At  A greater  for  despite  in  section  an  the  due  at  is  relative  having  values  contour  reproduce has  cross  integration.  second  the  line.  probe  station  stations  the  the  the  at  other  most  F i r s t ,  due  at  d i f f i c u l t i e s  monitored  centimeters  worst  main  datum.  accurate,  March  column  to  most  the  probe  referred  was  the  the  water  two  layer  depth  in  s a l i n i t y  of  h*.  parameterization. deepest  at  s a l i n i t y  was of The  0  h'from equotion ( 4 ) Sg =30.5 %o conductivity probes vertical scale: \.Q - 2.0 meters n  8 Figure 16. conductivity  10  12  March 18  14  C o m p a r i s o n o f h» c a l c u l a t e d f r o m e q u a t i o n s t r u c t u r e on March 1 8 , 1973 a t S t a t i o n 1.  18  16 (4)  and the  measured  20 Hours  52  however,  the  conductivity  equivalent  f o r the temperatures  Figures data  from  figures  both  contoured  time  periods  o f 28  station  %>  was  over  chosen.  this  several  figure  previously  results  exceeding  25 c e n t i m e t e r s .  the  periods.  These  as the c o n d u c t i v i t y data a comparison structure.  This  between t h e  In  order  The  value  to  on t h e deep difference  of  30.5 %  i n a d i f f e r e n c e i n the i n t e r f a c i a l  of  h e i g h t s not  wedge i s f l u s h e d o u t o f t h e e s t u a r y  on l a r g e  whereas  the •i n t e r f a c i a l  17 and 18 n e v e r  completely data  to zero  revealed  at station  that  c o l u m n was composed  estuary.  Station 1 i s  t h e mixing the  pockets  t h e main  in  values  of  Figures  17 and 18 i s an a r t i f a c t  does not r e p r e s e n t  ranging  shallowest  after  less  ebb  tide, from  o f remnant s a l t  remain  z  the  of s a l i n i t i e s  reflect  upstream  An e x a m i n a t i o n  following  probably  several  1.  Figures  which  of  the  section  t r a c e s of s a l t  there water Thus,  1 1/2 t o 2 m e t e r s t h e i n t e r f a c e  the s a l t  wedge  of the i n t e g r a t i o n position.  goes  digital  throughout and  that tides  1 t o 5 Hi ,  wedge has r e t r e a t e d downstream.  than  ebb  the e n t i r e  water  2.5  mentioned  Q  the s a l t  in  an  probes  The c o n d u c t i v i t y c h a r t s i n d i c a t e  line  to  presented  corresponds  recorded  cycles.  and  nearly  parameterization for  f o r Sg and f o r d a t a  o f t h e maximum s a l i n i t y 1  % o between  salinity  must be f o u n d  are  i n the estuary.  13 and 14 and a l l o w  1  average value at  same  h , a value  a figure  found  values  and March m e a s u r i n g  h* and t h e d e t a i l e d  evaluate here  the  i n Figures  calculated  salinity  17 and 18 show t h e t w o - l a y e r the February  span  and  water which the are would for  shown i n  p r o d e d u r e and  Bottom o  STN.2  o  g ' ____ If)  o cd '  _a> o •x>  (m  OJ  o o. CO  o o  Bottom  p cvi  O g  STN.3 '  o  .—. if)  CO "  o  QJ  £ —•  o O . CJ  o o  Bottom oooo HRS.  FEBRUARY 1973  10 _L_  F i g u r e 17. Two-layer p a r a m e t e r i z a t i o n of the c o n d u c t i v i t y d a t a o b t a i n e d in February 1973. Bottom l i n e s represent the r i v e r bed a t t h e p l a t f o r m sites. Free s u r f a c e l i n e s are p l o t t e d from measured data at S t a t i o n s 1 and 3.  12  _i  on  STN.I  Bottom STN.2  Bottom STN.3  Figure 18. Two-layer p a r a m e t e r i z a t i o n of the c o n d u c t i v i t y d a t a o b t a i n e d in March 1973. Bottom l i n e s r e p r e s e n t the r i v e r bed at the platform sites. Free s u r f a c e l i n e s are p l o t t e d from measured d a t a at S t a t i o n s 1 and 3.  55 Although position, provides between  dividing a  good  the  lags  the  forms  a  just  feature  ebb  tide  penetration, example,  the  salt  the  contour  spite This  and  wedge  of  implies  required  in  i s  charts the  the  range  actual  into  two  the  phase  figures  of  determined  at 2  out.  There  to  can  salt  wedge  consider  the  data  on  Figures  velocities water.  13)  past  within  penetration on  the  that 2,  hours,  order  the  no  the  in  3  salt  to  station three  to  1  60  to  the  maximum  water  come  a  often  point  maintain  10  (indicated  at 80  the  removed.  (Figure  four  recorded of  where  consistent  rapidly  February  way  maximum  The  longer  i s  this  relationship  show  seems  which  flushed  layers  station  since  water.  water  i n t e r f a c i a l  p r o f i l e s .  high  salt  completely  salt  Both  s a l i n i t y  stand  considerable  that the  when  we  the  following  does  of  the  particularly  the  easily  after  i f  in  in  column  layer.  water,  from  plateau  water  description  f a l l s  not  the  uncertainty  each  high  is  One  For  in  conclusion  penetration  in  graphic  difference  with  is  the  motion  penetration time  there  17), in  hours  in  station  3.  cm/sec  are  56  Chapter  4.  THEORETICAL  An important large 15  of  features  the  flood  of  small  tides  their  and  14).  u t i l i z e s such and  these  i s  the  is  for  a  to  be  density into  exceeding  even  for  masses  mixing  phase  (Figures  t i d a l  estuary  flows  relation  river  discharge.  d i s t i n c t  at  the  the  Since the  as  the  currents  furthest  does A  provides  in  boundary  upper  interface.  which  described  provides  model  stations  and  13  between  station  layers,  information  remaining  the  motions  and  across  by  distinct  position  water,  to  period  created  wedge  river  tend  t i d a l  salt  to  forced  water  quantitative  resulting  10  relatively  also  the  the  be  that  layer  not  allow  similar data  to  predictions.  The  hence  the  fresh  the  the  several  appears  can  throughout  model.  at  and  water  structure  two  It  water  tides,  mathematical  parameterization  the  salt  fresh  a  tide  the  low  of  of  heat  into  model  functions  or  the  and  revealed  lengths  i l l u s t r a t e  provide  salt  verify  also  the  measured  that  two  has  behaviour.  despite  as  two-layer  of  1,  salt  can  chapter,  assumed  mixing  the  decomposed  previous  The  parameters  forcing  seaward  data  data,  and  properties  data  data  intrusion  extremely  station  The  between  important the  on  A mathematical  If  the  above  wedge  produce  discharges.  currents.  relationship  prototype  salt  identifying  estuary  strong  the  Steveston,  estuary  freshwater  the  of  often  above  the  retain in  examination  kilometers  out  CONSIDERATIONS  f i e l d salt  the  data layer  density  also as  i t  indicate flows  contrast  that  fresh  upstream  between  the  water  reducing two  mixes  down  the  s a l i n i t y  water  masses.  57  This  effect  produces lost. the  would  a  well  At  any  be  mixed  zone  rate,  detailed  leading  edge  of  theoretical  work  the  a r b i t r a r i l y  chosen  These estuary When river  water  above  usual  which  the  traces  downstream  compatible  at  s t r a t i f i e d retain  the  solve  have  aim  motions  time  has  been in  neglected.  made. the  the  are  ).  The  the  salt The  by  be one  the  f i n a l  recourse  model  to  To  further  estuary  geometry  in  estuary  front  is  by  of  Figure or  an  in  the 19. the  computed  by  the  documented  in  the  and  or  baroclinic  the  calculations  wedge  for  meter.  shown  be  is  subsequent  defined  s t r a t i f i e d  modelling  The  to  can  two  probably  available  the  to  well  governing  derivatives.  variations  been  the  the  and  of  which  located  of  in  as  hydaulics  of  not  mathematical  out  position.  boundary  analytically  procedures l a t e r a l  t i d a l  a  t i d a l  motion  and  visualized  (1964,1970)  this  the  to  forced  are  equal  and  1  s t r a t i f i c a t i o n  considered  water  be  the  the  of  the  Since  lead  equations  (Dronkers  calculation flows  been  front,  barotropic  literature  to  has  i s  "toe'  distinct  wedge  salt  may  wedge  observations  toe  of  the  the  salt  wedge  depth  uear  where  the  assumptions  flows  salt  greatest  two-layer must  be  toe.  to  examine  the  d i f f e r e n t i a l  equations  equations  d i f f i c u l t  are  numerical simplify and  integration the  density  equations structure  seaward limit  sail front  fresh water discharge Q  barotropic  computation  Figure 19. Visualization into the Fraser estuary.  of  s a l i n i t y  intrusion  freshwater density p  river mouth  Figure 20. modelling.  Notation  used  i n  mathematical  59  The E q u a t i o n s In fluid  o f Motion  the  case  of  t w o - l a y e r model w i t h o u t m i x i n g , t h e  m o t i o n s i n e a c h l a y e r a r e g o v e r n e d by t h e l a w s  momentum c o n s e r v a t i o n . right-hand at  a  cartesian  the river  mouth  The e q u a t i o n s o f motion c o - o r d i n a t e system  ( F i g u r e 20 ) .  o f mass  and  are referred to a  with the origin located  Neglecting  lateral  variations  t h e l o n g i t u d i n a l momentum e q u a t i o n f o r a n i n f i n i t e s i m a l v o l u m e i n e i t h e r l a y e r c a n be w r i t t e n a s (Cameron a n d P r i t c h a r d  where  -a  du + u  dn dx  u  w a r e t h e i n s t a n t a n e o u s v e l o c i t i e s i n the x and z  dt  and  du = dz  + w  d i r e c t i o n s , p i s the pressure (  ).  In equation  neglected the  of  (5)  3p  dx  and  0!  i s the  specific  volume  (5) t h e m o l e c u l a r v i s c o u s s t r e s s e s h a v e been  s i n c e they a r e s e v e r a l o r d e r s o f magnitude s m a l l e r  turbulent  stresses.  c o n s i d e r e d t o be composed  (a)  (1963) ) :  a time  The  instantaneous  velocity  than u i s  o f two c o m p o n e n t s :  u o b t a i n e d by a v e r a g i n g o v e r  periods  s u f f i c i e n t d u r a t i o n t o remove t u r b u l e n t f l u c t u a t i o n s .  Thus, u  represents  mean v e l o c i t y ,  the slowly varying velocity  field  over time  intervals  longer than t h e averaging period.  (b)  a velocity  fluctuations in  deviation,  having  u* ,  arising  from  the turbulent  time s c a l e s s h o r t e r than used f o r averaging  ( a ) . S i m i l a r r e l a t i o n s a p p l y t o w. F u r t h e r , i f we  compared  with  neglect  velocity  turbulent  fluctuations,  density the  mass  fluctuations conservation  60  equations  for  du dx  +  d_v dz  d u dx  +  jTw. = dz  both  the  to  be  water to  are:  give  where  the  7  mean  du  at  ax  dz  < > indicates stresses  (1956)  -<u*w*>,  that  the  du dt  has  over  velocities  and  -  by  that  the  (8)  -  turbulent of  the  basis  be  The  (8)  kinematic  momentum  of  significant  can  combine  d <u* w*>  process.  the  only  (7)  di  terms  on  and  the  motion:  ax  the  concluded,  (6)  of  d <u*u*>  each  =  d_P d  - et  -<u*Uj>.  form his  study  of  w i l l  be  stress  further  transfers  the  simplified  " _d_<u*w*> dz  x  to  derive  the  f i n a l  the  depth  of  each  densities  du/dz=0  in  w i l l  hydrostatic,  du dt  (8)  equation  order  upper  equation  averaging  from  (5) ,  assuming  to  overbar):  integrated  be  time  + u _du + w d u dx dz  In  dp  - a  equation  v e l o c i t i e s ,  Equations  ax  the  estuary,  and  (dropping  =  arising  in  mean  longitudinal  + u du_ + ¥  River  and  incompressible.  time  Pritchard  (a)  ( )  0  instantaneous  represented  James  (6)  du  Reynolds are  0  layer.  are  Onder  and  the  model,  considered these f i n a l  (9)  equation  layer, to  where  be  the  can  the  uniform.  assumptions equations  (9)  be  mean  That  i s ,  pressure  are:  layer + u  where  d u = - CL C d p dx rj J, d x _dp_ = dx  p g d h dx  dz  - _1_  Tj  <u*w*>  z=h  -<u*w*>  \ z= h •  (10)  p  61 (b)  lower  layer  J2U  at  h'  2  -a^rap'dz  + u ' au« =  ax  ap'  where  dh  ax Since in  the  this  flow  In t h i s  and  i  = interfacial  T  b  = bottom  au + u au at ax dt  + u  i - b  T  T  (13)  yO'h'  dx  =(/o'-p)/p\  and  (13)  form  together  the governing  with  the c o n t i n u i t y  system  of non-linear  = -g  ah -  T±  dx  PV  = 0  dx  + u'  a u ' = - g X a h - g € dh' + ( T j dx  dx  (14)  p* h  dx  + _a_(u«h») = 0  ax  eguations  are c l a s s i f i e d  characteristics  definite  €  layer,  + _a_ ( U V )  ah'  real  (12)  dx  (12)  au  dt  These  be  become:  = - g X a_h_ - ge_a_h_2 +  dx  a u' at  will  equations:  dt  at  surface stress  other  = -<£>'u*w*> a t z=0,  =/o/yo'and  f o r each  au  the free  of  T  dx  differential  be r e q u i r e d i n t e r m s  evaluated  = - g ah - x ax prj  Equations equations  be e x p l i c i t l y  s t r e s s = -</3u*w*> a t z=h'  (11)  au' + u* a u '  X  will  analysis  stress  (10) and  where  terms cannot  letting  T  eguations  ax  a substitution  variables.  z=0  z=h •  1  ax  turbulent stress  form,  neglected,  h• + (yO - yO ) q ah '  h' J "air  = pq  (11)  -<u* w*>  -_L_J<U*W*>  in  requirements  the for  as h y p e r b o l i c i n t h a t x-t  the  plane,  and  presentation  they  possess  therefore  impose  of  boundary  and  62  i n i t i a l  data.  No  general  eguations are  (11)  even  negligible.  developed  by  application  solutions  for  flows  f l u i d  the  non-linear  Rattray  there  accelerations obtained  If  analytic  i s  are  in  (1964)  no  a  negligible.  this  although  method  characteristics  of  differencing  (Grubert  Equations s t r a t i f i e d conditions  are  In  the  the  four  discussed  Thg  but  in  the  the of  It  h«  suspect  basis  )  for  a  must  variables  the  ),  can a  and  in  have  been  as  implicit  be  this  difference  such  or  the f i n i t e  used.  mathematical data  solution be  method  convective  f i n i t e  boundary  before  the  solutions  (1966)  for  stresses  however,  procedures  (1972)  stresses  model  and  and  equations  i n i t i a l  can  be  obtained.  formulated  in  terms  of  considerations  are  these  Boundary are  Conditions  written  in  terms  of  V)  and 1 u /2 2  + g ( 77 + h » )  -  T  u i)  + a ax  u  , 2  /2  of  sections.  Structure  -n u«  the  subsequent  u  a  (Abbott  turbulent  used; to  found  excluded  e x p l i c i t  appropriate  flow  momentum h  using  required  dependent  be  numerical  form  boundary  are  reason  Abbott  the  also  Characteristic If  and  (14)  flows,  addition  other  terms  been  the  Approximate  study  techniques,  where  may  priori  have  + g(h» + Xi7 u'h«  i/y077  0 )  (  T i -  P'  Tb) h'  (15)  and  63  Or  d_V +  d F (V)  v,  Since  f  (16)  ax  at where  =  F (V)  and  V = V(x,t) dV  the  where  the  in O  O  O  (16)  and  au/  dx  fl  0  du/  at  0  0  0  gX  0  u'  1  g  0  dV/  dx  f.  0  0  0  0  h'  0 u'  0  dV/  at  0  dx  dt  0  0  0  0  0  0  au1/  dx  du  0  0  dx d t  0  0  0  0  auv  at  AV  0  0  0  0  dx d t  0  0  ah'/  dx  du'  0  0  0  0  0 dx  dt  ah«/  at  dh'  i s  of  by  [B]  the  0 n  =  [C]  number  discrete  the  of  become:  3  (18) dependent layers.  values  determinant  (17)  n  flow  characteristic  matrix  [A]  for  variables Abbott  this  = 0.  After  and  (1961,1966)  system  of  elementary  n  i s has  the shown  equations  are  operations  on  [A],  =x=dx/dt, x-t  g  equations  0  (u-c)  g  0  g  V  (u-c)  0  0  0 0  the  O  form,  0  I A| =  c  matrix  0  2n  (15).  (17)  1  2nx2n  equation  are:  u  the  given  variation  in  0  number that  g  defined  V  [A]  or  l  of  as  dx  together u  vectors  aV d x  at  Written  are  equations  dt +  _r3_v  =  f  plane.  the  (u'-c)  gX 0 inverse  h« slopes  g  (19)  (u«-c) of  the  characteristic  curves  in  64  Finally: [ (u-c) Equation  (20)  system)  be  the  evaluated  following c  =  two-layer  of  their  uh*  h  ,  and  ± /  two-layer  surfaces. to  with  each  the  speed  of  These  roots  can  e  the  order  by  (1953)):  gh  (21)  u'V  +  ± / • '  the  ge  77 h '  positive  positive  and  described  by  four  conditions  must  be  supplied  Abbott  2  rj h  h'  surface  internal  a l l to  c h a r a c t e r i s t i c  Now,  variables,  time.  the  gravity  waves.  dependent  for  (22)  2  negative  negative  boundary  the  (u-uM  and  known  with  -  h  be  and  a  represents  Schbnfeld  must  Grubert  (20)  associated  approximated  conditions  accordance  = 0 (for  pairs  roots  or  X 77 h '  2  quartic  into  boundary  in  g  J  the  flows  -  respective  (Schijf  represents cf  pair  +  h  gh' ]  divide  numerically,  = u  1  c* and  on  relations  cf  where  roots  each  waves  -  2  characteristic  four  Physically  gravity  waves  g 77 ][ (u •-<;)  is  whose  layer. long  -  2  four  Furthermore,  domain  of  in  the  computation  structure.  To  guote  (1972):  "The boundary data is of m-point type where m i s the number o f c h a r a c t e r i s t i c s e n t e r i n g the r e g i o n of c o m p u t a t i o n from the boundary in the d i r e c t i o n of computation."  Three  situations  consideration two-layer of  which  solution  and  region the is  are are of  interest  summarized  computation  equations being  of  have  advanced  been in  in in  for Figure  the  x-t  solved.  time  to  the  the 21.  In  plane We two  problem  may  each  is  points  graph  shown  imagine P,  under the  in  part  that and  the P  2  65  Subcritical  flows  at  both boundaries .'. two boundary  conditions  required at e a c h  x=0  end.  = toe  x  Supercritical both  outflow  at  boundaries  I boundary  condition at  seaward end,and 3 boundary conditions at  Solution determined x=0  upstream e n d .  x  = toe  Supercritical inflow both  at  boundaries  I boundary condition at upstream end , and 3 boundary conditions at  Solution  seaward  determined  x=  0  x  end.  = toe  Figure 21. P o s s i b l e flow s t a t e s f o r the two-layer s t r a t i f i e d computation. The r e q u i r e d number o f boundary c o n d i t i o n s i s i n d i c a t e d .  66  using  the  (1966) been  method  ).  For  that  and  the  Model  values  equivalent  steady  provide  the  here,  "arrested  salt  allowing  the  estuary  to  values  of  of  is  (14)  (1970)  were  and  use  of  provide into a  in  in  a  surface  these  flow  waves.  Figure  requires  The  21  and  numerical  et  a l .  (1967)  to  the  integrated  alternate  approach,  solution  required  mechanisms  stationary  or  numerically  analytic  the  the  Boulot  An  an  i n i t i a l  transformed  then  the  In  and  conditions.  to  result  show  technique.  motion  make  observations  internal  shown  have  s u p e r c r i t i c a l  flows)  variables.  relations  of  a l l  Abbott  Conditions  dependent  insight  existence  for  not  or  curves  flow,  f i e l d  do  equations  i n i t i a l  wedge"  provides  Since  Vreugdenhil  flow  i s  s u b c r i t i c a l  solution  of  (1965)  characteristic  c~<0  I n i t i a l  equations  (Smith  propagation  the  the  used . by  unsteady  adopted  -  for  and  boundary  of  to  the  the  solution  procedures  method  to  regardless  Any  to  of  Flow  four  inflow.  in  c+>0,  refer  specification  starting  the  corresponding  i s ,  conditions  A Steady  point  conditions  (that  applies  characteristics  s u p e r c r i t i c a l  t i d a l  bore,  the  each  sketched  outflow  of  for  values.  This  controlling,  salt  wedge  in  water  intrusion  the  or  suitable  estuaries.  studied  Steady-state  models  in  and  behaviour his  the  past  described,  analysis  Keulegan  for  the  mechanisms  principally deals  salt  mainly  by with  G.  governing H.  the  Keulegan penetration  have the  been wedge  (1966). length  In of  67  arrested  saline  wedges  experimental  data  the  equation  following L  where  = 6.0  0  L = h R  (2F  water  =  ,  U (L )// =  0  Equation  (23)  fresh was  water  the  i n t e r f a c i a l  forces  the  wedge.  similar  function  of A  by for  second  Farmer the  and  of  stress  varies  wedge.  To  penetration geometry is  in  this of  K p 0 (L)  an  to  the  the  also  of  estuary:  water,  in  river  present  of  not  a  assuming  and  w i l l  remain  must  be  using  to  effect,  an  was form  the  wedges to  be  a  or  from  then,  described solution  i n t e r f a c i a l  constant  coefficient  derive  and  determined  studies,  the  arresting  given.  closed  by  and  required  arrested  wedge  wedge  In  the  parameters  salt  flume  possible  shape  arrested  K  were  provide  is  situations. data  the  of  considerations  relation  solution  as  .  assumptions  which  They  2  x=L  no  found  range  the.arrested  prototype  is  wide  at  way  stresses  (1953).  length,  '•calibrated"  It  a  analysis  evaluate  viscosity  dimensional  this  although  as  an  at  number  Keulegan  Morgan  shape  kinematic  from  In  over  x/Lo,  in  arrives  number  velocity  derived  regarding  be  length  He  (23)  Froude  data.  to  intrusion  flumes.  from  )*  A  v -  experimental  on  the  forces  g e h  0  U (L )  laboratory  Reynold's  = densimetric  A  necessary  depth,  = densimetric  A  in  the  length,  = J g e hyC F  for  h R!  = total  evaluates  obtained  intrusion  D  and  the  along  the  from  the  the  wedge  solution  K.  analytic  solution  for  68  the  wedge  shape  wedge  to  be  takes  place,  in  the  stationary the  udu dx  + gdh dx  dJUT/ )  g X  dh dx  the  +  and  the  2  w i l l  h'  that  constant  be  where  C =  Solving  h  i  =  (14)  distance  at L  reduce  fresh  water  to:  defined for  i  r  the  in  Figure  or  i t  l a t t e r  22.  can  be  method  Either  a  eliminated  equations  (24)  + q d (h?) 2dx  Letting  flow  exists  u 17  an  The + q  6  h '2 2 of  V in  (from  h -  the  2  exact  h*  upper  equation  + _g_e_d_(h • ) 2 dx  f i n a l  = Q  +^e_d_(h»2) 2 dx  =  making  use  of  that  i s  a  layer,  (25)  )  we  have:  0  d i f f e r e n t i a l  result  and  with  respect  to  x  and  i s :  = C  (27)  integration.  h»: -  3  constant  either  and  (26)  h h '  2  +  (h  2  - C ) h '  +  (Ch  e The  salt  salt  0  Following  is  constant  for  i  P'h*  as  Q =  term  + gh£ 2  of  the  (24)  T  + g_d_(hZ) 2dx  integrable.  77  -  .  discharge  Q2  equations  required  d (uZ) dx  2  thus  mixing  assume  = 0  dh' dx  steady  each  we  to:  Q _d(!/7?) dx where  no  If  (25)  €={p'-p)/p'  fact  that  way.  0  =  + g e  reduce h  the  i  equations.  (26)  where  T  pi)  notation  substitution from  and  governing  dx  with  following  C x  is  is =  0  at  unknown  and  h3  -  e  determined or  -  x = at  L x  from where = 0  the  = 0  2Q2)  (28)  g ^ the  h'=  boundary 0.  depth  Now, of  in  salt  conditions, general water  is  the  69  z =h Fresh  water  d e n s i t y /O  x= 0 Figuce  x= L,  22.  Notation  used  o Barotropic  in  steady  flow  solution.  solution  K = 0.006 0.75 to  O  xrixO.5 0  0.2 5  0 Discharge Figure Fraser  23. Stags-discharge estuary.  Q  (m/sec.) relationship  for  70  unkown. the  However,  equation  required the  of  in  steady  the  effect  of  that  along  the  pass  the =  0  interface. control and  (uz where  -  = 0  gh)  (-gh)  The at  -  = h  constant x  = 0, C  of  where =  only term  wedge x h.  -  € a  2  shape  of  Only  the  the  in  hypothesis  on  showing  which  a  point;  just  at  long  flow  the  waves control.  waves  section and  in  in  the  conditions  narrower  channel  can  surface  gravity  wave  positive  +x d i r e c t i o n .  Thus  equation  of  prevent  control  internal  from  control  concept  conditions  "internal"  the  the  The  certain  0,  provides  produce  flows.  =  occur can  (20),  with  becomes: -  g^XT;  V  2  ( Q / g e )' 2  h'  =  0  2  (29)  /3  integration i f  h'(x=0)  + h2  = a  be  determined  (Figure  from  conditions  22): (30)  2  (28) i f  C can  + 2Q /g(h-a)  the  variation  This  an  communication those  can  stationary  flows  to  °- /  Equations salt  past  x  investigation  width  flow  become  speeds  reasonable  channel  from  for  ,  .-.gey  h«  in  c|  = Q/y  u  open  propagation  waters  a  (1952)  propagating  no  postulated wave  be  channel  two-layered  means receiving  in  current  upstream  to  Farmer's  comes  the  wider  u'  and  from  the  case  prevents  appears  section  against  is  This  two-layer  waves  section  characteristic  increases  progressive moving  control  the  Stommel  control  In  for  sudden  sections a  a  relation.  basis  that  i f  in  derivation  (29) surface  and  elevation  equation is  (30)  (28)  enable is  enters  substantially  the  us  specify  the  known;  indeed  the  through  the  same  to  as  surface described  71  by  Hodgins  the  choice  w i l l  be  given  and of  Quick  the  R  to -  3  h (L)  R  +  2  where  level  this  (1  -  previous  +  densimetric  =  u  (L)/y  that  F  parameter  g e h  of  unsteady  situation  for  in h  an  +  2  case  € h'  e l l i p t i c a l  with  the  use  C = solving  which  has  a  the  real  a  dimension  (31)  does  as  seem  be  a  result  to  be  a  of  and  flows.  than  du/dt  (24)  and  flows.  and  for  as  h'  (26) has  the i t  is  convective usually  therefore This  the  one  might  hypothesis  without the  we  can  udu/dx  form:  = C  (32) As  before  C can  be  evaluated  at  x = 0  (29): (33)  (3 2) -  the  useful  + hz  (C  was  number  directly  and  solution  equation  2  = +/  (28)  (L)  steady  equations  equation.  of  e a  2  equation h'  udu/dx,  solving  which  by  computations  = 0  2  neglected  similar  term,  2FA )  can less  by  new  with  computations  magnitude  tested  simplified  equation  tidal  of  be  1 -  s t r a t i f i e d  or  a  some  dividing  Froude  term,  term,  expect  -  appears  A  acceleration orders  and  been  study  by  (Ci  =  fundamental  two  has  (L)z  acceleration  most  i t  (L)  convective  In  datura  form  Ci ) R  = C/h  interesting  although  :  R = h/h C,  is  In  as  non-dimensional  equivalent  It  bottom  presented. in  (1972)  for  h )/  root  2  h': (34)  €  only  i f  C  > h . 2  Thus  the  value  of  x  at  72  which this  h  = C  2  very  Together  I  a  must  they  given  have  a  specify  momentum  and  coupled  model  is r  h  and  and  with  i s  a  continuity  provides  in  the  dh, at  only  a  crude  often  and  (9)  the  turn  evaluate  solved  is  integrated  continuity  h',  in  the over  equation  f r i c t i o n  where the  K  a  is  a  six  equations  were  technigue  similar width  a  per  approximation  improve to  to  the the  unit  width  rivers  having  simulation  whole  the  cross-sectional  (37)  width.  term  ^b  variable  equations for  on  = 0 ,  b = storage  bottom  unit  in  relationship  form:  + _a_(uA) ax  where  The  Q and  calculation  applied  conditions  discharge  (36)  is  then  independent.  = 0  equation  and  in  (35)  continuity  u|u|  not  b  To  Kp  wedge  obtained:  forms.  The  -  eguation  channel  b  salt  ax (36)  A,  the  are  derived  irregular  area,  of  ph  ax  + _a_(uh)  Q  stage  model  the  ax  and  unique  _£a = - g _3JL -  at  at  the  h  barotropic If  + u  dh  that  To  hydraulic  au  Eguation  noted  depth  barotropic  basis  be  way.  length"  analysis.  estuary.  t o t a l  "penetration  represent  used  following the  the  simple  It  for  is  were  days  solved to  calibrated  using  continuity  replaced  dimensionless  during  the  was  the an  scheme  equation  to  tide  measuring central  described  by  used  here  relation  coefficient,  and  e x p l i c i t  was  the  f r i c t i o n  the  March  with  discharge  period.  difference  Cronkers for  The  (1970).  ease  and  73  speed  in  computing;  procedure  based  sections.  Once  was  run  for  a  the  surface and  within  minutes  density  two  constant  in  Figure  increase  dh/dx.  in  excluding  incorporating  each  the  freshwater sign  for  a  velocity  parameter  equation  the  solution  can  be  with  i n t e r f a c i a l  internal  waves  density  gradient,  a  shears.  Ultimately  the  a  stress  associated  process  Thus  with  enhanced  convective  stress  arises  from  the by  and  the  €  varied  i s  plotted with  an  solutions than  term  those  resists  having  the  discharge  in  when  udu/dx  i s  the  growth  and  region increasing  acceleration  and  solutions  The  same  worst  dh/dx,  layer, the  4,  24).  also  this  in  hence  lengths  since  and  cm)  increased  dh/dx.  upper  lower  are  are  penetration  stress.  of  in  acceleration in  (34)  lengths  i n t e r f a c i a l  breaking  the  70  typical  Q and  The  (the  dh/dx  25(b)  the  The  four  3  (Figure  are  2 5 (a)  as  retained.  times  to  predicting  water  in  shorter  obtained  in  variation  of  changes  stations  low  model  shown  approximately  water  decrease  convective  is  successful  parameters  penetration  have  of  at  the  estuary.  way  at  following  discharges  lower  tides  in  obtained  this  percent  low  Figure  a  were  were  Figure  Solutions  and  du/dx  In  in  The  €  u  .  shown  while  25 (b).  and  important  are  € =0.025,  ± 5  appear  the  measured  computational  varying  in  difference  high  e  (28)  for  same  most  contrast  equation  the  for  in  equations  a  (37)  and  obtained  within to  and  tide  the  width  corresponds  ± 20  with  unit  with  sophistocated  (35)  slope  dh/dx  elevations  The  of  Q and  more  coefficients  surface  Compared  calibrated  f i t  f r i c t i o n  mean  between  a  equations  amplitude  relation  the  of  zero  the  23.  on the  produce  Fiyure  details  reduces  of  large velocity  the  2  r  Station  I  x = OKm  G.D  G.D  Station  4  x = 24.4Km  /  /  V  +  - \ T —  12  March 17  • o + Measured  _L_  values  18  _ l _  from tide  0  0 Hours  1.8  March 18 Barotropic prediction  gauges  Figure 24. Measured and predicted t h e M a i n Arm o f F r a s e r estuary.  12  surface  elevations  at  three  stations  G. D  on  75  d h  20 30 x (Kilometers )  xio  40  50  40  50  (a)  20 x  30 ( Kilometers )  (b) Figure wedge.  2 5 .  Typical  solutions  f o r an a r r e s t e d  salt  6  76  velocity  gradient  hypothetical  system  Once calculated r  i  along  the  the  the  toe.  The  from  depict  the  situation  would  be  increasing  provide  the  flow.  The  velocity near an of  This  the  the  for  the  upper right The to  may  Since an  increasing  layer  stresses  the  these  forces,  (1953)  assumed  at  of  toward  zero  at  stresses  are  accurately  velocity  shear  in  i  is  surface  slope  to  form  calculated  be  increase  driving  to  to  not  thickness  conditions  maximum  these  and  force  a  can  x,  T  variation  decreases  mouth  an  the  to  that  estuaries.  pressure  stress  larger  values  experimental  examples.  to  average  approximately  slope  Morgan  using  the  appropriate.  Mississippi  the  and  and  model  surface  in  shows  rapidly  a  term.  stress,  zero  with  the  upper  and a  serve  in  layer  increasing  control  here  least  T  the  section to  f i x  v i c i n i t y  toe.  particular  wedge was  2  then  compared  the  26  near  out  result  mouth.  Farmer K^ou(L)  would  magnitude  wedge  from  toward  decreasing  of  Figure  pointed  real  necessary  river  order  in  stress  established  stress  uniform  produce  acceleration  an  (26).  be  calculated  expected.  such  increasing  must a  the  is  eguation  end.  reduces  without  wedge  It  hence  interface  from  upstream  the  and  1.8  shown  River 0;25,  their  River  data  dynes/cm , 2  in has  derived  Figure a  I  and find  which 26.  from  discuss state this  The  the  as  evaluated  f i t t i n g  that  a  K  their  K of  0.001  corresponds  to  an  favourably  to  the  of  the  South  West  Froude data  varied  data,  compares  densimetric both  stress  prototype  b r i e f l y  Mississippi  Using  of  They  or  the  of  Pass  number  Keulegan  and  of  77  x/L Figure 26. Typical a r r e s t e d s a l t wedges slope.  i n t e r f a c i a l assuming a  stress curves for uniform surface  78  Farmer  and  Morgan.  unsteady  analysis  closely  with  experimental expected would  (K  the  and  a  function  equations absence f i n a l  Morgan  of  2  i t  derived.  the  longitudinal mixing  the  uniform  with  stress  variation  due  the  The  importance  (28)  which  provides  the  required  stresses  T i  Boundary  The each  layer  and  Tb  now in  to  of  gives  the  a  this  i n i t i a l  remains  terms  terms,  studies,  to  with  values  flow in  the  stress  stresses  but  l i e s  concept  of near  equation  solving the  flow  of  provides  in  for  the  slope,  section  formulate  dependent  but  the  control  wedge  only.  surface  maximum  study  the  steady  of  the  squared  x=L  stress  the  flows stress  shear  at  be  allows  along  variation  of  might  The  the  in  their  water  solve  other  formation  salt  squared  his more  for  value  velocity  c o n f l i c t i n g  mouth.  It  or  slope  river  model.  to  form  report  constant  in  compares  masses.  variations  the  unsteady  is  i n t e r f a c i a l  agreement  to  local i t  0.005  Vreugdenhil  velocity  about  A  in  assume  of  which  turbulent  since  the  K  larger  water  possible  regarding  dynes/cm?,  increased  is  information  be  of  freshwater  eliminating  conclusions  cannot  a  and the  where the  a  Morgan  The  identical  function  summary by  case  a  of  and  0.006).  between  not  as  Farmer  In  about  are  vary  =  used  Waterway,  Farmer  unsteady  mixing  (1970)  Rotterdam  studies  formulations  whereas  the value  in  to  of  the  enhance  stress  Vreugdenhil  the  boundary  variables.  Stresses  Reynold's appear  in  stresses equations  resulting (14)  as  from  the  the  bottom  turbulence and  in  i n t e r f a c i a l  79 shear  stresses  a l l  turbulent  six  unknown  and  flows.  In  an  flow  closure  case  variables  associated  four  is  the  no  e x p l i c i t  substituted  in  of  bottom.  on  the  in  way  or  - < pu*v*>  of  with  equations  interface  dependence  is  are  there  at  assumed  problem  there  since  -<pu*w*>  Traditionally,  the  this  quantities,  representing  dependent  represent  the  other  equations  of  motion.  The drag  bottom  force  which  squared.  Both  replaced  T  by  b  dimensionless assumes are  that  changes  the  lower  in  the  barotropic  layer. and  understood be  involved  examples.  vertical  turbulent  the  intensity  interface. the the  lower  and The  bottom  may  the the  also  the  of  are have  boundary used  the  due  K  relation  (1967)  being  a  formulation diffusion  neglects  generated  this  to  of  the  of  s u f f i c i e n t l y enough  in  any  turbulence  for  T  both  b,  density  stresses  either layer  large, scales  of  arise  side  of i f  turbulence produce  is  mechanisms between  from  momentum  system,  to  gradient  generalizing  horizontal  on  two  a  complexity  d i f f i c u l t y  turbulence  large  a l .  This  a  equations.  Reynold's  the  et  and  like  velocity  momentum  variation  2  be  layer  Boulot  turbulent u '  to  K yO'u ' | u ' | ,  presence  diffusion  Considering layer  by  subject  mean  and form  of  s t r a t i f i e d  in  the  assumed  proportionality.  rate  with  have  mixing  specific  upon  I  often  with  the  of  the  associated  Turbulent  may  in  i s  (1970)  of  represented  in  which  only  relations  scales  well  ^b,  Vreugdenhil  length  a  varies  coefficient  adequately  not  stress,  and  the  the depend  density  velocities  in  generated  at  mixing  at  the  80  interface. order  of  When  the  reduces  Biles a  i s  growth  due  to  proposed  Richardson  number,  N (z)  is  -q(dp/ dz)/p water  ,  mean  and  has  and  parcel  column.  not  i n s t a b i l i t y to  Taylor  for  some  (1931).  profiles  3.0  cm /second 2  Compared  with  a  persist  Richardson  to  for  compare  Taylor  and  some the  of  the  pointed when  that  as  in  by  V= €  shown  boundaries  the  a  gradient in  the by  o s c i l l a t i o n  of  out Ri  in  given  in  that  f a l l s  that  c r i t i c a l  Ri  the  he  results  stable  a this  does  below  1/4  mixing  can  f  numbers  on  the  of  viscosity  turbulent  momentum  River of  1.0.  It  observations  0.25.  I  have  and  eddy  molecular  exceeding  discussed  velocity  reported  -<uV*>/(du/dz)  numbers Fraser  turbulent  continuous  Richardson  kinematic seems  of  displacement  results  channel,  for  it  2  of  or  (1973)).  everywhere  frequency  has  the  waves  (Turner  that  the  case  frequency,  i n i t i a l  at  disturbances  > 1/4  2  appears  analyzing  cm /second,  this internal  is  the  examples.  1/4,  defined  small  on  considerably  influence  f l u i d  the  $4.1)  always  t i d a l  a  the to  dz)  small  i t  »  In  from  coefficients, to  Ri  from  dn/  approximates  (1973,  of  not  generated  In  breakdown  s t a b i l i t y  a  be  shear.  Brunt-Vaisala  given  referred  also  i n s t a b i l i t i e s  away  = N(z)/(  Turner  that  even  the  are  dissipation  may  s t r a t i f i e d  Alternatively, persist  with  the  turbulence  viscous  velocity  for  continuously  water  the  that  condition  Ri  wall  Turbulence  i n v i s c i d ,  a  the  Kelvin-Helmholtz  (1961)  flow.  of  thickness,  associated  of  sufficient  scales  effect.  i t s e l f  turbulence the  layer  this  interface  the  density  viscosity  order  ten of  by  of  or  1.0  more.  order  0.02  diffusion  can  is  interesting  with  taken  the  those  of  velocity  81  profiles  from  shear,  d u / d z ,  using  required  about  minutes  numbers  March  10  are  using  A z  plotted  in  of  Richardson than  with  and  March  I  30,  few  from  the  salt  As stresses,  and  as  have  Such  investigations  where  the  measuring and  Turner  usual the  are  based  I  on  know  the a  strong two  of  their  have  been  confined  has  been  practice  found  terms the  in  rate  the of  at  to  computed  Table  was  with  in  as  of  entrainment  Although stations  on  viscosity  probe  lines  of  bends  too  as  the the  v a l i d i t y .  Reynold's  velocity  estuary  -p  had  at  even  the  to  and  flows.  experiments <u*w*>  motion. by  case,  generated  doubtful  of  both  comparison  laboratory  equation  on  one  make  calculate  and  eddy  many  to  3  produce  specified  s t r a t i f i e d to  to  two  relationship in  also  mixing  measurements  made  velocity  the  the  enough  been  of  estuary.  since  stations  direct  and  density  river  density  and  calculate  not  remaining  (1959)  in  1.0,  collected  to  the  diffuse  turbulent  equation  and  to  profile  Richardson  sufficient  Fraser  were  each  in  quite  order  the  was  listed  was  0.5  velocity  gradient  N (z) ,  are  that  attempted  damage  Since  completion  were  this  in  data  determination  profiles  the  of  indicate  momentum  balance  far  on  the  Furthermore  shears  Ri  currents  the  results  order  Furthermore,  secondary  straight  density  not  meter.  pycnocline  expected  considerable  points.  Fraser,  of  conductivity have  coefficients  the  computed  frequency,  The  velocity on  be  one  u n t i l  The  Taylor to  and  complete,  made  27.  Values  of is  to  2  of  A z  meter.  the  0.25.  velocity  suffered  one  numbers  i n t e r n a l l y ,  a  Brunt-Vaisal'a  but  those  station  averaged".  not  Figure  observations  less  were  The  a  at  "time  determinations p r o f i l i n g .  29  surface  by  Ellison jets  82  Table  3  Comparison of R i c h a r d s o n numbers o b t a i n e d from F r a s e r R i v e r and T a y l o r ( 1 9 3 1 ) . N (z) =-gA/o / p {\z i s t h e B r u n t - V a i s a l a f r e q u e n c y , R i = N ( z ) / ( A u / A z ) 2 t h e R i c h a r d s o n number and V the k i n e m a t i c eddy viscosity. €  Depth (meters) March  1.5 2.5 3.5 4.5 5.5 March  0.5 1.5 2.5 3.5 4.5 5.5 Shultz• s  2.5 5.0 7.5 10.0 12.5 15.0 17.5  Au/ A z (sec  - 1  N(z) (sec- )  )  29,  1973 (0830  0.10 0.30 0.26 0.23 0.08 29,  0.03 0*10 0. 25 0.18 0.23 0.09 Grund  -0.010. -0.017 -0.022 -0.024 -0.019 -0.008 0  Ri  1  0.0078 0.0176 0.0578 0.0392 0.0166 1973  (1552  0.0039 0.0127 0.0235 0.0461 0.0235 0.0539 Taylor  7.4x10-6  11.0 27.9 58.9 103.0 80.8 45.6  (cm /sec) 2  hours)  station  2  station  2  0.78 0.20 0.85 0.74 2.77 hours)  4. 33 0.75 0.38 1.42 0.44 6.65 (1931) 7.14 3.85 5.88 10.2 28.6 125.0  3.1 3.1 2.7 2.2 1.9 3.8  data is  83  cr =( _ |.0) x I 0 t  .5  /D  10  U  3  15  20  25  30 0  20  40  (cm/sec) 60  80  100  120  0 8 3 0 March 29 Station 2  Az=  I m.  u> 2 CD CD  sz Q_ CD  ,  51  *>l.2  Q  10  20  30  N ( z ) = - x 10  10  20  40  I0  3  60 0  0.2  (Rad/sec)  15  20  30  40  N(Z)  50  0.4  0.6  0.8  Ri(z)=N(z)/(AUy2 U  1.0  12  100  120  1.0  1.2  (cm/sec)  25  30 0  20  40  60  80  50  60 0  0.2  0.4  0.6  0.8  Ri(z)  Figure 27. P r o f i l e s o f °"t and v e l o c i t y on March 2 9 , 1973 a t s t a t i o n 2. D i s t r i b u t i o n s o f t h e B r u n t V a i s a l a f r e q u e n c y and g r a d i e n t R i c h a r d s o n number a r e shown.  84  and  inclined  number, the  R i  =  Q  to  where  1/U  as  e f f e c t i v e l y  R i  Reynold's  stress  at  not  number  characterize  the  beneath  s t i l l  at  the  interface  and  a  inverse  with  g'=  observed  increase  was  primarily  density  The flows  over  velocity, plume.  the  both  the  and  Since  flow  an  s t r a t i f i e d can  experimental  an  i s  0  and  and and  have results  in  overall the  Fi  did  and  the  f l u i d be  between • flow a  appear  to  a  series  of  flowing  number  salt  layer.  Froude  The number,  and  ft  w  Lofguist's the  attempt  of  was  Richardson  to  layer  a  properties.  almost  developed  Fraser  estuary  possible  and  derive  confined  v e l o c i t i e s ,  a  study  velocity  well  neither  f a l l i n g  stress  to  teen  of  shear  Re.  not  have  ,  water  (1951))  integrated  the  In  i n t e r f a c i a l  s i g n i f i c a n t is  showed  -<u*w*>  the  ambient  flows  salt  E,  however,  would  '^2  of  Farmer  he  would  —  with  the  experiments  turbulence  layers  both  0  other  work;  flow.  (1960)  R i  the  the  layer  relating  stress  under)  of  to  and  0  is  series  A relationship  Ri  or  1  increasing  at  laboratory (or  R i  with  the  _  0  U  Entrainment  this  associated  (Stommel  in  between  R i  upon  of  aimed  p r o f i l e s  relation  and  e g  0.9.  and  two  0.3.  from  Lofquist  Re,  in  interface  turbulent  depended  root  to  Richardson  c o e f f i c i e n t ,  related  to  properties  water  Fi=U/ J g • h, to  a  number,  square  0.2  the  overall  thickness  determined  > 0.8  0  an  entrainment  non-linearly  as  mixing  to  layer  The  emerge  such  fresh  Reynold's  be  R i  experiments  the  was  to  for  does  is  approached  Q  dimensionless  flume  h  related  velocity.  found  zero  variables  be  [d(Uh)/dx],  and  sharply  the  g e h/U , layer  experiments off  could  2  average  equal  plumes  to  steady  negligible only are  in  the  unsteady  extrapolating or  reasonable.  s  85  However the an  an  interfacial  flows  and  the  ratio  terms  i s  internal  gravity  absence  of  relative  upper  waves  cannot  J  number  %r  defined  conditions shown of  in  correct  under  layer  layer  against the  way  (22)  the  the  depths  functional  not  form  velocities.  to  simulate  If  ~  0),  a  phase Fi=1,  the  speed  of  the  be  w i l l  internal mixing  improved The  the  arrested;  complicated  of  as  function  possesses  approach  by  Froude  depict  be  Fi  the  is  vigorous  Instead  the  in  U = u-u'  can  9'V  J  infinitesimal  accurately  is  and  interface.  g»i7 h * / h .  waves  speed  be  of  and  /  to  internal  phase  if  has  can  u'  the  estimate  meant  the  where  current  | /  it  discontinuity  for  Fi=U/  of  number  speed  compares  speed  characterize  terms  where  F i = 0 / y g ,  the  , in  on  phase  writing is  waves  velocity,  to  Froude  density  phase  which  equation  the  the  i  r  fjords,  the  Then,  and  this  in  velocity,  h'/h<1, h*/h,  qq  internal  on  layer and  the  approximate  waves  travel  When  using  the  seem  stress,  i n t e r f a c i a l  (as  currents.  waves  ensues.  1  the  does  The  of  h */h «  20)  internal  basis.  in  of  (Figure  number  parameterizing  observational  interpreted  Froude  the  c r i t i c a l  conditions.  Both assumed  the  expression  Vreugdenhil interfacial  stress  which  the  dimensionless only  the  changes internal water  has  f r i c t i o n  relative  in  layer waves.  depth  (1970)  can  which  Fraser very  Boulot  of  Such u-u*  also  stress a  near  a l .  and  to  Kp  and  allows  makes  influence  the  (1967)  formulation  observations  small  et  proportional  dimensions  velocity,  thickness  become  is  coefficient.  layer  The  and  show  estuary  no  have  U|U|,  an  for  includes  reference  the  speed  that  the  mouth  a  and  to of  fresh that  86  the  salt  layer  variations, mixing, Since  be  of  various shape  which  can  one  thickness  our  the  substitutions  study  for  formulation  was  to  examine  form  of  the  s a l t  and  water  the  using  the  Fi.  influence  predicted  in  promote  wedge  estuary,  four  made:  (ii)  T i  = Ki  p UJU|  (39)  (iii)  T i  = Ri  p U I U I F i  (40)  i  = Ki  ^ U I D I F i  T  (i).  In  becomes  what  having  a h  may  never role  sensitive thickness i  s t r a t i f i e d  to  be  called  when  of  an  is  often flows.  the  (41)  2  Ki  a  weak  -  h'  shear  a  dimensionless  model  function  = h/2.  l i m i t i n g  rapidly.  assumed  as  two-layer  In  values  amplification  velocity  decreases  (38)  preserves  have  the  Fi  no-mixing  maximum  1  the  a  of  salt  p  except  T  been  speeds  These  = Ki  formula  since  of  toe.  T i  each  on  time  wave  stress  the  the  (i)  where  and  on  have  i  T  the  objectives  residence  near  i n t e r f a c i a l  in  functions  (iv)  V  the  included  stress  and  reduce  decreases  and  the  the  the  numerical  layer  zero. making  increasing  Relation  proportional  denominator  of  of  factor  coefficent  (i) to  Thus the  when has u-u'  Fi  depths solution  Fi  takes  stress  more  either been in  of  layer  included modelling  87  Chapter  5.  SOLVING  By  recasting  e x p l i c i t  f i n i t e  barotropic for  the  THE  periods.  of  The  specifying  the  free  surface  For  example,  currents channels  in  which  of  heavier  was  immeasurably  f l u i d  occupying  about  reasonable  to  salt  Georgia  and  discharge  the  any only  the from  free the  difference model,  along  half  of  the  laboratory  the  free  driven  provides section  experiments  are  by  barotropic  nearly  tide Under  free  at this  surface flows  layer  eguations.  This  fresh  a  discussion  matched water This  brief of  discharge chapter  independent  of  Strait  of  assumption  the  also  of  computational  the  be  the  net  computed  means  that  salt  front  either  side  presents  description  the  is  can  on  despite i t  and  across  surface  estuary  the  baroclinic  model.  and  be  the  perfectly and  to  two  allowing  free  the  discharge.  and  the  depth.  In  gravity  removed  water,  the  into,  progress  the  the  flume  in  flows.  on  current's  surface only  accuracy  baroclinic  long  fresh  water  both  lower  was  the  the  upstream  a  water,  of  suddenly  surface  with  sea  presence  by  the  s t r a t i f i e d  those  the  simulates  of  to  under  observation  Observations  water  salt  obtained  the  similar  of  a  from  and  one  equations  principally  model  a  flow  the  numerical  in  with  were  the  dividing  disturbed  calculations  since come  to  the  at  the  during  (14)  them  solutions  barrier  flows,  model  considering  a  a  conditions.  series  expect  water  barotropic  a  wedge  which  eguations  combining  estuary,  derived  feels  flow  and  salt  densities  fresh  the  the  for  barely  in  with  boundary  that  form,  the  is  MODEL  s t r a t i f i e d  entire  of  accuracy  behaviour  show  the  motions  prototype  flows  the  difference  model  t i d a l  TWO-LAYER  the  the  f i n i t e  barotropic  procedure  and  88  application  of  motions  are  features  of  The  Finite  the  boundary  then the  compared  model  three  which and  broad  e x p l i c i t  techniques,  both  differencing of  wave  (1967)  have  made  (1967)  central  conditions. i m p l i c i t  In  to  general,  algorithmic  The and  (37)  Fraser  in  the  properties f i n i t e  of  problem. view  Grubert scheme  however,  the  salt  some  wedge  essential  and  (1970)  Explicit but  suffer  variable  from  (1972)  Abbott  the  stratified  flow  time  increments  by  implicit  solving and  schemes  are  Boulot  in  equations  a l . and  solve  attractive  a  et  time  and the  from  a  s t a b i l i t y  successfully  require  kinds  (Richtmyer  to  s t a b i l i t y  central  many  restrictive  have  no  differencing  differences  schemes  are  E x p l i c i t  techniques  spatial  equations  There  f i n i t e  in  f a l l  characteristics  schemes.  application  forward  the  of  weaknesses.  Vreugdenhil  equations  d i f f e r e n t i a l  the  and  to  small  of  "Lax-Wendroff"  in  of  method  between  u t i l i z i n g  point  and  hyperbolic  difference  repeated while  use  observations  solving  strengths  found  ),  flow  programming  confined  have  differences  two-layer  for  choosing  equations,  Morton  an  has  for  computed  examined.  methods  i m p l i c i t  reasons  The  Eguations  natural  or  with  categories:  u t i l i z e s  dominant  are  Difference  Approximate into  conditions.  which  applied is  not  considerations. more  involved  structure.  one-dimensional central  estuary  hydraulic  difference  including  a l l  form  model  was  major  using  developed  branches  and  equations for  the  Pitt  (35) entire  Lake.  In  89  the  discussion  plane the  and  j  to  w i l l  continuity bj  (h  refer  i+i  i-l  -h  1  the  that  h |'  =  j  1  1  -  1  computation  exactly  what  equation  bj  line  in  the  p o s i t i o n .  Consider  difference  form:  j-l  A  x-t f i r s t  (42)  i -  Sx  they by  are  arithmetic  )/2  =  A); ,  )/2  =  Vr\  the  molecule  is  information  i s  replaced  by  the  averaging,  from  the  1  average.  Thus: (43)  i l l u s t r a t e d known  in  and  Figure  2 8 (a)  u t i l i z e d  for  and  shows  advancing  ( 4 3 ) •.  Proceeding (35)  time  St Sx  1  J  The  1  denoting  h -:  a  i s :  (Ij-jtA -  here  x  -U  Ajll  obtained  +  —  or  central  j-t  (A]^ A;-  1  j+I  overbar  in  unknown  row;  '  space  (37)  are  preceding  A  a  reference  2  values,  A  to  >  corresponding time  w i l l  S t  A j j | , A j i |  A  i  equation  2 Since  follow  (Figure  b =  r  u-'j  2 8 (b)  ) ,  Kb/0 u } 1  1  =<  (43)  1  a  similar  where  l u  1  ]  the  manner bottom  for  the  and  momentum  | :  1  1  -ujj>)  (44)  equation  stress  i-l  | i . ( u j ^ 2 Sx Equations  in  •  2 StKb  comprise  the  lu'J  1  |  +  / h j  barotropic  (44) model.  90  initial conditions J"  2  J"'  J  j+l  j+2  (a) advancing the continuity equations it  initial conditions J*»  J+2  - x  (b) advancing The momentum equations h ,h'known ©u,u'known Qh.h' to be determined rju,u' to be determined Figure 28. molecules.  Finite  difference  computation  91 For unit  s i m p l i c i t y  width  written  basis  in  a  and  for  the  form  !  the  bottom 1  1  stress,  =iu» J i  -  l  and  U '.  =  F •ii  oV  i s  =  continuity d  Since  h  j-i  on  Figure  and t h e  -!»._!,)+  X ( h j | ,  uij-1 - u ' i - '  = velocity  V j  the  i n  (14)  are  +h«) = _a_h = - a  (ui?  at in  dx  d h  -= - a ( . . h ) - -  u  = barotropic  b  ax ^ "  has  equation  f r i c t i o n  equation eCh-jj,  - h ' . j . ,  |/h» j  constant  of  law  i s : )  ) l /  + 1  (46)  shear,  and  Figure  28(b).  s t r a t i f i e d  /  ax  velocity.  If  the  two  summed: )  +  and (UT/  (u»h')  barotropic  computations,  ) + (u'h«)  Thus  solving  f o r  u't  1  :  i4lri  the  been  (45)  Using  1  a  h» j / h -  molecule  from  on  -1  quadratic  St  done  (43):  28 ( a ) .  momentum  i d e n t i c a l  b  j-l  J+I  difference  i s  at  where  1  / /g e  equations (V  at  I  !  (u-u*)^  computed  equation  IT i - l U ' T 'I |I u | F i - K b u» ' - ' | u « j  S t  1  - u « .' , h»  8x  28t(Ki  where  u'.' . h  i n  are  equation  to  stress  the  continuity  analagous  molecule  i n t e r f a c i a l  computations  layer  J+I  computation  u' '}  lower  j  the f o r  s t r a t i f i e d  = h» T  J  (40)  the  difference  h' '+ '  with  the  integration  (47) being  zero.  The  five  equations  (43)  92  to  (U7)  form  the  seen  from  can  be  grid  lines  basis  required  define  the  i s  l i m i t a t i o n  a  minimum  unfortunate one  kilometers. is  Sx  structure. triangle  this  at  point  numerical  flow  be  unique  (1956)  in  characteristic  as a  the  and  must  numerical  dependence.  Stated  at in  related 29  and  other  terms,  characteristic  must curves.  the  of  spacings  curvilinear  dependence  are for  the  on  the  to  state (CFL)  the  1928,  what  has  s t a b i l i t y  not  follow  the  difference  domain  of  the less In  PR  back  they  Lewy  and  the  inside  paper  dates  does  the  be  for  determined PQ  are  characteristic  shaded  which  f i n i t e  include  2.7  equations  characteristics  which  least  characteristics  to  is  equations  grid  is  i n i t i a l  c  in  and  only  grid  fundamental  Lawy,  This  of  the  curves  -  to  order is  The  The  the  2  the  the  domain  ).  c+  the  1 and  of  Courant-Friedrichs-  directions,  dependence  the  the  on  of  serves  admitted.  hyperbolic  solution  hyperbolic  Friedrichs  known  difference  of  for  Figure  number  differences  are  as  2.  choice  equations.  treatment  condition:  of  a  (Crandall  Courant,  slope  and  station  continuum  characteristics,  s t r a t i f i e d  to  P,  at  directly  the  be  establishing  the  in  can  Sx  and  minimum which  stations  schemes  in  example,  of  the  central  for  in  f e l t  are  defines  domain  come  error  difference  which  For PQR  dominant  by  ,  values  algorithm  six,  that  the  separation  any  is  length  from  immediately  St  solution  the  flow  molecules  computation  reasonable  r e s t r i c t i o n s  to  and  a  arising  and  E x p l i c i t  s t r a t i f i e d  computation  for  Thus  conditions  the  penetration  since  kilometer  subject  the  of  continuum slope than  Figure  29  domain  of  the  or  equal  this  of  f i n i t e to  the  requires  Figure 29. I l l u s t r a t i o n of r e l a t i o n s h i p between continuum and f i n i t e difference domains of dependence for a stable e x p l i c i t difference scheme.  94  that  the  f i n i t e  information domain  from  (below  we  the  points  P).  explanation: than  difference  This must  maximum  of  before  the  <  Sx  /  where  max(c )  is  the  which  w i l l  St  the  +  value  of  s t a b i l i t y (Roach  the  for  the the  need  defined  assess  as  equations  difference  whose  is  defined  (Smith  a  in  faster  the  would  completed  are  physical  equations  solution is  continuum  simple  waves  the  the  the  (1965)).  has  for  to  flow. be  out  within  each  ensured  Sx  obtain  the  f i n i t e  bean  i f  gravity  chosed  as  wave  close  we  are of  (46),  and  convergence systems  dependent  of on  to  and  equations experiment  numerical  solutions  and  to  serves  f i n i t e the  approach  St  solution accuracy, at  exact  through  to  underscore  difference  scheme  solution zero.  of  Since  a  series  of  round-off  errors  are  each  point.  growth  or  decay  dissipative  and  stable  the a  for  linear  variables  of In  surface  approaches  as  terms  St  convergent  solution  of  the  accuracy (43)  A  of  theories  that  dependent in  on  practicable.  only  equation  operations into  errors  study as  the  data.  equations  introduced usually  value  means  to  d i f f e r e n t i a l  arithmetic  this  This  one  gravity  advance  advanced  (48)  developed  f i e l d  as  has  numerical  of  mathematical  (1972)).  such  S,  inside  condition  restrictions  largest In  are' well  i n t u i t i o n  l i e  integration  these  / m a x (c+)  Sx  systems  i s  spatial  must  the  to  point  max (c+)  occur.  Rigorous  and  used  Quantitatively,  R,  s t a b i l i t y  celerity  information  pass.  Q and  integrate  Otherwise date  solution  S t a b i l i t y of  these  difference  95  scheme,  numerical  bounded schemes  to  always  and  constant  coefficients,  c r i t e r i a  for  deriving  The  the  the  simulation  the  and  Sea  an  widths  by  Department  river  sounding.  for  linear to  is  within  difference in  systems  derive  with  convergence  in  judged  the  are  d i f f i c u l t i e s  involved  solutions  of  shown  depth  of  this  in  study.  terms  assumptions  model  the  river  in  branches  the  storage. depths  Public  Works  30.  of  the  made  in  (3)  obtained  (Government was  computed  than  two  meters  at  85  percent  are  not  calculated  Detailed  bathymetric  data  over  at  low  does areas,  every  data  of  width  was  at  the  notable  which  were  sounding  outlines  most  cross-sectional  the  into  show  The  from  and  estuary  heavy  The  and  (1)  mouths  The  lines  scheme.  evaluates  partitioned  The  lighter  branches  Lake,  influence.  Figure the  P i t t  various  t i d a l  i n  included  greater  barotropic  major  while  conveyance depths  at  seven  channel  in  or  end  between  and  those  the  having  channel  as  appreciable  except  practice  into  not  Reach  point the  the  branches  channels  conveyance  the  the  attempted  starting  to  segments  these  is  to  equations  data  (44),  schematized  remaining  have  f i e l d  upstream  kilometer  omission  of  not  Unstable  or  Model  (43)  indicate  have  one-dimensional  integrating  one  values. Due  exponentially  equations.  The  been  small  s t a b i l i t y  non-linear  the  Barotropic  has  I  accuracy  of  equations  decay  non-convergent.  convergence  Instead,  either  s u f f i c i e n t l y  are  proving  errors  grid  provided  Canada). the  portion  water of  and  the  available  In  for  of the  greatest Pitt  96  Figure 30. used in the  S c h e m a t i z a t i o n o f Lower Fraser barotropic hydraulic model.  R iver  97  Lake, but  so  a  shore  depths  and  kilometer in  the  to  programme  The measured  boundary  the  absence  detailed  s p a t i a l against of  at  stations  data  dispersion  comparisons  30,  lower  the  1973  Main  to  along  i s  a  crude  of  the  elevations  are  accurately  predicted  centimeters  of  to  lead  the  40  minutes,  5  measure  junction  to  response  suggesting  that  Canoe  the  of  below  the  at  station depths  The on  were  also  after  station  3.  storage 3 the 4  order  for the is the I  capacity and  the  phase  and  (within  10  predictions  the  study  additional  just  Both  station  5  his  Within  station  passage.  elevation). at  in  agreement  error  on  calibrated  32.  at  based  positions  phase  water  river  of  and  the  significant  influence  minutes  4)  be  surface  provide  and  the  can  model  surface  the  along  calibration  31  In  Kb  (1974)  To  simulation  the  Arm.  measured  Joy  the  Agassiz  extensively  by  higher-high  Main  used.  were  the  points  to  measured  station  there  bank  was  Figures  model  A similar  Joy's  and  been  coefficient  River.  from  the  various  6.  feet  in  (below  the  at  (1952,1953)  plotted  to  and  and  Fraser  following  south  5  predicted  however  this  the  Baines  Arm  1  calibrated  5000  the  station  one  convenience  has  this  was 4,  seconds  maps,  equals  for  to  f r i c t i o n  3,  and  of  from §x  applied  section  data  taken  Since  60  the  predictions  are  ebb  attribute  of  The  satisfactory, turn  of  in  incorporated. March  model  was  (48)  of  St  at  discharge  increments the  a  velocity  which  the  elevations  equation  conditions  f i n a l  (from  determined),  by  elevations  at  width  estimated.  bookkeeping,  discharge  estuary  were  seconds  surface  of  conveyance  areas  < 83  St  shore  to  appear 30  to  98  1.00 r  Station 3 Barotropic  prediction  Sx - I Kilometer •  Sx = 5000feet  o  observed  G.D.  G.D.  -I.OOL  8  10  March  12  14  16  18  20  22  24  30,1973  Figure 31, Comparison of elevations with obervations at  predicted surface stations 3 and 4.  Hour,  99  i.oor  Station 5 Barotropic prediction  0.75  8x = I Kilometer  ~  •  Bx- 5 0 0 0 feet  o  observed  G.D.  G.D.  8  10 March  12  14  16  18  20  22  3 0 , 1973  Piyuce 32. Comparison of elevations with obervations at  predicted surface s t a t i o n s 5 and 6.  24 H o u r ,  100  downstream (the  are  river  water)  is  and  the  approximately  The averaged 5  the  phase  may  10  the  to  area  33).  is  Computational  Once flows  were  River  storage  covered  only  junctions  are  satisfactory are  at  areas  at  high  poorly  station  6,;  over-estimated  station  predicted  geometry the  were  an  Control  the  and  to  with  basic  were  in  the  Fortran  (1974)  necessary of  the  by  33  was  and  through  station  of  by  which  that  achieve  the  large  1.  This ebb  conveyance  altering  found  of  would  the  only  the  changes  in  the  best As  a  barotropic  calibrated,  the A l l  solved  the  limited,  magnitude at  3  f i t tool  model  satisfactory.  was  interfacing  IV  sections  Conditions  model  model.  spatially  very  Reach  to  at  schematization.  flows,  Boundary  barotropic  eguations  available  31  the  sea  model  s t r a t i f i e d  Figures  are  overestimate  Joy  limitations  the  but  in  2 were  velocities  especially  this  also  1 and  measurements  storage  although  by  computer  banks  satisfactory  calibrated  in  at  the  1 or  Station  computed  coded  the  of  have  as  to  the  investigating  calibrated  complicated  waters  measured  neglecting  within  Pitt  underestimated,  coefficients  for  the  low  seems  f r i c t i o n  possible  extensive  Although  I  channel  the  relationship - is  and  areas.  the  of  that  centimeters.  agreement  due  and  with  compared  currents  into  phase  velocities  (Figure  be  wide  high  and  and  large  influence  The  however,  ebb  very  the  modelled.  too  lower  f i n i t e  using  University  the of  the  layer  difference  difference IBM  370  British  s t r a t i f i e d  eguations Model  Columbia  168  101  Station  l  Barotropic prediction —'— Sx - I Kilometer  8  10 March  12  14  30,  1973  Figure 33. Comparison of predicted v e l o c i t i e s on March 3 0 , 1973 a t s t a t i o n s 1 and 2 .  16  18  with  •  8x = 5000 feet  o  measure d  20  22  24  Houn  observations  102  Computing  Centre.  evaluated  throughout  computation boundary turn  water  layer  lower  part  to  level  a  of  p r o f i l e r s in  is  the  the  by  If  at  flow  was  by  domain  34  appropriate  were  used  velocities pass.  depth,  datum model the  the  In  is  the  ref.erred  the  s t r a t i f i e d  and  prototype  three  configuration.  taking  (47).  h,  for  by  in  Finally  equation  and  advancing  the  (46)  were  conductivity  Model  datum  is  of  there and  integration from  the  internal  were  domain.  the  three  supercritical pass  equation  s u b c r i t i c a l  and  are  the  and  flow and  of  inflow  state  was  examining  the  at  each  everywhere  (cj  > 0;  cJ  each  end  of  the  at  the  toe  front  (h•  imposed The  states  outflow  (22)  waves  flow  salt  between  nearest  at water  the  depth  velocity  height  moving section  salt  grid <  downstream  0)  of  boundary.  When x  22  interpolation  meter)  as  between  cf  heights  computation  one  serves  March  flow  evaluating  determined  < 0;  Figure  direction  and  water  (44)  computation.  complete  i n t e r f a c i a l  fixed  (cf  each  the  s t r a t i f i e d  the  in  with  and  from  and  regular  barotropic  Figure  their  s u b c r i t i c a l  propagation line.  in  depths  total  which  . in  barotropic  following  defined  was  shown  (45)  computed  the  (43)  a  seconds  the  relationship  shown  interest:  from  Arm  defined  are  60  layer  were  bottom  The  As  and  Main  model  parameters  h,  in  equations  lower  depth,  the  =  Next  the  equations  estuary  St  velocities  equations.  used  on  update  total  upper  based  barotropic  the  conditions.  to  the  The  the  > 0)  the  flows  are  i n t e r f a c i a l  supercritical boundary  out  condition  at h»  the at  mouth  x = 0  is  z = l6.84m(Geodetic datum) z = l4.24m(Sandheads datum)  z = 4.25m (Model bottom)  Deepest  Channel  Bottom  z = 0 ( Model datum)  8  10  J  12  L  14  16  18  Figure 34. Relationship between the estuary Conductivity p r o f i l e r s at stations 1, 2 and configuration.  20  and 3 are  J  22  L  24  model shown i n  J 26 Kilometers  parameters. their March  o  104  released. no  Physically  this  means t h a t  longer  be  maintained  at  conditions  in  the  are  structure of  throughout  x = 0 a  between  river  control  the  corresponding  enters the f i n i t e 22)  will  occur  flows  the  positive  computations mouth. was  and  Throughout flooding  supercritical suhcritical  in  the  i n the  conditions  would  interface  propagating  numerical  scheme  i t  be n e g l e c t e d .  t h i s reason during  requires  u using  The  wave no  once  the  in  the  velocity  layer  the  field  flows  were  Flows  were  The  The  unsteady  weak s u r g e waves on  inflows,  flux  (Figure  s e c t i o n s near  layer.  s o l u t i o n s may  the b a r o t r o p i c  side  waves.  the  boundary  longer  t o advance  mouth,  the  and  in  the  lost  i n such  w e l l be i n e r r o r f o r however  the  additional  t h e domain from the seaward  velocity  stratified  characteristic  that the energy  reasonable.  entering a  assumed  supercritical  appears  characteristic  evaluating  was  boundary  near the t o e i n the upper  upper  from  seaward  the  the  entire  p r o b a b l y produce upstream  column  Somewhere  only  upper  and  water  imposed.  interfacial  a transition  flow  simulation  to  layer  implying  the  boundary  the  the  lower  layer  waves c o u l d  and  with respect  flow  to the v e l o c i t y  the lower estuary  upstream  since  the s e a w a r d  occured  were c o n f i n e d  boundary  internal  T h e r e f o r e h' a t x = 0 i s n o t inflows  can'  the normal  Since  d i f f e r e n c e domain from  Supercritical  water  marking  and  of G e o r g i a .  to  of s a l t  domain.  i n f o r m a t i o n c a n n o t be drawn f r o m t h i s  solution.  22)  determining  dominated  c o n d i t i o n s i n the S t r a i t curve  seaward  the c a l c u l a t i o n section  river  the  the head  condition,  side  overall internal (Figure  supplied  i n eguation (47).  by  105 I n i t i a l i z a t i o n and  observations  The  completely  washed out  this feature. computation concerned,  Wash-Oat  the  out i s defined, when  of section  6.'  the toe position T h e wedge r e m o v a l  I n the more u s u a l  floods.  tidal  fairly  convergent,  i t w i l l o v e r c o m e the e f f e c t s o f bad  crudely  and e v e n t u a l l y approach a r e "run-in"  the  I n t h i s case  2 and  The  26,  surface  initialization scheme i s  s t a r t i n g values these  Normally  cycles t o eliminate  from  for (28)  eguation  between  grid from  discharge.  initialization  the validity  procedure  requires  o f the s t a r t i n g values  be unacceptably  large  kilometers  criteria can  t o o small  and vice  penetration length exceeds 7 kilometers 5  slope  u ' i s s e t e q u a l t o z e r o and u i s c a l c u l a t e d  example, i f the s u r f a c e slope becomes  below  and by  a m e a s u r e d v a l u e o f h ' a t x = 0. T h e r e q u i r e d v a l u e s o f h  the barotropic  will  large ebb  the s t a r t i n g v a l u e s  calculated  computed by assuming a u n i f o r m  which  solution.  f o r twoo r three t i d a l  1  lines  flow s t u d i e s ,  correct  effects.  has retreated  and i f t h e numerical  the i n t e r f a c i a l height, h ,are are  include  models,  can b e done  using  must  must be r e - i n i t i a l i z e d  i nthe other s t r a t i f i e d  the i n i t i a l i z a t i o n  c a n be  on each  implication  models  wedge  a s f a r a s t h e model i s  t i d e a l s o means the s t r a t i f i e d c o m p u t a t i o n on s u b s e q u e n t  salt  past s t a t i o n 1 a n dthe model  as occuring  downstream  that  s i x g r i d l i n e s are reguired for an advancing  Since  wash  imply  versa. (grid line  against For  be judged.  the intrusion I f the 8)  the s t a r t i n g values are r e j e c t e d .  or  initial falls  Further  if  106 the  value  of  h»  i n i t i a l i z a t i o n what  can  values  only  are  with  was  not  Since  this  every  25  for  penetrated  reasonable  to  affected  bad  by  The with  the  scheme that  the  into  flux  front  assumes  that  CoBiparincj  centred  on  those  by  the  the  10  time  the  or  12  of  start  to  at  that  least  effects  The  bad  validity  predictions  t i d a l  cycle  to  when  kilometers. at  once  of  overall  the  arrival  move  cycle.  repeated  of  inserted  suggesting  flood  was  met,  beginning  was  would  comparing  parts  than  has  position of  salt or  during the  basic  been  where  salt  Predictions  The  the  solutions.  judged  wedge  flood,  computation, the  a  layer  procedure  in  more  toe  increasing  moving  into  are  salt  It  profiler  3  i s  to  be  i n i t i a l i z a t i o n .  wedge  toe  be  expect  position  the  late  meters  reasonable  such  the  two  r e s t r i c t i o n s  as  lower to  of  felt  observations  these  after  the  too  hours  only  has  practice  entire  are  exceeds  i n t u i t i v e l y  reversing  can  water  go  In  toe  ensuring  zero,  before  method  wedge  judged  to  i n i t i a l i z a t i o n  the  By  be  i n i t i a l i z a t i o n  the  f a i l s .  equal  downstream  of  the  obtained.  u'  within  at  has  = 1  been  water  each  with  the  In or  downstream the  storage  computation  water  defined  meter.  advanced  just  decreasing  problem  finding  h*  a r b i t r a r i l y  discharge  is  as  this  coinciding  computational  retreated of  the  toe,  associated  interval constant  assuming  of for  w i l l with  2 St. 2  a l l the This  St.  Observations  in  applying  correct  the  balance  numerical between  the  algorithm two  stress  107 T±  terms  and  the  solutions:  the  greatest  cycle,  and  the  for  and  Kb  Ki  "Th. the  phase  of  salt  water  magnitude  the  velocities.  stress  layer  by  comparing  with  for  of  found  periods.  Kb=0.0055  duration  three  during  and  f i t  and  affected  distance  coefficients  overall  imbalances  penetration  were  The  Large  systematically  solutions  formulation f i n a l  the  a  in  to  £§rticular  at  data  particular  (40)  values  barotropic  two  measuring  gave  of  values  the  both  3,  t i d a l  Optimum  from  of  station  altering  equation  coefficient  aspects  the  best  Ki=0.0075  solution  and  discussed  previously.  Two-layer  results  The  numerical  solutions  observations  using  data  velocities  35  and  the  solutions  together model  the  with  effect  the  i s  worst  predicted  both  stations  1  solutions except  agreement  is  peak  salt  salt  station  and  2  the for  and  due  maximum the  low  zero  wash-out  second  agrees  is  flood  at  within  on  station 40  of  the  30th.  have  the  in  the  almost  become this data.  In  reasonably  well  17th. both the  at  earlier.  March  of  l i n e ;  to  simultaneously  is  minutes  plotted  February  defined  for  Figure  that  height  3  In  relative  probe  to  p r o f i l e r  been  errors  on  as  water  compared  observations  Contain  to  salt  and  17  particularly  goes to  29  Harch  thickness  water  3,  satisfactory  intrusion  March  observations  the  at  on  10  layer  conveniently  parameterization  recorded  interface  modelled  the  two-layer  February  The  when  The  both  for  bottom.  appreciable  the  are  The  records,  phase where  observations.  Observations x Station I 0 Station 2 + Stalion 3  1  MARCH  17, 1973  Hours  Figure 35. Comparison of typical i n t e r f a c i a l p o s i t i o n s p r e d i c t e d by t h e s t r a t i f i e d flow model with two-layer parameterization of observations at stations 1, 2 a n d 3 .  109 In station 1700  a l l  2.  The  hours  stations slope  on  March 2  near  i n i t i a l i z a t i o n ,  into i s  the  when  compared  The the  ebb  1.  At  this  numerical between (x=9  tide  point  model  stations  kilometers)  horizontal length  of  rapidly whole  In  a  the  than of  the  salt  model.  On  during  March,  the  at  the  a  the  rounded  model)  which  hand  predicted  of  is  Canoe  water  lowering  the  advect  measurements  at  station and:  water This of  shorter f a l l s  junction  i s  the  nearly  penetration  slope  increases  flows  along  freshwater  to  the layer  supercritical  height is  the  heights  Passage  on  the  turn  out  at  interface  solution  interface  contour  velocities  released  s u p e r c r i t i c a l  the  a  such  fresh  the  i n t e r f a c i a l  salt  with  of  of  depending  response. must  The  i n t e r f a c i a l  the  meters  the  measured  other  10th  (4.1  and  for  to  following  layer  from  The  u n t i l  nose  upper  condition  the  between  reproduce  s u p e r c r i t i c a l  v i c i n i t y  toe  and  solution.  to  height  February thin  water  the  the  rapidly  Near  relatively by  and  f a l l  toe.  wedge.  predicted  volume  1  boundary  not  mixing  diverge  changes  10th  separation  effect  consistently.  located  forming  remains  slowly  and the  the  also  at  February  accurate.  the  the  early  .immediately  that  of  too  corresponding  least  no-mixing  state  behaves  is  have  the  on  could  except  suggest  solutions flow  model  reversal  would  hours  meters,  end  14  flood  i n t e r f a c i a l  2  solution and  with  an  about  during  model  when  show  to  0000  numerical  the  and  tends  near  seaward  13  layer  considerable  interface  the  Figures  salt  17th  The  3  in  model  averaging  0.7x10~ .  slopes  charts  the  observations  1 and  of  large  cases  due  the  f a l l s to  more  the  estuary  as  large  in  the  penetration  lenghts  away  rapidly  very  110  from  the  measurements,  wedge  behaviour  To February  check 8th  It  this  The  supercritical  water  thickness  was  l i k e l y  barotropic  spike  from  this  point  lower  level  promoted  the the  and  salt the  Consequently  remained  until  The  to  since  March  i t  had  but  17th.  closely  by The  the  similar  the  matched  are  only loss  to  tidal  turn 25  to to  in  30  salt  measurements.  associated  u , 0  a  heights  ebb  90  near  allowing  or  100  curve  outflow  adjustment  with  the  March  17th  conditions.  At  1 collapsed  of  layer  the  imposition  flows  on  station  centimeters  supercritical  data  upper  regions  layer  velocity,  1  supercritical  flow,  flows. the  from  layer  p r o f i l e r s ,  enough  station  water  some  velocity  conductivity  to  the  were  a  velocites  of  above  to  a  measured  the  previous  re-established  and  wash-out.  predicted  passed  the  s u b c r i t i c a l .  lower  on  more  resulting  level.  the  of  predictions,  observations  differences  turn  condition  deep  simulation  Harch  occurred the  60  also  in  boundary  with  to  the  computed  lead  the  poor  model.  The resulted  of  trend  50  a  phase.  was  outflow with  provides  aspect  same  compared  seems  this  solution  conditions.  minutes  during  and  velocity  of  and in  30th  Figure  measurements  the  estuary  To  compute  which  29  velocities  i n t e r f a c i a l  subroutine  March  height  to  at  integrated  36.  were  provide  the  are  a  the  As not  good  observed each  compared with  the  made  in  picture  upper  of  layer  applicable  time  was  measurements  over  the  Ill  March 2 9 , 1973 —  prediction section 5  O  observation  March  10 12 14 Time ( Hours)  30,1973  prediction  section  3  —  prediction  section  5  A  observation  O  observation  ....  8  station 2  16  18  station I station  20  Figure 36. Comparison o f p r e d i c t e d and measured upper layer v e l o c i t i e s at s t a t i o n s 1 and 2 f o r March 29 and 3 0 , 1 9 7 3 .  22  2  24  112  upper  layer; u  where to  that  yJ  =  0  u (z)  7)  =  compare  velocity  i  i s , u(z)dz  h  measured  velocities  phase  varies  on  a  section  3  and  2  with  kilometers  2.8  only  two  velocities  agree  the  solutions  model station  2.  Qualitative  been  in  Figures  derived and  14  from using  horizontal indicate above column  the  the  due  cm/sec to in  more  along  since  the  estuary compared  is  section  5  which  in  predictions  the The  for the  part  to  with  measured  both  the  the  and  is  with  reflects  a  compared  and  predicted  stations.  observed  the  d i f f i c u l t  depths  1  lead  consistent  and  during  and  38.  i s  time  in  in  meters  However,  flows  especially  distance  from  i n t e r f a c i a l  three  the The  and to  exactly of  data  1  is  in  the  response.  data.  assumed  supercritical  of  constant  the  imposed  outflow  in  were  °j  Figures before  columns  river  two-layer  of  As  axes  clearly  the  measuring  contoured  vertical  the  each  terms  v e r t i c a l  show the  in  charts  densities  temperature and  days  contour  The  station  follows periods  on  probes.  relation at  for  conductivity  background  bottom  line  solutions  same  operative  i n t e r f a c i a l  except  is  37  the  monitored  condition  ±15  is  Station  estuary.  superimposed  axis  model  the  It  layer  distance  with  appear  numerical  have  density  than  grid. 2  in  also  way  z.  Comparisons  The period  i s  height  kilometers  within  This  but  with  station  of  at  this  kilometer  separation  boundary,  velocity  the  computed  at  (49)  of  give  the zeros  distance  extent bed.  13  of  water  The  solid  seaward  boundary  parameterization which  have  been  o 2  o g u>  o  inittobzation •  O  m«osurad boundary condition  STN.I  c,'<0  o  o o  »s ^  CO  o . o .  STN.2  Model  Bottom  o o o CO  o 10  o o  FEBRUARY  1973  Figure 37. I n t e r f a c i a l s o l u t i o n s from the s t r a t i f i e d f l o w model a r e shown s u p e r i m p o s e d on c o n t o u r c h a r t s o f c o n s t a n t d e n s i t y ( Ct) for three days in February 1 9 7 3 . T h e p e r i o d s o f s u p e r c r i t i c a l o u t f l o w a r e i n d i c a t e d b y c ~ <0 on t h e s t a t i o n 1 c o n t o u r chart. +  r—  LO  1  o  J  I  MARCH  F i g u r e 38. Interfacial so superimposed on charts 1973. P e r i o d s of s u p e r c r i t station 1 contour chart, s  1973  l u t i o n s from the s t r a t i f i e d flow model are shown of c o n s t a n t d e n s i t y ( Ct) f o r three days in March ical outflow are indicated by <0 on the u p e r c r i t i c a l i n f l o w s by c f >0.  M  115  indicated have  by  also  cj  been  These barotropic with  the  The  solution  model  water  figures  the  at  outflow  occurs. as  shown  salt  to  be  judging  by  accurate  within  series  of  longitudinal in  time  on  computed  layer  Until  turn  the  isohaline, s a l i n i t y flow  out  minutes  of  was  for  to  February  the  of  computation,  and  the  river  the  duration the  previously,  the  model  for  once  tides  10  has  is  least  small  diurnal  allows  the  Steveston,  the  1  salt  predicted  model  above  station  of  supercritical  of  numerical  mouth,  upstream.  in  at  s a l i n i t y  the  predictions. at  s u p e r c r i t i c a l which  the  the  kilometers  estuary  sections  s a l i n i t y  structure.  at  using  confidence  The  charts  velocites  after  condition  worst  the  the  to  s t r a t i f i e d  of  timing  and  appears  minutes.  solution  superimposed  150  38.  contour ±30  interpolating  must  Figure of  capable  several  measurements  outflow.  thicknesses  is  The  corresponds  layer  out  two-layer  is  estimate  effect  washed  the  for  noted  the  in  the  allows  As  This  model  boundary  and  simulating  inequality  the  reasonable  lengths.  in  water  a  station  accurate  that  flows  The  supercritical  i n i t i a l i z e  water  provides  penetration  show  to  charts.  during  internal  salt  each  the  indicated  measured  calculate  on  <0  time  In  the  estuary  reguired  i t  in  data,  2  and  interface  appears  the  of  to  Figure  the  f i n a l  section and  have  by been  show  the  near  the  wedge  toe.  l i e s  near  in  a l l  lower  12  a  also  rise  model  in  Each  39.  sections  station  within  plotted  isohalines  The  the  been  Figure  profiles  numerical  beyond  also  relation  of  the  layer  section  the  in  and  salt a  Figure  15%o to  the  water further 39  116  x ( kilometers )  x  ( ki lome te r s )  Figure 39. Interfacial solutions f o r the t i d a l cycle on February 10, 1973. Isohalines interpolated f r o m t h e d a t a i n F i g u r e 12 a r e s h o w n in each s e c t i o n .  117  for  this  water  to  masses  estuary, in  occur.  the  in  giving  model  on  each  layer  rise  to  a  found  sections  ebb  downstream  -  of  that  plays  different  an  mixing  between  important  removal  the  ebb.  the  tendency  for  3  and  numerical  which  an  role  mechanism  reduced  could  i n t e r f a c i a l  slope  due  the  solutions  computed  pronounced  change  behaviour.  This  (1970)  which  near  to  the  in  than  the  maximum e b b  the  salt  account  for  they  layer  although  the  occurs  about a  retain data  is  a  no  level  off  upstream.  I  junction  10  per  change  the  although  exhibit  a  same  less  overall  Vreugenhil's  distinct  comment  at cent  in  and  the in  numerical  to  the  velocity  forming  there  by  Passage  limited  the  slope  flow  Canoe  of  interface  firm  decreased  slope,  contrasts  the  influenced  Main  without in  shows  was  the  effect  behaviour  increasing  model  This  even  turbulent  i l l u s t r a t e  the  station  Passage  on  contrast,  model.  These  Canoe  In  paper  wedge  shape  the  flow  on  state.  One excursion  piece of  the  March  tides  above  Steveston  kilometers. greatest  New  crabs  which  indirect  data wedge  produced  The  very (36  Westminster are  I  and  1)  unable  this  to  would  those  collect have  (station  in  caught such  a  water  New  long  the  maximum  valuable. 18  The  kilometers  were  February  would  Salt near  been  February on  which  4).  was  averaging  ineguality  kilometers)  support  to  lengths  while  large  occasionally  evidence  was  penetration  (station  excursion  above  of  11  about gave  put  salt  fish  species  the  water  Westminster penetration.  27  and  provide I  would  118 expect  the  two-layer  lengths  due  layer  the  in  the of  to  well  water  on  As  scheme and  the  detailed  outflow.  The  early  which  becomes  Vreugdenhil's  where  the  minutes  solutions each  values  which  and  the  ebb  severe  model  to  salt  hydraulics the  duration  does  not  perform  to  during  ebb  peak  and  s u p e r c r i t i c a l  characteristic  upstream,  water  ty  turn  seems  (Vreugdenhil  appear  of  a  number  February  range be  of  of  to  (1970),  be  the shared  figure  approximately  40  is  wedge  procedure  dissipation  of  by  the  in  numerical  was  is  7/) to  If  60  The  definite  stress  washed  out  i n t e r f a c i a l  errors  and  the  varying  stress  the  of  investigated  and  a  i n t e r f a c i a l  repeatedly  f a i l s .  29  turn,  There  fixed. is  characteristics  March  constant  values.  assumed  condition  of  10 a n d  parameter  i n i t i a l i z e d  i n i t i a l i z a t i o n provides  a  can  boundary the  for  stress  through  large,  less  It  thickness  the  gross  judged  predictions.  flood  s e n s i t i v i t y  other  the  the  satisfactory,  especially  on  penetration  Analysis  The  holding  mixing  modelling  layer  two-layer  of  the  early.  Sensitivity  model  salt  predictions  too  as  aspects,  the  overestimate  effect  velocity  of  by  far  seems  maintenance  solutions,  to  d i l u t i n g  estuary.  numerical salt  the  model  cannot  the  limit T i  by  to  since  becomes  too  until  the  stress  also  assume  a  zero  value.  A of  the  mean  velocity  s t r a t i f i e d  shear,  flows  and  U=u-u',  of  0.300  corresponds  to  m/sec a  is  stress  typical of  2.44  119  dynes/cm  for  2  Ki=0.0075. r  and Three  were  The  3.  in  Kb  which  10th ^"i.  is  is  The  solutions,  a  bottom  stress  b±50%  and  T  for  for  shall On  the  40%, from  r  i+50%,  of  also 4.95  typical  dynes/cm . 2  b=0.  T  10  refer  to  the  other  hand  a  zero  bottom  provides  a  poor  simulation  form  of  the  penetration  i s  per  almost  only  the  ±6  are  of  and  The  is  February  variation  characteristic  this  zero  to  outflow  time  of  bottom this  cent  solution  more  about  described  solutions  such  significant  possibly  to  apparent  i n s e n s i t i v i t y  long  stresses  only  the per  ±6  stress  that  at T  sensitive  delays  cent.  outflows errors  the  affect  the  In  the  b to  salt  this  time  February range  of  turning  point  37  thicknesses  the  the  the  February  and  i s  the  for  Compared  on  in  stress  solutions  minutes  layer  penetration, to  the  occurs.  stress  on 5  of  f i r s t  varied  about  produce  Both  I  s u p e r c r i t i c a l  the  coefficient  K i .  effect  the  a  parameter.  the  confined  by  clear  s u p e r c r i t i c a l  minutes. 1  (as  important  However,  the  computed  m/sec,  lengths  i , showing  than  solutions  were  and  u'=0.300  investigated:  section).  It  An at  represents  excursion  important  changes  velocity,  solution  the  station an  T  previous  increases  i s  of  standard the  solutions  penetration  independent the  water  Kb=0.0055  values  meters)  i + 30055.  r  salt  for  C7 = h ' = 6  Numerical  i + 100% and  A  in  Fi=0.36  at  with  may  the  10th  layer  station March  do  not  depth,  explain  due the  parameters.  wash-out  times  at  station  1;  in  120 this  i+300%  r  T  case, the  wash-out  of  35  produce  f a i r l y the  (0.0075)  seems  station  increase  The  to in  3,  did  of back  allow  the  0.007. upper  onto upper  this  sensitive Some  the  near  of  the  station  3.  a  l i m i t .  wash-out  time  and  higher  values  of  trends  are  Ki  not  Lower  large  the  ebb  remains between  u-u .  Since  1  depths  values  h'  are  not  of  Ki  value  produced  flood-ebb  about  do  level  standard  the  lack  coupling  layer  The  i-503L  but  in  stress  with delays  T  ^"i  very  reducing  solution,  lower  to  Increases  increased  effect  each at  the  for  general  the  is  only  minutes  u n t i l  L  it  stress  i n t e r f a c i a l  but  coupling  the  upper  the  phase  for  layer  barotropic  layer  to  is  flood  not  in  the  basis  i t  Variations layer  the  increased  Increases on  l i e  T  as  With  behaviour  same  percentage  not.  velocity  and  has  except  most  analysis.  in  minutes,  60  solutions.  cent)  in  60  important.  bottom  about  appear  average  per  whereas  slowing  them  the  by  zero  with  changes  imposed  changes  effect  various  becomes  reduced  the  rate  velocities  affected,  stress  conclusive  (+10  i d e n t i c a l l y  at  a  the  similar  marked  and  Rather  layer  i s  compared  proportionate  greatly  The  time  in  currents.  is  minutes  prevents  apparent  time  comparison  removal data  i n t e r f a c i a l  removal  By  b-5Q%.  The  the  of  velocity  and  higher  velocities solution) ebb  noticeably  bottom is  ±50%  r  b  compared  (in while  with  of  Ki  fact,  has  the  collapsing  decreases  higher  in  Ki  v e l o c i t i e s .  changed.  stress  possible in  values  to  delay  the  reject  have  almost  with  the  ebb  values no  at  station  of  effect  measurements.  Kb  3  above  on As  the b  T  121 decreases reduced 7  to  10  the  peak  since  u'  per  cent  Based discussed stress  extent  of  of  are  0.010  smaller  (41)  solutions  for  the  to  s e n s i t i v i t y optimum  the  solutions  that  greatly  from  largest located stress  forms  be  the  0.006  the  order  and  the  estimated both  the  of  Ki  and  stress  model for  the  accuracy  influence  for  are  unaffected.  reflect  bottom  and  Fi=0.362,  common  the the  same  This  Ki  in  of  a  the  maximum  would  occupy  a  stress  numerical The as  equivalent does  each  of  not  form,  longitudinal form  standard. salt  kilometers providing  the  equations model  stress  the  (40)  values  necessarily but  was  and  coefficient  equation to  (38),  for  used  in  represent  designed  to  give  basis.  overall  in  forms,  evaluated.  the  for  stress  into  give  value a  were  analysis.  difference 10  of  alternate  17th  Superposition revealed  on  layer  Forms  substituted  March  m/sec  the  can  and  The  Stress  three  were  calculated  u-u^O.300  w i l l  value  i s  observations  monitoring  A minimum  upper  appears  limits  values  the  reduction  phase  section  in  Kb=0.0055±0.0010.  of  and  The  between  These  Interfacial  Each  currents  The  appropriate.  range:  Alternate  the  f i t t i n g  f i e l d  model.  flood  b-50%.  previous  barotropic  was  T  the  the  and  increased.  coefficients.  and  (39),  i s for  on  in  ebb  On  water  above the  of  sections the  both  wedge flood  thickness the  weakest  from  boundary coupling,  each  did and  was at  solution  not  early 30  ebb,  the  centimeters  station  KiyOFi  d i f f e r  and  1.  The  K i p U | U |,  122  did  not  allow  forms,  the  and  wedge  in  to  general  be  removed  were  as  rapidly  associated  with  as  greater  the  other  lower  layer  depths.  The ±4  per  penetration from  the  standard,  coupling  delayed  the  turn  minutes.  The  the  cent  length  lower  solution  stress  stations. for  Kip  U|U|Fi  once  the  change  coupling; lowest  levels  Conversely,  The  but  2  of  the  stress  upper  layer  stress  form  the  relative  does  the  stress  forms  were  was  most  the  numerical Equations and  with  also  produced  closer appears  and  one  outflow.  I  match to  removal had  the  form  varied  providing  outflow  a  longest  salt  was water  of  56  f i r s t ,  but  duration  delayed was  at  the  the  only  greater  total  s u p e r c r i t i c a l  flow  a l l  longest  most  rapid  place.  i s  also  forms  in  equations  affected  by  (40)  the  and  (41)  degree  of  produce  the  velocities  and  greatest  salt  not  change  the  phase  the  velocities,  only  u and  u'.  numerical  procedures  a l l  of  tried  and  (41)  the  of  calibrated.  could  are  chosen  of  however  which  greatest  have  in  f i e l d  exception, the  went  of  each  stresses  Fi  taken  development  solution  the  s u p e r c r i t i c a l  satisfactory,  (40)  Kip  resulted  the  magnitude  During  but  by  s u p e r c r i t i c a l  for  state  velocity  The  to  predicted  the  each be  most  water  Overall  stress  f i t t e d  responsive  to  supercritical  delay  the  KyOU|0|Fi  to  observations  have  reasonable  than  the  turn  since the  theoretical  it  a  observations. changes inflows.  to  i n  U  They  s u p e r c r i t i c a l  provided  alternative  validity.  (40)  permitted  the  prevented for  eguation  form  to  currents.  a  s l i g h t l y  forms  and  Unfortunately,  123  the  observations  to  provide  the  pressure  which,  water  several flows  required  for  by  and  lower  a  barotropic  surface  slopes  layer)  formulation  solution  (entering  prevent  for  pressure  hydraulic  water  w i l l for  be  low  the  the  a  more  i n t e r f a c i a l  within  percent  10  agreement  within  excursion  average  layer  of ±40  the  assumptions,  succeeds  the  the  is  total at  distance.  The  velocities  which  observed  model  neglects  the  depth  river and  boundary  can draws  from  a  condition  i s  neglects  mixing  of  but  includes  the  model  predicts  that  relation.  the  estuary  of  on  of  each  and  the  approximately also  agree  is  daily  predicted  phase  one-half  provides  within  large  r e - i n i t i a l i z a t i o n  penetration  depth  model  the  conditions  model  capable  extent  minutes  and  interface,  of  of The  boundary  empirical  The  chapter  assumes  A further  the  and  this  width  observations,  flows,  wash-out.  and  Finally,  out  in  estuary.  uniform  model.  an  broad  velocity,  forces  flushed  following  of  across  with  even  average  and  channel  described  characteristics  density  Consistent  ebb,  f a i r l y  Fraser  using  water  some  the  stresses  salt  been  important  in a  has  measurements.  fresh  turbulent  on  in  by  one-dimensional  the  the  the  Model  model  variations  supplied  The  based  approximated  salt  in  of  and  concerning  of  numerical  simulating  data  use  flows  term  Features  although  l a t e r a l be  the  term.  A  salt  with  layer  statement  Essential  in  upper  gradient  definitive stress  coupled  ±15  shews of  estimates cm/sec  of  the of the  124  observations.  On removal good.  the  other  mechanism This  is  The insensitive  expected  shape  of  the  to  both  appears  to  be  I  found  barotropic depths the  estuary  previously  expected effects would  along be  a  improvements, monitoring  the  phase  independent due to  during  to the  the use  that  of  the  the  south  the  bank  of  the  and  to  properly  done,  measurements.  In  in  summary,  s t r a t i f i e d  calculation  accurately  as  that  of  Main  influence boundary  the  warrant  is  the  simulation model  The  to  the  model  and  price  be  1  and and  described for could  and  careful  the  condition.  the be  storage for  model. and  emphasizing  essential  barotropic  of  velocities  computer a  .fieid  s t r a t i f i e d  delta  Arm.  and  assumptions.  improvements  estuary  i t  velocity  obtainable  expensive  the  i n t e r f a c i a l  layer  f i t  Further  representation  relatively  barotropic  best  complex  programme  the  not  is  the  the  is  and  effects.  the  one-dimensional  more be  both of  reached  stress  measured  depths  mixing  the  of  the  of  of  The  about  better  the  a  phase  accuracy  of  over-riding  development  geometry.  a  of  are  wedge  addition,  schematization.  with  salt  In  represents  particular  calculated  layer  without  form  and  upon  model  and  models,  depend  a  the  flows  magnitude  are  model  in  ebb  of  the  almost  results  simulation  s u p e r c r i t i c a l  be  stresses.  barotropic  once  the  to  bottom  These  hand,  success  this Such  detailed velocity of  calibrated  the as  possible.  Currents  in  the  upper  fresh  water  layer  of  the  estuary  125  are  affected  along  the  both  by  the  interface.  the  and  of  Figure  together  The  phases u*,  of  f a i r l y  bottom  makes  stress  bottom  i s  For  the  values  of  can  be  explained  in  near  the  interface  due  The  10  to  12  is  the  forcing  upstream,  and  the  estuary  depends  condition a l .  (1967)  downstream  is  80  those  for the  turbulent  height  the In  two  in  4  stresses for  the  flows  in  with  have  terms  of  remains type  of  ebb  the  during ^ ~ i .  an  arrested  case.  This stresses  layer.  at salt  the  river  water  layer  throughout  which  studies  gave compared  2  Reynold's  the  this  both  formulated river  stresses  dynes/cm  simulation  previous  i  analyses  condition  drives  the  in  for  each  and  variation  This  than  in  a l l  Also  but  A  nearly  unsteady  increased  which  (1970)  to  the  plotted  i n t e r f a c i a l  the  accuracy  condition  2  boundary  of  both  wedge  approximately  of  is  calculated  stationary  Vreugdenhil  boundary  larger  unsteady  2  17th  that  generalize,  of  modelled.  outflows.  percent  than  accuracy  specified. and  to  mechanism  upon  is  stress.  terms  i n t e r f a c i a l  in  i n t e r f a c i a l  dynes/cm  to  March  mixing  velocities  value  well  follows  maximum  of  by  for  turbulent layer  which  the  stresses  with  must  observation  to  greater  example,  i n t e r f a c i a l  mouth  60  to  total  variations  d i f f i c u l t  addition,  the  s u p e r c r i t i c a l  about  considerably  wedge.  time  due  correct  and  stress,  the  i t  the  solutions  the  during  flows  stresses  important  than  constant  In  with  the  larger  variation  magnitude  wedge  most  flow  i s  are  salt  water  calculate  bottom  sequence  u-u'.  To  relative  i n t e r f a c i a l  40  salt  flow  boundary  Boulot the  the  et  internal  parameters.  126  Distance above Station I ( kilometers)  F i g u r e 40. Tidal variations i n the interfacial and bottom stresses and t h e mean l a y e r v e l o c i t y s h e a r a t s t a t i o n 2 f o r March 17, 1973 (upper). Six l o n g i t u d i n a l s e c t i o n s a r e shown f o r f l o o d and ebb p h a s e s (lower).  127  Basically that the  they  postulate,  a  control  fresh  water  section layer  hydraulic  conditions  outflowing  upper  further  and waves  equation  (22)  where  define  a  i s  one  flow  conditions  that  salt  questioned tendency  a  velocities  layer  generality  since  during  positive  each  evaluated  for  values  h  1  the and  momentum  the  determined  by  the  presence  an  cj"  of  ct  and  both solving  (47):  of  this  inflow and  eguation  no  layer in  flow  to  for  mechanism  Rigter  velocity  Figure  (41).  the  discharge  in  hydraulic must River,  be the  with  upstream  for  arresting  conditions with  must  to  has  the  calculated It  Then  (1970)  Fraser  existed  compared  the  tends  arrests  assumption the  in  where  optimum  boundary  and  (1953)  velocity  maximum  of  assumption  direction.  corresponded  These tide  This  in  0.  the  (51)  flow,  layer  kind  (50)  Schb'nfeld  layer  corresponding  17th  lower  and  -c~—-*•  gives  goes  inflow  = 0  width.  upper  that  Vreugdenhil  opposite  lower  where  wave.  March  and  be  exchange  calculations  layer  internal  mouth  h (0,t)/2  Schijf  the the  s u p e r c r i t i c a l in  g e unit  but  situation  The  to  for  such  + /  by  layer  and  case  water  conditions.  each  a  equation  c r i t i c a l "  in  producing  In  setting  per  work  equal  wave  will  analysis,  + q ( 0 , t ) / ( 2 J g e h (0 , t ) )  "double  internal  river  supercritical  by  using  the  they  the  u'  and  wedge  assumed.  during  discharge  from  suggested  from  is  net  follow  other,  the  that  and  to  unique  the  = 0  = g(0,t)/(2h(0,t))  discharge  arrest  c"|  h(0,t)/2  the  the  estuary.  the  u'(0,t) =  near  within  stationary h'  stationary  form  =  appears  for  w i l l  h»(0,t)  q  which  for  the  there  layer  are  in  thickness  assumes  internal  as  be  were  measured directly  emphasized  128  .5r-  \>  f  N  2  \  v  o  w \  ®0.5  /  E  \  I  1  >  1  4  1  6  / /  I  8  *^-<S  10  I  12  v\  boundary  x  ^  \ ./  «L  Supercritical  / \  i  14  16  inflow  condition  Computed  boundary  velocity  18  20  JL  22  March 17, 1973 F i g u r e 4 1 . C o m p a r i s o n o f t h e measured boundary c o n d i t i o n f o r h' a t s t a t i o n 1 w i t h t h e t h e o r e t i c a l condition of Vreugdenhil (1970) (upper). Comparison o f u' c a l c u l a t e d from the s t r a t i f i e d flow model and t h e t h e o r e t i c a l r e l a t i o n of V r e u g d e n h i l (lower) .  24 Hours  129  that  the  Fraser  Vreugdenhil  applies  The observed water,  h  very u'  is  1  (50)  to  are  model  destroyed  tests  where  flows,  and  the  poor  is  the  a  two  internal  boundary  flood  estuaries  with  specification the  developed  of  flow  as  part  of  this  was  flow  are  w i l l  the to  for  in  of  but  Such the a  that  behave  similarly  at  river  large  numerical  be  used  mouth  an  can  measuring  to  estuary  column  other  of  i .  T  Fraser  and  the  series  cannot  water  both  largely  lowering  the  entire  straightforward work.  by  salt meter.  depend  during  assumption  the  phase  matched,  condition  the  high one  apart.  induced  and  corresponding  the  model  cm/sec  expect  of  time  closely  conditions  conditions  relatively  the  (50)  within  Since  calculation  reasonable tides  in  boundary  conditions  large  80  equation  a  and  case.  duration  at  g(0,t).  to  a  agree  h'  they  inflow  c r i t i c a l  is  in  s t r a t i f i e d  doubly  It  heights  40  The  under  as  supercritically  such  from  calculated  as  to  h*  calculation  used  flood  between  maximum  s u p e r c r i t i c a l  upstream.  with  (51)  not  only  maximum  consistently  water  since  the  the  did  (51)  maximum  predicts  salt  provide  the  barotropic  velocities  equation  agreement  equation  the  flows  particularly  closely  from  on  phase  however  Equation  model  flows  shallow accurate be  made  techniques  130  Chapter  into  6.  SUMMARY  The  work  two  programme water  AND  carried  d i s t i n c t of  f i e l d  intrusion  relationship important  between  of  changes  touched  upon  by  series  for  very  i n s t a l l e d  at  three  water  tides. tides  duration. (upstream of  the  intrusions  low  large  salt  of  Steveston,  The fresh  water  absence  of  mixing  took  large place  a  the  study  a salt  into  the  and  some  wedge  motions.  The  for  predicting  the  tool an  aspect  which  is  only  were  discharges  estuary of  detected, the  and  nature or  also on  the  winter  tides  of  large  instruments  were  monitored  the  days.  Significant  extent  and  of  Strait  the  more  having removed  each  in  which  several  the  kilometers  B.C.)  out  Self-contained  periods  was  carried  large  were a  duration of  Georgia  produced  long  high  from  the  daily  ebb,  of  by  water  estuary in  spite  discharges.  conductivity were  salt  inequality  wedge  of  the  the  by  diurnal  The  winter  in  15  nature  f i r s t l y  conditions  estuary,  water  were  of  the  f a l l s  examples.  for  determined  thesis  catagories,  theoretical  observations  points  this  discharge  ineguality.  Penetrations of  of  the  two  structure  were  a  and  fresh  diurnal  conductivity  which  of  in  reveal  provide  to  low  to  secondly t i d a l  of  reported  complementary  also  way  Two  small  salt  and  characteristics  outcome  and  but  and  models  1973  out  measurements  mathematical  of  CONCLUSIONS  profiles  mixed density within  across  indicate the  gradients each  layer.  that  i n t e r f a c i a l suggested Surface  both  salt  region that  and  and the  turbulent  s a l i n i t i e s  usually  131  exceeding  10  %  longitudinal  s a l i n i t y  surface  and  Fraser  River  (Cameron  accompanied  B  at  and  since  In  estuaries  the  i t  horizontal  advection  and  The simulated were salt  the  a in  fresh  turbulent  momentum  was  in  a  barotropic  measured reasonable in  the  currents  effects were  The magnitude accuracy  of of  Vreugdenhil's Waterway  were  of  as of  a  the  function  the  of  by  the and  salt the  conclusion  water  in  (1970)).  The  included. in  been layers  mixing  neglected  but The  The  water  model  use  depth  of  of the  conjunction  with of  a  enabled  salt  water  tide  at  Steveston.  flows  on  the  predicting  penetration  for  vertical  the  duration  the  by  fresh  The water  model.  model  barotropic  was  salt  and  of  with  which  estuary.  extent  cycle.  in  the  the  unique  have  form  for  a  estuary  difference entire  estuaries  governed  structure.  empirically  lower  t i d a l  is  the  layers.  model  fluxes  over  the  of  each  and  the  of  along  Fraser  interface  condition  (Vreugdenhil  the  the  currents the  between  mathematical  f i n i t e  salt  water  across  predicted  success  of  class  1 near  place  s a l i n i t y  density  predictions  modifying  salt  of  the  e x p l i c i t  estuary  of  both  somewhat  of  Calculation  lower  flushed  diffusion  terms  boundary  be  dynamics  water  although  of  two-layer  station  present  s t r a t i f i e d "  d i s t r i b u t i o n  advection  unsteady  with  solved  the  to  near  characteristics  (1966)),  appears  tide were  "moderately  turbulent  defined and  These  Pritchard  example these  gradients  depth. into  high  depended  calculation. a Of  the  similar nearly  phase  primarily This  model equal  of  on  was the  and the also  Rotterdam  importance  in  132  terms the  of  the  measured  duration  boundary  of  salt  condition  water for  throughout  the  interface  at  the  estuary the  was river  mouth. The also  a  duration  function  i n t e r f a c i a l had  maximum  stress  energy  values  in  the  of  to  the  the  in  to  r i g i d of  in  the  mixing was  The  stress near  modelled  calibrated  mean  the  and  greater, the  were  bottom  i n t e r f a c i a l 2  in  magnitudes the  dynes/cm ,  significant  the  namely  and  stress  the  bottom 18  to  dissipation  shear  condition  for  i t  was  the  same  form  mainly  of  the  on  to  the  predicted  to  small  were  the  magnitude  not  and  number the  supercritical  20 of  coefficient  of  water  could  the  Fi  f i n a l to  has  of  and a  calibrated of  measured included increased  bottom  KbyOu'|u'|  positions  make  the  influence  were  depth  choice  been  The  layers.  to be  were  degrees  the  possible  flows.  relation  interfacial  changes  salt  relation  represent  each  between  the  stress  increasing  correspondence  Froude  quadratic  for  interfacial  expressing  Each  onset  the  velocity  i n t e r f a c i a l  using  for  model,  data,  formulation  The  in  between  percent  relations  insensitive seen  10  them.  made  values  Kb=0.0055.  of  among  much  was  velocities.  are  current  typically  80  numerical  the  to  in  about  and  balance  order  boundary  choice  KioU|U|Fi  the  the  conclusive data  water  stresses;  stresses  the  resolution  the  correct  empirical  s e n s i t i v i t y  Due  salt  flows.  Four substituted  on  usually Both  2  the  turbulent  was  dynes/cm .  of  of  stress  and  the  Ki=0.0075  and  were  relatively differences  in  these  coefficients;  the  layer  velocities.  Using  mainly  133 the  correspondence  velocities  and  following  between  the  measured  and  interfacial  ranges  for  predictions each  estimated:  0.010 < Ki < 0.006  and  the  coefficients  within  stress  predicted water  salt  depth  minutes  and a  compared  kilometers showed ebb  currents  £2l!£ludin,g  and  these  models  mouth.  the  ±15 c m / s e c  on the order  theoretical  the  only  of  of  2  were  ranges  If  the of  model  the  intrusion  obtained  total  within  ±40  approximately  10  The f r e s h  of  3 the  10 p e r c e n t  maximum  values  station  < Kb < 0 . 0 0 4 5 .  these  within at  water  water  velocities  the observations.  Maximum  meters/sec.  Remarks  i n  In  agreement  at  fresh  coefficient  0.0065  measured  within  were  Two  neglect  with  were  thicknesses  phase  upstream  agreement  reported  water  predicted  the past, mixing  one case  of  solved  of  both  which  salt  were  measurements  were  studies  i n  of  unsteady  and f r e s h  are  occupied  based  water  the predictions less  salt  e x p l i c i t  difference  monitoring  programme  the  with  one t i d a l form  have  been  on two l a y e r s  across  compared  than  wedges  and  interface. observations  cycle.  using  Both  Lax-Wendroff  techniques.  present salt  The  f i e l d  work  succeeded  wedge  motions  different  t i d a l  to  between  be  model  made  i n  i n the  producing Fraser  conditions.  and the a c t u a l  hydraulic  detailed  River  This  the predictions  a  forming  over  allowed from  behaviour  a  a  of  description several  the  of  days  rigorous  two-layer in  part  the and  comparison "no-mixing"  the estuary.  I  found  134  such  a  model  phase  of  the  i f the  the  provides  penetration,  correct  layer  as  boundary  i n t e r f a c i a l  measurements. the  reasonable  height The  near  the does  the  outflows,  however  even  velocities  are  modelled.  some i t  of  Two  examples  the  more  relates  hydraulic in  the  well  to  salt  throughout  guantitative through  the  aspects  of  serve  to  use the  of salt  and  provide  for  dispersion water  mouth  mouth  in  a  was good  state  layer  this  study  found  from  simulation  the  upper  layer  of  the  s a l i n i t y  intrusion  water  quality.  Basically  is  found  in  in  of  the  each  layer  to  make  or  water  the  more  the  as  variations  reguired  sedimentation Some  i l l u s t r a t e  the  velocities  which  models.  which  on  of  supercritical  Appendix  the  A  and  each In  during  flow  extent  in  and  intrusion  the  applied.  information  information  predictions  are  this  of  currents  provide  river  aspects  location  estuary,  not  discussed  important  water  the  are  the  river  during  sedimentation  models  as  conditions at  model  thicknesses  well  estimates  guality important  examples  are:  (i) D r e d g i n g o f t h e s h i p p i n g c h a n n e l t o p r o v i d e an a d d i t i o n a l 3 meters o f c l e a r a n c e w o u l d i n c r e a s e maximum p e n e t r a t i o n s a b o u t 20 percent. This would r e s u l t i n s a l t water l o c a t e d in and above the t r i f u r c a t i o n a t New W e s t m i n s t e r f o r much g r e a t e r p e r i o d s o f time than at p r e s e n t and would i n c r e a s e the s e d i m e n t a t i o n i n this r e g i o n w h i c h i s a l r e a d y d r e d g e d on a c o n t i n u a l b a s i s . (ii) The t i m e r e q u i r e d t o f l u s h p o l l u t a n t s c o n f i n e d t o t h e fresh w a t e r l a y e r i s s i g n i f i c a n t l y d e c r e a s e d by t h e s a l t wedge presence compared with times computed using the unstratified velocity f i e l d . (iii) The distribution of p a r c e l s of contaminated water within the estuary is s i g n i f i c a n t l y changed by the baroclinic flows compared with the unstratified distribution. In g e n e r a l , the s t r a t i f i e d computation shows that water p a r c e l s o r i g i n a t i n g both from Gilbert Road and Annacis Island pass l e s s often through o u t f a l l r e g i o n s , w h i c h w o u l d t e n d t o i n c r e a s e e f f l u e n t l o a d i n g on  135  the f r e s h water l a y e r , barotropic velocities.  than  those  water  parcels  computed  with  the  (iv) Host high tides during the measuring periods produce predicted excursions exceeding 18 k i l o m e t e r s a b o v e s t a t i o n 1, thereby bringing s t r a t i f i e d flows into the vicinity of the Annacis Island sewage treatment plant. The suppression of v e r t i c a l mixing associated with the s t r a t i f i c a t i o n means that effluents discharged into either layer might tend to remain in t h a t l a y e r r e s u l t i n g i n higher c o n c e n t r a t i o n s than would be the case i n u n s t r a t i f i e d r i v e r s . (v) Increased salt water penetration associated with further d r e d g i n g would i n c r e a s e the d u r a t i o n of s t r a t i f i e d flews around Annacis Island, thereby i n c r e a s i n g e f f l u e n t c o n c e n t r a t i o n s due t o reduced rates of v e r t i c a l mixing. It  is  clear  that  circulation  in  which  be  may  water  the  must  Recommendations  this across  on  (Rossiter  and  the  i n t e r f a c i a l  hydraulic  turbulent step  i s  the  diffusion  the  of )  in  hydraulic in  on  models  sedimentation  of  however wedge  or  two  main  discussed  fresh  water  longitudinal is  be  usually  an  terms in  mixed  negligible  to of  in  the  influence a  Froude  development  mixing  across  entrainment  term  d i f f i c u l t y  additional  the  in  density  variations expected  in  step  incorporate of  and  the  can  next  flows  salt  motion  terms The  of  of  parameterized  to  term.  introduction  effects  flows.  s t r a t i f i e d  logical  is  formulated  changes  effect  the  when  the  model  subsequent  effects  The  along  stress  important  baroclinic  for  (1960)  Therefore  interface,  model  Lennon  that  has  Research  equations  contrast  number. the  the  the  Future  interface.  gradients  wedge  predicting  include  neglects  the  density  for  and  for  numerical  thesis  salt  estuary  used  quality,  The  the  involved  empirical  in  of the  plus  a  this  coefficients  136  for  the  mixing  by  obtaining  coefficients were  not  and  to  f i e l d  on  determination  of  station.  to  provide due  depth  and  the  would  probably  model  also  the  There  requires  density  at  river  suitable  parameterization  the  the  the  of  but in  at  least  specification this  of  data  each  balance  across  the  currents by  the  a  and bends.  the  maximum  f i r s t  station  can  such  of  of  salt  the  one  permit  loss  location  near  additional  type  the  the  the  to  stations  between  although  coefficients example,  proper  located  adeguate,  is  extensive  produced  l o g i s t i c s  mouth, of  a  average  with  make  to  the  effects introduce  For  to  the  they  mixing  enough  one  simultaneously  channel.  and  part  part  mid-way  be  of  in  currents  located  problem  operating  mixing  in  derive  insufficient  Fraser,  width,  banks  shipping  due  require  two  the  and  secondary  across  the  were  cross-sectional  to  model  to  however,  Mixing  since  predictions.  the  resolved  estuary  study  determine  1973  2  other  stations  a  l i k e  the  be  calculation.  rates,  probably a  to  30,  can  numerical  the  the  appreciate  the  both  March  rivers  from  present  the  1 and  stations  the  to  stations  Three  and  the  verify  w i l l  s a l i n i t i e s  in  mixing  In  which  balance  the  calculation width  data  salt  data,  properly  at  d i f f i c u l t y  complexity  observations  probes  a  included  for  a  -sufficient from  considerable demands  terms,  immediately  project!  four  Six  located  in  consideration of  can  the be  that  s a l i n i t y  obtained  collected  or  by  in  a  this  project.  Calibration need  to  include  diffusion  terms  of  numerical  empirical and  in  relations this  models for  regard,  is  necessary  turbulent velocity  because  stresses data  from  we or the  137  prototype be  is  collected  allow  part  across  of  i t the A  problem  should  of  the  of  project.  The  three  but  station  1 failed  clamps  and  submerged  located  as  similar  the  c o i l s  estuary If  close  could from  be  as  this  where  only  one  data  should  feasible station  possible  anchor  could  more  inch  to  tube  fame.  wire  be  to  to  can  be  the  deepest  for  future  along To  exceeding  another units  platforms  or  be on 300  here.  s i g n i f i c a n t l y  sealed  3/8  angles  made reported  or  durable  fatigue  be one  plastic  hollow  made  1/4  weights  loss  can the  triangular  through steel  to  in  the  pile  constant  recommended.  probe  than  thickness  maintaining  the  recommendations  probe  rather  designed  of  Furthermore  averaging.  conductivity  compound  are  width  programmes  casting  clamp  be  valuable.  channel.  number  monitoring  as  the  cross-sectional  occupied  by  particularly  by  1/2  in  this  satisfactory  increasing inch.  reduced  waterproof  used  were  The  The  the  pile  clamps  the  weld  between  certain  of  eliminating  the pounds  at the or  instrumentation, on  the  guide  wires  138  BIBLIOGRAPHY Abbott, P a r t I",  M . , 1 9 6 1 . "On t h e S p r e a d i n g o f One F l u i d Over Another, La Houille Blanche, V o l . 1 6 , N o . 5, p. 6 2 2 - 6 2 8 .  Abbott, M., 1 9 6 1 . " O n t h e S p r e a d i n g o f One F l u i d O v e r Another, Part II", L a H o u i l l e B l a n c h e , V o l . 1 6 , N o . 6, p. 827 - 8 4 6 . Abbott, M., 1966. An Introduction to £!}2l§£i2£istics Thames a n d H u d s o n , L o n d o n .  The  Method  of  x  Baines, W., 1952. "Water Surface Elevations and Tidal Discharges i n the Fraser River Estuary, J a n u a r y 23 and 2 4 , 1952", R e p o r t N o . MH - 3 2 , N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a , Ottawa. Baines, W., 1 9 5 3 . "Survey of Tidal Effects on Fraser River Estuary, J u n e 10 a n d 1 1 , 1 9 5 2 " , R e p o r t National Research Council of Canada, Ottawa.  Flew No.  In the MH - 4 0 ,  Boulot, F., Braconnot, P. a n d Marvaud, P h . , 1967. " D e t e r m i n a t i o n Num^rigue des Mouvements d'un Coin Sale", La Houille Blanche, V o l . 2 2 , No. 8, p. 871 - 8 7 7 . Cameron, W. a n d P r i t c h a r d , D . (1963). "Estuaries", i n T h e S e a ( e d . M. H i l l ) , V o l . 2 , J o h n W i l e y & Sons, p. 3 0 6 - 3 2 4 .  C h a p t e r 15 New York,  Courant, R., Friedrichs, K. a n d L e w y , H., 1928. "Uber die Partiellen Differenzengleichurgen der Mathematischen Physik", M a t h e m a t i s c h e A n n a l e n , V o l . 1 0 0 , p. 32 - 7 4 . Dronkers, J . , Waters^ North Netherlands.  1964. Holland  Tidal Computations i n R i v e r s and C o a s t a l Publishing Company, Amsterdam, The  Dronkers, J . , 1969. "Tidal Computations Areas, and Seas", Journal of the Hydraulics No. 6 3 4 1 , H Y 1 , p. 29 - 7 7 . E l l i s o n , T. S t r a t i f i e d 423 - 4 4 8 .  and Turner, J . , Flows", Journal  f o r Rivers, Coastal Division, ASCE, Paper  1959. "Turbulent Entrainment of Fluid Mechanics, V o l . 6,  F a r m e r , D. a n d O s b o r n , T . , 1 9 7 3 . "An Instrument Conductivity Profiles i n Inlets", Journal of Research B o a r d , Canada, 2 9 ( 1 2 ) , p. 1767 -1 7 6 9 . Farmer, H. a n d M o r g a n , G . , 1 9 5 3 . "The Salt of the Third Coastal Engineering Conference,  f o r the  i n p.  Measuring Fisheries  Wedge", Proceedings p. 54 - 6 4 .  Grubert, H. a n d A b b o t t , M., 1972. "Numerical Computation of S t r a t i f i e d Nearly Horizontal Flows", Journal of the Hydraulics D i v i s i o n , ASCE, Paper No. 9 3 0 0 , H Y 1 0 , p. 1847 - 1 8 6 5 .  139  Hodgins, D. a n d Quick, M., 1 9 7 2 . "Computer Studies of Estuary Water Q u a l i t y " , Proceedings 13th Coastal Engineering Conference, July 10 - 1 4 , 1 9 7 2 , V a n c o u v e r , C a n a d a , p. 2327 - 2338. Joy, C. , 1974. Thesis, University Keulegan, G., Hydrodynamics 574?  Water finality M o n i t o r i n g i n E s t u a r i e s ^ , of B r i t i s h Columbia, Vancouver, Canada.  1966. Chapter 11 in Estuary and (ed. A. I p p e n ) , M c G r a w - H i l l , New Y o r k ,  L a f o n d , E., 1951. EE2£§§§iS9. 2 2 § i . n o g r a p h i c Office Publication No. 6 1 4 , U. S Navy W a s h i n g t o n , D. C . , p. 9 1. L o f q u i s t , K., 1960. Stratified Fluids", p. 158 - 1 7 5 . Miles, Flows",  "Flow The  J . , 1 9 6 1 . "On Journal of Fluid  Pritchard, D., 1956. Estuary", Journal of p. 33 - 4 2 .  Ph.D.  Coastline p. 546 -  Cata Hydrographic Hydrographic Office, x  and S t r e s s Near an Interface Physics of Fluids, V o l . 3,  Eetween No. 2.,  The S t a b i l i t y of Heterogeneous Shear Mechanics, V o l . 1 0 , p. 496 - 5 0 8 . "The Dynamic S t r u c t u r e o f a C o a s t a l Marine Research, V o l . 15, No.  Plain 1,  R a t t r a y , M . , 1 9 6 4 . " t i m e - D e p e n d e n t Motion i n an Ocean; A U n i f i e d Two-Layer, Beta-Plane Approximation", Studies i n Oceanography^ (ed. K. Yoshida), University of Washington Press, Seattle, Washington, p. 19 - 2 9 . Richtmyer, R. a n d Morton, K. 1 9 6 6 . Difference Methods Initia1^value Problems^ 2nd e d i t i o n , Interscience Publishers, York7 p . ~ 2 8 8 . Rigter, B., 1970. "Density Induced Return Currents in Channels", Journal of the Hydaulics Division, ASCE, No. 7 0 8 6 , H Y 2 , p. 529 - 5 4 6 . Roach, p., Publishers,  1972. Computational A l b u g u e r g u e , New M e x i c o ,  Fluid U.S.A.  for New  Outlet Paper  Dynamics^  Hermosa  Rossiter, J . and Lennon, G., 1965. "Computation of C o n d i t i o n s i n t h e Thames E s t u a r y by t h e I n i t i a l Value Proceedings of the Institution of C i v i l Engineers, 6 8 5 5 , p. 25, 56.  the Tidal Method", Paper No.  Schijf, J . and S c h o n f e l d , J . , 1 9 5 3 . " T h e o r e t i c a l Considerations on the Motion of S a l t and Fresh Water", P r o c e e d i n g s Minnesota International Hydraulics Convention, I.A.H.R., September 1-4, 1953, Minneapolis, Minnesota. Smith,  G., 1965. Numerical Solution of J. O x f o r d U n i v e r s i t y P r e s s , Oxford.  Partial  Differential  140 S t o m m e l , H. a n d F a r m e r , H., 1952. "Abrupt Change in Width in Two-Layer Open C h a n n e l F l o w " , J o u r n a l o f M a r i n e R e s e a r c h , Volume XI, N o . 2 , p. 2 0 5 - 2 1 4 . Taylor, G., 1931. "Internal Waves and T u r b u l e n c e i n a Fluid Variable Density", Conseil. Perm. Intern. Pour L ' E x p l . De Mer, Rapp. E t P r o c - V e r b . , V o l . 7 6 , p. 33 - 4 2 . Turner, J . , 1973. Buoyancy University Press, Cambridge. Vreugdenhil, an E s t u a r y " ,  C , 1970. La H o u i l l e  Effects  "Two - L a y e r Blanche, Vol.  in  Fluids^  of la  Cambridge  Model of S t r a t i f i e d Flow 2 5 , N o . 1, p . 3 5 - 4 0 .  in  Waldichuk, M., M a r k e r t , J . and M e i k l e , J . , 1968. "Fraser River Estuary, Burrard Inlet, Howe S o u n d a n d M a l a s p i n a S t r a i t Physical and C h e m i c a l o c e a n o g r a p h i c D a t a , 1957 - 1 9 6 6 " , M a n u s c r i p t Report Series No. 939, Fisheries Research Board of Canada, Pacific O c e a n o g r a p h i c G r o u p , N a n a i m o , B. C.  141  APPENDIX  A.  ENGINEERING  The to  provide  outcome the  numerical part  of  changes  present  produces with  of  effects  speaking  velocity  fields  dispersion be  models i s  of  derived before  possible  considering  to  resulting  which  contaminants  and  in  a  used  predictive  i l l u s t r a t e  only  the  to  some  of  information  the in  intrusion  problems  dealing  lower  estuary.  time  varying  the  of  salt  water  sedimentation  or  the  velocity  with be  the  used -  predict  extent  the  can  be  modifications  the  the  conjunction capacity  in in  relate  can  s a l i n i t y  provide  and  possible  to  from  The  models  layer  thesis  required  quality  hydraulic each  this  considered  water  Submodels of  be  STUDY  in  exploitation.  and  in  THE  developed  estuary  must  the  OF  information  the  which  Generally  must  in  sedimentation  penetration.  models the  forms  ASPECTS  the  information  basic  realized.  salt  provided  However  wedge by  hydraulic  effects  the  i t by  hydraulic  models.  Sedimentation produces the may  a  region  v e l o c i t i e s be  duration  next  The  a  meters  to  estuary  to  to  bottom  by  and  in  mouth  examine  the  effects  dredging  to  i t s  near  of  depth  are  the or,  natural  salt the  promoting  toe  the  return  the  flocculation  variations  average  by  mixing  of  further the  accentuated  turbulent  the  upstream  interest  estuary:  of  accompanied  sedimentation.  of  is  which  toe,  important two  the  state  and  down  salt  changes to  hand,  (reducing  This  increases  parameters.  channel  other  i t  slowing  further  imagined  shipping  since  deposition.  position  of  on  water  water It in  add  allowing  the  depth  is the  three the by  142  about  2  meters  February the  10th  total  using  results  penetration  time.  expected  the  shallowest boundary  two over  A l l  showed  the  basis  of  three  the  have  evaluated  boundary  the  conditions  order  of  magnitude  two i s  and  shipping  to  15  not  a l l  and  present  mean  model  but  for  altering  expect  the  would salt  would  channel  also  usually  be  the  occupies  time.  the  measured  arise  depth  much  solution.  On  dredging  about  for  in  very  20  in  depths  penetration decreased  changes  percent  on by  of  estuary  15  of  percent  predicted  the  than  As  wedge;  water  additional  in  less  the  the  duration  case  and  differences  depth  altered  the  cycle,  fresh  the  accompany  s i g n i f i c a n t l y  the  Since  reduction  water  of  longest  penetration A  terms  same  i n t e r f a c i a l  distances.  The  the  the  similar  might  in t i d a l  at  runs,  "standard"  percent  meters.  this  for  the  we  the  admitted  increase  excursion  the  model  values  in  4  penetration.  remained  the  Table  i n i t i a l i z e d  used  with  in  times  channel  of  meters  present  were  was  these  three  shortest  compared  approximately  the  for  wedges  of  the  summarized  runs  extrapolation  or  are  condition  penetration  the  measured  deepest  various  an  I  the  lengths  wash-out  as  average).  depths.  The  along  on  this since  of  the  width.  The deepening. cycles,  the  significance The  increased  presence  New  Westminster  this  area.  This  does  of  w i l l part  of  in  the  penetration  salt be  l i e  water  increased the  river,  in  changes  means the  and  that  brought over  which  many  t r i f u r c a t i o n  sedimentation presently  about  t i d a l  area  enhanced receives  by  at in  143  Table  4  S a l t wedge i n t r u s i o n c h a r a c t e r i s t i c s i n the F r a s e r R i v e r v a r i o u s model d e p t h s . The deep c h a n n e l i s 3 m e t e r s below p r e s e n t and the s h a l l o w i s 2 meters above the present. PENETRATION (KILOMETERS) ESTUARI  TYPE  Deep  Present  Shallow  Time Feb. 10, 1973 0300 hours 0500 1200  21.6 21.0 32.0  17.4 16.2 27.2  14.3 12.9 23. 5  Wash-out  17h53m  17h43m  17h27m  for the  144  continual  dredging,  deposition have  to  and  be  and  and  been  In  neglected  examined  with  the  lower  the  introduced  of  and  i s  for  a  been  using  a  course  followed  relation  to  particles  the  fresh  of  the  velocity  f i e l d ,  paths.  The  upstream  on  Arm  would  the  f i e l d  baroclinic this  Fraser  monitoring models  (Joy  effects  are  assumption far  ebb  the and  as  can  be  flushing  in  and plant  can  be  Two  Main  salt  seen  particle  s i g n i f i c a n t l y  water  (1)  flows:  one  barotropic  near  an  I  runs  1 and  treatment  were  plant  the  on  a  proposed  tide.  in  Figure  have  have  2  ebb  sketched  The 42  assumed  in the  flows.  layer  compared in  us  separate  River. Arm  let  the  Numbers  during is  water  into  released  Fraser  the  the  one  sewage 4  mixing,  fresh  days.  Road  velocities  this  but  3  the  in  of  vertical  particle  of  " s t r a t i f i e d " flood  on  dispersion  particles.  treatment  effect  and  of  maintenance.  both  as  rates  shipping  issue  by  least  by  two  Gilbert  remain  water  of  four  each  Main  main  at  model  particles  by  a l l  of  the  sewage  w i l l  The  period  total  and  Island  an  of  and  advected  f i e l d  Annacis  recently  longitudinal  velocity  tide  channel  v a l i d i t y  two-layer  flooding  expanded  becoming  model,  increased  concerned.  particles  offshore  of  studies,  the  the  injected  by  one-dimensional  into  made  cost  rapidly  two-layer  estuary  two  the  dispersion  Neglecting follow  is  to  generated  investigated  these  usually  subjected  against  development  (1974)).  be  revenues  quality  has  the  the  balanced  Hater River  would  the  with  to the  particle  advects  further  is  increase barotropic 1  s l i g h t l y  downstream  on  and  2  further the  145  Figure 42. Advection paths of four particles r e l e a s e d i n t o t h e M a i n Arm o f the Fraser River. The small numbers along each path i n d i c a t e the time i n hours f o l l o w i n g r e l e a s e .  146  subsequent i t  does  ebb. not  pass  flood  a  second  about  3  hours  appear  in the  tidal  cycle  salt  back  time  Annacis  beyond  to  wedge,  the  with Island  model that  flush the  return  o u t f a l l  and  area  and  number  1.  Much  does  not  paths  flush  number in  the  3.  consequence,'  Particle  flushing the  and  i t  s  In  fresh  reduction  of  region.  o u t f a l l  of  of  modified  particle  particles  extent  is  into, the  into  barotropic  required  i t s  compared  the  that  Also  i t  does  is  delayed  same  trends  is  to  be  noted  particle  u n t i l  general  the  water  depending  2  i s  one time  reduced  by  the  the  point  of  there  would  be  upon  release.  These  particle  paths  considerable  differences  contaminants  between  s t r a t i f i e d on  the  particle the the the  f i e l d  and  released  Annacis  Road  s t r a t i f i e d fresh  effects.  water  o u t f a l l particle near  the  dispersion The  both  at  same  released  baroclinic  flows  purely  advective  account  in  do  than  one  apparent  dispersion  be  in  models.  barotopic through  higher the  from  salt  on a  water  (1)  and  show  that  on  the  taken  into  results influence be  for  loading  particles  must  the  passes  effluent much  on  times  three  for  s t r i c t l y  the  five  These  and  case  based  including  significant  dispersion  one  example,  with  would  a  case,  predicted  Road.  in  passes  mouth  Gilbert  have  For  compared  also  concentrations  based  other  (4)  Thus  river  of  the  Island  (3).  is  models  f i e l d .  region  from  part  numerical  in  model  trend  that  predicted  dispersion  velocity  Gilbert  (2),  in  barotropic  barotropic  the  velocity  imply  147  The  Effects  of  The  region  deleterious  end  from  the  the  dispersion  incorporation s t r a t i f i e d  of  the  improved  model  mixing  however, the  i t  i s  layers  salt  wedge  the  river  is  and  effluents  result  tend  to  than  compensated  the  on  they the  be  for the the  salt  suffer  rate  of  confined  in  some  to  from of  motions.  or  that  the  once  the  measured  model  basic rates  for  i t s e l f  use  can  be  vary.  important each  the  thinner  degree  dispersion  provide  been  vertical  effluent  wedge  to  within  corresponding  loading  The  from  the  In  the  layer.  surface one  considerable  to  flushed  models.  also  depth  being  some  dispersion  clear  either  in  the  within  at  whole  the  flush  influences of  the  s t r a t i f i e d  concentrations  to  discharges  over  a  mixing  that  require  have  is  means  a  therefore  hydraulic  intrusion  v e r t i c a l  mixed as  layer  the  produces  w i l l ,  effluent  used  densities  and  knowledge  be  the  usually  these  could  layer  of  the  across  This  before  would into  and  mass  simulation  by  river,  required  water  the  unstratified  i s  other  studies,  allowing  wedge  either  dispersion  of  This  into  terms  between  salt  diffusion  properties.  contaminants  diffusion  standpoint  release  the  information,  The  are  in  turbulent  the  released  A complete  flow  vertical  in  water  of  of  that  of  up  estuary.  show  along  substances  proportion,  S t r a t i f i c a t i o n  occurs  transfer  hydraulic  and  observations  i n t e r f a c i a l two-way  Mixing  to  or two  hours  d i l u t i o n .  mixing  i s  layers  by  the  the  estuary.  of  When  suppressed  with  unstratified  contaminants  bottom  higher  situation.  decreased  time  Predicting  relies  on  a  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



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"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items