NUMERICAL MODELS OF WIND DRIVEN CmCULATION IN LAKE MELVILLE, LABRADOR

NUMERICAL MODELS OF WIND DRIVEN CmCULATION IN LAKE MELVILLE, LABRADOR

by

(~> .

'A mrltpal SIDjh

B~olall

^{B.Be (HoD')}

A The.I..ub~IUedIn partialfulflllment oftbereqUlremeD~_tortbe desree

or

Muter ofS'c1eDce

..

^'

DepartmeM-Ctt Ph)'.ICI MemorialUDIYet~lt7o(Newfouodla lld

.).

·

---~,

I ..

\

....

,Permiss ien.has been ora nt'ed to the Na tio na l .Li brary of Ca na d a ec microfUm this thesis and- to lend or sell .«'c.op i esof the fqm .

The author (\copyrigh,towne r )' has r e setrv ee c u n e,»

_ _.publfcat ion righ t s, and neith e r the the s i s no r extens i ve extra cts from'it may be-printed or ot he r wise .reproduc ed witho ut his/her wr i t ten pa £~ission~'

L'auto r i s a t i o n a~t ~ecc oe c e e

a

la Bibliothl!que natio nale du Ca n ada de micr ofilm er cette tMse'et de pd !it er au de.vendre'des.exe mpl ai r escu film .

\

L'auteu t,(tlt u l al r e du dro it-.

I d'.iiuteut") sa rA'Serv e tes eutres dro lts de put;>li.cation l n1 lil thlJs e nl 'd,e :lo ng s extra lts de c eLk e^ect ne do i vent 8tr e. lmp r lm ~s au autrea ent; re produ l ts, sans son autor l s a t i on ~crl te.

ISBN' g':'llS-llU9-X .If

.

^.;'

/ J /

. I . . •

To

my

pareDt~,ror thelr love,ca~eandqD~entaDd~&.

.----t,.--,--- - - r : -..:-- -,.

.:

:<

Ablltrad' "

In this lI'ork; .DumberofDumtfi~al^modelshaTeb;e~n^ad'aptedto$~udy^{the elud-} '"d riveD circulation.ofL'keMelville.Thefinttwo

~c:ui~ls exam~Dtd

^{are tbe}steady:,t.te aod theti'mC:~epeDdeDiI:iO~~geDeoU~^eedele..The'result, indicate t'hatthecomplex' bottom'topouaph,r,forces.' compGeated circulationpattern wh ich is

.relativel~

~D.lrC~~ed

by"the;a!ue ofthe'bottomst re$llcoefficientaltlnfu'sb.the

choi~e

of such affeet. thecurren t,p~^directly.For'-,const lult.i~dof,enDmetef'!!.per~~d,:tlle nrticallyanra,edhorizoDtai

,~Ia:c;ity

ISabout teo

ceDtilll~~n'

^{persecond ,}suggestillla surface nlocity01aoout thirtytofortycenti~eters,per second.'The third and. IMk . modelis av~rticall1 iDtCKR~t~o-Iaycr^modelals~^drivenby • constantwindof seveo -

.-r-r-.'--~7~;nffl)tl'RcODd;""""bn·esultf1rom1btn~-oQi:l iildic:-afi1.baro-ahiC1iiiiceffedi!suc·'"... . -- - -

'''~e~iDert.ial

^{o,cillations'an dintffllJ'1}

w~v,:,

a:re'importan t,

sinte-ibe'hitemar ~--"

phenomenaM:'ociated with.stratifiedlake~ dO~iD.a~s.'.heir dynal1lics;To~.~te,

D C,

eld'." .. '

tDe~UremeDU

^{have been'}ealTied outonLake Mello-iIIe.Thesimulatonsfromtbe odels .

•studied.in panieulartbetwo-layer moddisllDest thatcurr entmeMur elllcntswou be

v~I\l.bleformodel.ealibration3. . _ • , ' I

J .. ' -1--'· •

, -;'

,

.

^{.. 111"}

'-

:,~fo.

I wou llt,liketothank my supervisor,Dr.Tim Keliherlorhis

(l1i~ance '

^{andll - -' ,}

eDcouragemeD~.du~ngthe.course.of thi, work. - - " ,\

,

Th.

~uth.", ^'''1 .''''''''10

0,:I..

W .b"''''d ~A1" H I , ^{r ..}

^{pm,Id;',..ere}

"" "11,h' en,,,

di".":",, , , ' ,\ . " .. .

.'The ...,i,t ance of Dr.T..J.Simoni in the lormoflite~aturereferencesaodcom pu.ter

algorithm" is most gnt erullyaclr.nowl~ged.

The authoralso expresses gratitudeto Dr.P.P.Narayall~wamifor his ani,tanc'ein thewordproce,,~ngand printing ofmythesis.

"T he financiallWlist aneeofthe MemorialUniversityof Newfo undlandin theror m01I

- - - ;, -::gra d uat e fellow,hip'aDd

~"in, a"j~taD:t,bips

^isgreatly appreciated.• Last,but Dot least,I am indebtedto my partoheed my ramilywhocon tinua lly ea ee ueaged medurins thewhc le.ccurse ofmy programme and',ervtda.'la snatinspjra.

" '

uc n

illmyeedeevcre.

• .- -..p;'

,;-

Table orContentl

Dedica~ioo

... ...: (iii)

..····.. ··· .. t··

⁽ⁱⁱ⁾

. :~ :.Ivii). ... ... . ... ... (xiii

Co.otent e,,' ,..;.,-.(iv)

~Figui~, . Li~t ~r Tablc,

CHAPTERI:INT RODUCTI ON·..

1.1. Batkgrou~d•.

~•1.2.

1.3.

u .

(I) (I.)

Mtltivation rortbePre3eotStudy. . (S)

\ .

.

GeDtr1F~~or'orCleeula rlc u.. . (Ill

scope ortbePre,e D~St ud y lUI.

I.S. Rcsult,br~heWork : , , tlSI

:2.1. GencralEquationsrortheBarotropicModt>1 1171

dIAPTER3:TilE STEAD'!"·STATEMODE'L OFLAKEMELVILLE

2.2. G~~.era.1Equa.tions'rortbe Baroeli oic~odel. . : (21I :t.3.' FiniteDilJ~ffnteForms

or

Derivat ives , r.•...•....••...•...•..•.l231. .·...1")

:

..

;

3.1.· Der i~ l\ l io n, ortbt>Strea mFUDct ionEquerlcn... ... 1"1.

3.2. Method of Sol,'qtion . .. (27) 3.3. The Input Data.. ...•., (,0)

3.4. The Resultsif tbe Model 132)

CHAPT ER 4: THETIME-DEPE NDENTBAROTROPI C MO DELOFLAKE

~,ELVILLE:.

u .

, , . -

Intro d uction'...

. (39)

· · ·1:19 )

.. (40)

.(43)

. (<l.~)

. (43!

4.2•.2~talCitcultii,~D.EDetgyfotH~mlll~neou,B~iu : ., '(39)

4.3 . The Method..of'Solut·ion " (401

4.3.1..

The 'Stagirred\~tid·

.. \ ^{: :.}

4.3.2. The Bo~~aatya'ndinitial'Condition! 1~21·

.. .1' . ', ' .

4.3.3. NumerICalSolutIon of the EqllatlOO! , ..(42)

,

4.3.4. Predictionof tbe SurfaceElevation ....

4.3.6. Ptcdictiolof the MM' Trauport'Compooenu .

.4.4'. Reeultaof the Time-Depeedem

I

M!X/cl \ 141i)

4.4.1: Rt,ponJofLakeMelville to WiodrOtti'og .

. I

4.4.2.Re!ponse

10f

Lake Melville.AfterWiodCu~o lf (49)

4.5. EnergyCollider~tion' " ,." :.;.: : (621

CHAPTE R5 :THETI E-DEPENDENT TWO·LAYERMODEL OF LAKE

MEL:~~LE .;.~.~:~~~.~;:

^..

:::::::::::::::::::::~:::::.:::;::::::.::::::::::::::::::::::::::::::::::::::::::::::::::::::::

^{... ::::::}

.. (73)

;

I'

5.2. Total Circulat ion Ene;'gyrorTwo-LayerBlUiD!..

5.3. Theslld aJ andlatuoal

Mod~

^ofaTwo-Layer Sy!tem

. I ' .

5.4. MethodorSolutioo...

I ... .

5.4.1. TheNuml;;ricalS)'! tem

...(IlRI ...(1101

(73)

·1

"

5.4.2. Con t i ~u i tyEquatiollS : , (76)

5"'.3. Momt ot wn.-Equat ioo", . ...(77) 5.•.4.•Sum mar)'oftb~ComputerAlgorithm.

5.5. Ruullsoft be Model

.(781, ... ...(83)

5.5. 1. The VelocityField inBasin.1 ~^{.•..' ,,}:•.•••••••••••(83)

...: (OS)

...(122) ...:...•..(122) I ..

. (1.22)

. (125)

Introduction ""

6.1..

6.2.

6.3. Field Program .

5.5.2. Reepcese ofthe Surfaceandthe Interface

5.6.

E;~aiY Di,tribU~;OD

ⁱⁿ

~ake

^Melvilie

^{. 1} ~::)

⁽¹¹⁶⁾

CHAPTER

e :

DISCUSSION . .

J

- I'"

REFERENCES , ~ (127)

•. . - ^{. " - .}

I

/ '

'f1

LIlt~tFlAurea

EiI~l.I;LocatiO!l.orSl udyArea(ah c;Bobbiu .. adAkcobcat!.i( 82). (2)

<Figure 1:2i-HamiltonIn let and LakeMelville (after Bebbiuand Aknbcadf". (31

~igllJ'c1.3jWindroses for(lOO3CBay Airportfor various mootu.!I'bcoumbe"

repre3eDub~mea nwind"speed in hots andthe leDgthorthe"ec to ris dire1:t1y proportionaltoth~direct ionalfrequencyof the ...i~d(after KrugerandBoncaud,

I<)

FiKur.e1.4:locatioD ofsampling 5tatioos(rom"hich-dil a-'wereused (afterBo~

bin andAkenhead , 1982).AbbruiatiolUBB, I and BDretertovariousexpedi-

.

tioll5 [see text] , .

.

~ {al

FilureI.~;PIOLSofsigm..tvenus depthfor dill'creotsu.llolU(afterBobbittaDd Akenbcad;H182)

FigllrC 1.0iPlotsof salinityagaiD)tdcplbtor'l'u iou. !latio D!in Lake Mclville (atterBobbitt ead Akcuhead,1982)..

17}

{'I

vl'11

ursoabothaxes.

FilUlt3.1;Tbe bl t bymcLrJ of.Lake.MeIYilleiomcun~f~rIlD00thio,ladni-

,"ted

iostru mnl \ moonll.' .tltiollsA ladB(lee Chapkr6).'Tbe oumk n 00 the In s

dtDot~

^.hetrid

lor~.ioDl,

^{OaeuidIII' DI.hi.}1.833kilo.mt k "n OD.both

(0)

...•.•..~,:.._~ ._,.:,_. ••_.__...•..•.•.(31)

Fi,ure3.2 ; Stream

~uDCtio~ ~ ' (or

stud y;. tate

oud~r

^{alout h-ester;ywiad'?f7}

'11I./'

eedIbottomatm.cacflicira.tof

~

^_:0.025/H

Hr-' .

^TheDumber!.orit'he

~.es^{deeete theVid}l~atiDUI.^'OneVid length i. 1.833kilometers ODboth axn. ...•,...(33)

'C Fi(Ur,e3.3;Strum (lIDctioll~for.tu dy -state UDderawesterlyw,iDdof.7

mi .

aad I bottomst re"cod'")cirDtofK,-O.OlfH I~·I.The DU,mbenon theun deDO kthecridIocatiou;ODe

end

leD&1,hi"1.833kilometen onllothu~:

__-: _ _ "'_

(34)

t.i~U! 3." :Stre~

^fUllcttoli

~

^{.for .t}ead,...tlte UDderawnLerl,-.iad:f7

rib

aodI bottom.tresscodkicDtofK-0.025/ H ~,"I.-Tbe'IIDmbenOD tlleaxil"

FiSUfC3.5 ; Stream 'uDctioll~ fonteady.si.'tt":'Dnd~rIwbtrrlywiadof7

m i'

.,

.

. .

lind.'bollomstrcncoefficicntofK.,,;,.O.O&/H ~c·I.Tbc^numbersqn.h.c'XC!!.. denote the "idlon tioll'.01111' lI:ridICDlI:th le 1.833 kilometcrs011both un....,..~,.,,,.(36)

,

FiIIllC,3Jt.;.Jloftlont al cutrtllt.(orstudy.s tateUDderI"nwly..ie dof7m/ i

/

", 1x

aDd a~ott.om·stre~.^eoeffidcntofK _~,02S/H^{,_ -I.} ."',(lSI'.

."!

. 2-

,

.

FiSure

.

4.1,;

.

(a)'tbc'staueredg..^"ld^,repmtnt:tioo^.of^,

1'3ri.bl~

^,

~(b)

^the(rid~'-

^.

^-,'

squar;: ,.., , , ,,., .

... 1"1 .

: :.

. .

,'

.

^{; , . \'}

\

Figure,..2iR~pon5eof.La.xeMclvill~to windfor.cing.Tbe wind'/lehtorfoui

days

0; .nin~ty:~i;h~un

^{fromtLewe,t : , .:' ,.: : :.:,, ,,.:..}

~

.'

.

. ,Figu.r~^-(;3iR~POIlHof Laxe Mdviile~rt.er ~i~dtuvolJ.at ni.oety·,ix.ho~sfrom

;1 ,

iIlu,tiitC'thecu~tot, , ' ~ ...

"

... (50)

' .

!,igure.4.4

i

(a)Vo'rticit;y di,trib utiona.noci:t~~

-IJrit,\

wind'fo~i ng'io^abas~o';

(b) voriidty

distribu~;on

^ina

ba.'lj~ arte~

^wiod

c~olf.

(after,..O!Ianady,1982) (54)

Figure

~

ⁱ

Con~ounl

⁰¹eurface devation ofLake Melville

i,!!

cent imeters

d~riof

^.>,"

and aftert~eWind~9relllgepl,od,eThe _Iodcpt-oO'is atOlnety.sll(h9unIafter' onset.(all

val~es

mnltlphed by'a

.f~tor

^{of;00) "}

r.l .

50J

, ~-, .

Figure 4.6;Surrat e.!!evation at 'electedpo.iot,at'boppo,iteend! oftheI~k eas a

._·~uDctio~^ortjm""l"d~iDgthe first twelveheursQf.iD~fordng~ .1011 '~.^t

. -

F',,,,

'.1..

To'" ""IY I.

Leke

,;",m 'li" '''1 .

^\

r "

d"!,,"

·,,,",, . r b ''' .m

^..

\"..

!trnscoefficient~.as afunct ion oftime.~hcan-ow in'e~hploti~a.te!the.'. ', •• begi~DioS"of."dip"(seetell!.). .. ; .') :

: ?

(o~),

.

^,~

"

ril~e ^{4 ..} 8l(~tiaJ

^{tDerv iaLake}

~eh'iIIe

^{(ia trp )aa8}

r~DctioD

^{of timefor'}

dill'ueDl'TL~a

of the bottom ,lresa codicieDt K durin, wiod forciDI0011.

... ... ...

(~)

F:~~, ~ ^{:(.) Th,} '''''''~ ^!'id ~~"" ^.. :..c:;-;~:.hb : (hi,h.,,:d

lMIuare ,.: "... . (1~)

'.

. .

^'.

FillU'C5.2.;Velocity6eld in the upper laleraty.rio~ &t~!es^{io the}', im·ul. lio.n•

. . . , ^,

^{:: :}

^{::::::: ,}

^(")

^.

Fi~~

^5.3;Ca) x-componentofvelocit; atpoint.(12,20)iDtbe upper I'lerasa' rUDetioD of time;(bl x-campoDeD'"ofYelodtl~t,point(14.10)

ia

't he upper layer

~.'!!J.Jl.cUoo of iime^jee) curreot bC?dographalpoiot (12,20);(d)cu,:ent bode-

. ^{. . .}

^' graph at POiol (14,10)• . ~...(89)

-,

"

~i'Ule^S.4iVel~it)'^fieldi~the lower layerat ,,:arioll3&~a«es^illthe~lmulatioll.

The willd cut-offi~'at twellty-rour houn arter eeeer, . (Q3)

Filure 5.5 ;ta) x-componentorvel~ityat point'(12,20)in the lower layera,.,a fUllctioD'or time;(b) Nomponentor velocityat poiut (H,ICfjnthelower'laycr ua

ru~etioll'or

^timei(C)CUfflllt

~odOgraph

^{at pointtI2,20);(d) cu'?uthodo-.}

lTapb at peillt (14,18). • (09)

~"

. /

Fi«ure 5.CiCODLOllnor~lIrfac'ee1CvatiOllor LakeMelvilleat diB'uelJt~talCsill

,

^.

.

," tbe.lmula~.loll,(all "lues ShOWD multiplied by a ractor or 100)

..

.

--'- -

~...(102)

"

."

Fi( ure

.

5.7 ; Surfac-t elentioo

^'

IteeleetedpoiD~at the oPJlO'itt nd" oftheI, ie ./

loS..fUd ioooftifDt"durill' thelinttwrlyeboW'Sof_iod fOKinl. . _._..1108)

FilW't&.8;~oDtollnofiOlerf,dal elentioDofLai cMeh'iIIe It

" noll'

slacnio ...(110) ..

PilUl eS.VjPote~ti.illtau?,.iDe~bl~JuofLake Meh ille (iDrra:s)..,afllDelillo

oI'time. • (1171

ortime. . (1191

PilUl e 5:11;Total tDer D' distrib utionio

Lak~

^{Mdville{ieup).., a}

rUD~lioD

^of

•... ..• .. .•... ..•.. ... ..(1111

•

xr

t

Llst

or

Tables

Table3.1;Maximum nlue or tlU1'elllas a function oft{. ...(32)

Table 4.1 ;Spin.upand spin.down limes or Lake~eh'iI1ecomputed(romthe

~t.1COt l'l1inthe model ..-.(uacliollor the bottom ItreueoelJieiea t K•... •:••.•.•.(&2)

Table 4.7'";Spin.up times

tor

aDEk~aDeaeuee model or coutant depth.0&~ the Ekman depth lor Lab Melvilleof thirty-seven meters.whichhasbeenwed ill eomputiDIl:the above times iD3tnd of the meande~thof d,bty.six meters (see

tex'tbeloll'l· . : (031

,-/

-1-

»:

CHAPTER I , INTRODUCTI ON

.1.1.Sa-eili r ouad

LakeMelville,Labrador,.illODe~tthethrulaai~••teebediesmakin,upnllllil.

ton Inlet,theIUles!iolet.alDolthe'L.~r.~orrout..The other two".UrbodiesIn Gros.I terBay andGoose Bay(Fi(Ure1.1).-As3how~in Fieur 1.2, thefntrance 10 Hamiltoa-Inletrowi , ts of Gro,,,aterBay"hithisabo ut 6fty kilometers in Itn(th

,nd

• • 0

CODstrictlioto•naJ'r'?".,ballo...uneras iol.bOlll2.8k\lo~elr~ill"!dt b aed thirty met ersill.~cptb.ith•• leDlth or twenty-twoItilomrtcnhawDalltbe~arro••.Betore

o •

uten DI L,ke·Meh·iI1e,",heNarrow,aredivided iat o 'woc~aD Drl,byHCllrirUa.I,llod aDdf:,kimo lslaed (f i(ure 1.2).

.Lake Melvillelits-to-the "n',ortbe Nu ro,,,'ee dbu anI.cn.rt drpc.b orabout

tiooin trrmsorrUDolfaDdthe pfTntQ crorlet...disd~ri bf'dby "rucl crandBout..d 1I!ila31fft) r:Dd3t aeelleeted at(;oo,eBayAirport.Thewntht r paUtrD5 orG_~D!y_

Airporthavt a~e adtDC1to..Ittra at t bttweu tbose ormarilitDtloadcootiototalcit.

o 0

matn.and tbe n.-Ulmt r tempcr..turrsiatbeG?Ox Bay..rn tend tobe.co mfort a ble b.ut.

oh encool.Wiat eri;uually chut.( tcrh ed byraId, rrispy wu tbtr loa d nia, but mid_iotertbaw,aie 001 uncommoa. .

Fisure1.3~iVfl ~bc'wiadrow l rorGoosen..

r

Airport.AI·un.beStu:the dam-

o •

inl.llt wiads1Io~thewcsttrliuload tbe !IOut bwt,lc r licl.Thue windsa~pcarto~(

inBur accd by the aOtt bflUt-IOlllbw.c'1orteota tio..ofIhmi lto a1.le( load line ..mUD

- ,-

FilUle1.1iLoulioll ofStu dy Area(d ter"BobbiuandAkt obead, IQ82)

I

.J.

-oj \

!

, " "

^~

J

^,

-4-

~ ^{' ' -} '~ ^{. ,.} . ,

I

^.

i - ' . ' .

· l~ : l ^.. ~.

. I • .

.:..:.'

wiud speed

or

aboutsn~ Qm~npu eeeeed.

Themajorityof ocuDorr aphicdltaforLakeMel,iIle wefteelteetedfromIlWIlo IgS;Sbythe BlueOoiphio expeditiolUledby Ca ptai o O...idNuttof DartmollLhColle~.

NewHUDpshift.Salioity aod~emperature meua re'me~tsweft biet! throulh ouLHami\- toululet duriul 'ummff~illthe yun 19SOtoIDS3. 10all.about3SO.hydrolfaph.ie sampl~wereeoU",ted aDdthe four mljo r nyenwereIIUI~todetermioetheIIDo_at--"-

offm b'wat t r di5chul eintoth~ lik e. Ad~iLiooaJdat aeoll",l ed bythtfi'heries_

Rexan::hB!:,~d2..f~an ad aiothe latesamm~r011952abo!,rdthe,"~ItheIOVt5LiI I IOr. 11

inc1~ded

^.the

u~pliol 'of

^{fOllr'statioll'in LakeMelY}ilie Ind one-in

G ro.~~llter

^Dar_

Themost reeeDtBtld trip.iu,the poSl--Cburehill,hydroel~triedmwvmeDt periodwa~

carr ie:d'out in AII&Ust1981~ytheDepartme.b~'or'Fisheri~sa~a ll5aboardtheir ve':lelth~'Burio BI)'.ThepO,itioo~_ortbest at ions sampl edby.theV:u'~OIlS'tx ptd it ioos are ,in o:io Fi,ure1.4.ThedeusiLYprofite,for~tll.L io o,88- -4,DB-7, 8D-52aodnD-·n arepresen tedinFigure1.5aud ,ho":thatItwo-IlIff'tructur~of Lake Md yilletaUbe as,utaedwith'"", _g for the upper lal er and "",- 22ror Ihe lower layft.The~a1io' ity'enusdepthpr06l! ,tFilure 1.01more tln"yshow atwo-layer,truct ure wit bthe ,aliu.ityoftheopperlayer(thetpilimnioo l heinl iutherallge threetohe pm' per thouu ndaudthe "Iinityofrbelowerlarerltbe hypolimuionl brio,iuIheralll e ,weDtyto'weoty-&npartsperIhouSllld.The thiciaeuor theupperlaytrurit'!fro m

.

..

teato tweat ymeten.Forth~study,aDupper!:iyertbicin~,Orlirltt h mel"".ha.

be~o

^takeD.Thebathy met"

or

LakeMtl' iilt

i~ ~howa

^{ia'Filllr: 1.7:}

1.2.Mol!vat1o D ror t-he-Prflaent-St udy

Cil'n lat ioDSiDbod iesoreorera, largea~Lake~fdviU eare lIrlrt:llint"rt.Lfrom_ .__ bot blhe tbeort ti calaad practicalpoiat slIrview.

From a thtoret!n.1poi.at of ,iew,Lake~ltl~:iIte^{i' or}~1I~b^{a siltIbMthe}tltt<" L.'I~r theeartb'srotltlo Dare import lattoit,dyDamiu. blltaltbe sametime aot !arKe

·6-

. . ,....

. ' .

: (

-1-

Sf.TOol '0-02

J..

.

'-.'"

200

AUGUST 1981 AUGUST19:12

bead,1982).

.... .

-8-

~ (lIl)IUdJO

~

.g

i :3

i :3 . j

~

, '~".

:! ..

.;

.~

i

!>

g

-a

i

'0

ii

~ j

.s ..

^<

!

^:;;~

~ II

-\

·9·

.. ·10·

enoughtomtokethe el1'ectsof th'ecu" ature ofthe earth',,unate and tbevariation or tbeCorioUspara mel.erwith

latitud~impo~aDt

^{ractors .'In}

ad~ition, ~e

^{lake i,alm05t}

detac hed from theIt a hut .till has'a twoola)(er,a1illitl anddell,it,.., tr ucture.Other

"

^{\- .}

^{. .}

modellin,

ot

wiod-drivell cireul,ation"es~eeiallyin theGreatLakes,eo uaidered thermal ,trati6.cati on only,hut Lake Melvillei,elsestronglysalinity ,tratI6ed.It wa,i~te.re't.

ingtosee the eft"eet or't ron ~,t ratification,on simulations eleeem~e1,were gellu al}y. adapted rrom theGreat Lake;w~~k .

Onth~ praetk~lsi.de, a,tu~yo( circulation in'Lake.:.1~~Yillecanhelp-ilMbe-

.ceono~ic

develcpmeut cir

th'earea'~Dd a,;'?,iatcdo.~aYigllo;tional .pr;bl~in'

^{into theinland}

." \Labrad or-communitiesorNorthwe,t Riverand0005"C Bay:

~tb

illdustri al

de:,ei~pmellt c'un~ntly 'takiDg~lace

in thi, area,'Port

Labta~bein"

^{planned to', ervicesuch}

. , . - i ' ..

developmeot,.For thi, particular lake, modellinlcaD helptoebedlilht iuthi,data-poor at'eaby,ul gesti ngimporta-otcirculationfeat ure,~odbelp plan,6e1d program,(see Cha pter6 )..

The con,tr uction of the hydroell"ct ric,devdo pIDl"ot~ftbe~hurchillRive~began'in 10 67and was com pletcd in1071.A, aj, uh , hundreds

~(exi,ting

^lakesand

~

^..undrcd,

ofsqu&re'ki!ometcraorbog and,mu,kegwerelinkedto Cormlhe SmallwoodReservo", --"-

tra m wh1eh wateri,releasedthrough various control ,y, tems.TheieeeeeseindrailJ.a~. arearesultedin an increa, id andregula tedfr~'hwattrinDow into I.alc,e'Me!ville,Thi, laeeeese intruhwaterinputha'tbe pote ntialrorchallgiog the'waterpropertie~orthi,.' leebere waterma,u'andlocal lhhermen·have rorecraetime'rclt thatthe decreaseio cod6'h3loehin the

r~gion

^aleee1071

m~y.

^hedu,c in part to thl, hydroelectcicdevelop-

. " . I '

m~ot(Bobbit andAkcDllead,1082).Fur t herbydr,oclect.ri~de~,e1opmcntinthi,ereacould intro ducc Ireatcrch3ngesint~e^waterprdperti."orLake~ielvillc.^'Inndditio~tb~^ror- mal ionoficcin thelakedepeede

~t

leL'lt in'partulJ,? 0ihe.wlaterpl'Opert.,ln -Rod 'a cha uge in'uehpro~rtkf'^{or Llike}~elvil1e^wou'ldp~b3b1y^cballgethc patt erps or,

~

fret'llC>up andaffect wintersca:lon oav.igatio n.

,.

./ 7'--/;

\

The tum'fjord'isappliedto an·ClI tU ll.f)'Jr1.0inlet that bu'steep ,id clI.-a-deep"

.

- ^{. .}

": . b~inandasmat themout h,",hb~ lIaliDit~distributi onaffected bya rat herIball ow surfac elayerwhich is appreeia blydiluted byfusbwate r runolf.Belowthislayer, .the . horiwotaland

t~e

vertica l .salinity

gradic~tll

^{arcsma';,'Siueel.ake'Melville}

·.'tII~~al\Y'"

lIatisfi~^the,lIt! criteriaquitereadily,!ome or.iU'.circulatioo·rcllturcs mI.,. be~:~il (\r^to .Il

'

. .

-u-, . ^...

^.

^{. /} ~ ^~

".1.3,GeneralFAdon orCI..c~l.UoD \

\

(

'-

1"'\'

hallie fjor d (eaturell.

Estua rinecireulat;oD

i~

^{determined-bythe.}

rrcll~ .~lcr iD~O"

^and

the ':Dilli;g~~ii.h

sU 1!..at crinllucDt ed by~idalcurrents.Itisappanot(e.g..Kt;tcbum.1951;Pickard~nd^.j.

. ~ ~ " .

Rodge,::,'195~)thatthe·....ind~aDb:J.v.eanilD. pqrta.~tin8uent e 0:drtul:\tioD.~ll,d,miliinK as well•.Byexenin~st rns on thesurfa ce or the lake, thewindas ao l'xteroal for t e,

.

.

^'

.

can prod uce anettrao~portorwate~andthewavu generatedwillincrease theioten~ityI

of verticalmixing.T~~~atertnnsport intbesutf~elayerwillbemainly7n tht dir: c:

. ' . . . .

tiono(thewind and hecee,the norma lseawardBow willbe iocre.a5tdi(the winaiii::

blowing5ei",'ard5alongtheestuary.TheBdw.iIIbedecreased~rin someC:k!II'S,

"

.

.

.

rev~r5edilldirecliopifthe wiodhlow5int~eopposite direction along thee~"",rr,

External

(orc~, whi~h

^eaesewater·lD. o vemen; , in

lak~,

^cODsisto( chtlflge,in,al.iD4:"

,phericpressur e at the lake.surla c:, thegravitatiollal Ic rees ortile sun and t,h..-moon thatgener at e tide5,andorinternthe"re,tbewind oraircurrent!blowinKcvee thr.l ake, Althou gh the fir;t threeof.t heabovementiqlledf~ton^.'i1100\beco~id('fr.1

in

t.hi~

,

,

. ,,'

5tudy,theirimport anceininB,uroci ng circ ulat ionrelativ e 10~e'tI'~~_~~n dr~Dd~o'n eachlak e or

ba5i~

^understudy.

A~

^{far asthe tida;}

inB~cnce.from lhc'su~

^and

l~C

^mOOD'

i~eeeeeeeed,itwould appear tbaliti~direct!t-E0port iooalto the....he oftheh",inin qUC5t,on It15difficultto study suchtidal 05clllal lolu In laku smeetbey uhl blt

~~

. ,-' },-

5malltidalmovements io thefirst plaee.Furthe rmore,10 order to.llt°e.urately,deter mine ) _ the?,agol t ude ofthe tr ue tide,It would be occe"ary to,o~eho"l!lJrere~uale.thetid~~ ⁰

~'':: ^{. '}

-

^{, '}

'.. ~~ .

)

(

__12-

o!leillation.Jrom"Utheotherilia.!!f1uetuatioulikein.ternland externalseiche,.~ it tu:u out,the dect oftid"islenerallyD:, lip bleODthecirculat iollpa~tcrtlllin mo,t Ilk" accord inl.t.pHarlemail-;(I96II. However, LakeMelvillemay behave3'en Hclmb olu

~,dllator

(a quarter-wave

r~soDator)

^witb

,igbi~eaDt

^tidalrorciog whicb ceeurs thl'oulJb tberises aedrallsofwaterIcvclt at its eerra eee.There is somedataon :tid .1 levete in thelak e[J.Bobbrtt ,personal communitat ioo)but itW~^DOtavailable tee

tbis study.

--'ny-rar, the mostimport antnternalcurrcnt·generatin grceeeinalak eis thewind.

. .

The .indalJeds the c:irculatioDill two 1II'ay',Fint,the aireur reeteexert a sbearing 'trn;,(the wind 'trc!!) at'theair-wat erinterfaceull sin gthe waterat theinterl aceto

\lo(~e1ente.·Viscous(ridioD,then(!lllSes the watuIllyer,deeper down to gainmOlllcn- tulZl.A,...-ucondcOD3h!ue~ce"lbe wind actioDontbe surlace of,tb ela ke cau"ntbe surface 10 OKillate and produce,travellinlwaves..Tbe v!locity of tbe euereateina lake is relatedtotbt' wiod slressanddoesoot depend00 ibewavei! directly,-bur, sincetbe

.

~~

.

^.

waVt" determin ewbetbertbelake ,urlatei, ,1Zl00tbor rougb, they in8uencethe wind' sl rn, on

tb~

lake sudareand brnc;dect the efficiencywith

wbic~

^{a givenwind pro-}

~ ', ' ,

duceseurre n ts.Whentbe wind blowingoveralaleereaches acert aincrit icalspeed;sur- face waves are'generated.Muok(19.7)h~arrivedat avalueof sevenmeters per seee ed for rbe criticalwind speed.for wiod, hlowiogat a speedof great ertba nseven II1clt'n per second;~ur1ace""avnar~'cfuledaod tbe lake slll'facebecom; shydraulically ro ugh,wb~rcasforspeeds or" Ie!,tbantbi! criticalwind speed tbe!urlace maycon- sider«luslZlootb .

Sleeethewindthat

b10~, _.

^overalake

s~rlact'

t'Xert s a·shea.ring

.. stres,~ tb~ .

^surface

.

.oftbewalt'f,tbedctermina'tion~rtbt',bt'aring'st~nTfrom.observt'd "Indvclocitic!

\" blLS

b~eo

undertakenby

~

lar genumber of rest'&tcbt'n.

~IOllt invtstilato~

beve

,c~~ :­

rlud t'd tbat tbt'wind sirenva ries as 'somt'pOWt'f of,tbt'windVt'1~dlyrelativeto tbe

\watt'f

.~d

I, ,in n hy, .

...-'

~1 3~

U·I) .

j

at thelake',,"ace.a~dW

n

tbr speed01thr.wiud,10~on:ll.M« 1\\1.aadtbr

.iad5t ~ 5may be .riUrDM

<,

T-C. ,.IW}· (1.1)

Taylor(l9 l Sfdrdured tbatfortllrbul~nt·air,n-2.ad m05trneanbu'!bavf'aJ'Tindat

"the.sa m.eor,imilarYaI\l~5or c.~IOITr~cC'ntob5tryatiouby"Largeand,·o.ndIIORI) conclude'thatt~i5qulldrl!:\ic wind51r~55law i5 quile Ynlitlrormod~rat C'orlIt~n .r;wind ~.

Althoughvalutsrerthedrllg fodficieolCdh~YeuriC'tIalllongdilfC'f'f'Rtre~:UC'bfro,wii"

son(1960)ded ucestbatC.-O.OO;?i,a good value in aeeeedseee wit b tbC'wo'rk'of~('vf'r:tI

.. . . ' .

TtMafchen.A"umiuc,.-0.001I:fam,per('ubiccn tilUet nlllI:tooavera,t' valueforthf'

·..ritteDas

T-::xIO ·W~ ILl)

'I _,

.- /'

..hicbi,,..Ii~for modnaleto stroQl(iocludiulrritica.l)wiodspeeds.llere,Ti~thf'~U~:

facesir';' iDd1.0~persquareeee tleereeandWi,Iht' .iudspeediu ct'Dtilllf'tf'' 'ptr seeee d.Thi, foctDlll;forthe';'i,od,1m,i,to.be1I'OC'dfor the dllr, .oll.oftbi,worl.

In tbi, t.hr,i" o~c,Olllputatiootwill bemadefor,divC';c eot.iod field.luvie~of the f:'lCttbat tbe ,!io'dttTf'~'"00thC'5u~f:'lCeof Lake!\1elvillf'i~duemaiuly totbewt'~tf'r·

linwhich bavelI,tD'ur'bIarll:frsenlethantb;dimeeaionsof tbtlab,auoiformit)'in tllf' xaed y

di~rctioofi'

^ee

3~e~II:'1~e

approximat ion for wind,t;u, where

~~~)'.'tate

^{ri; r u.}

lauc epatlero ll arer~~crTl1td,3lI~ho.oby'fhoandMllr~)'(1070 )..

10I~o~ral, lake tureot stao be separat ediototwo utegories:qU Mi. ! t~adyaed tim e-d e ~nd ~ot.10prac,tice.00!teadycu "~ oUlexi, t io alake beesuaeofthe timeseale of thefacto nthateaasecurreouto vary.However,iti, tr uethattheu.are period, dUliDIwhichthewiodis varyili[~ufficiently!IowlyMIa! topermit a steady-'tate

\, -

..

aoaly!i,.Such aoa~alysispves.nee'to" what auhowo M qUa!i-,teadycumbts. (referredto laterin thiswor k) and is appropri at;if.equilibriumcallbe attailled. The

.

.

!hort~st^periodoscillationsofwater80.are,imple capillarywavu.III deeperpartsof thelake,capillarywavu themselnsarenotsignificant astran 'port~nofwat~r, but' when they reach sb allow areas theychanle character from an~rb ital-ty pemotion to a simpletoand fro motioo.

1•••Scope or thePre.e ntStudy

,

IDthiswork.tbest udy of the wind-ledueedcirculatioodyoamicsof Lake Melville revolve!ar~uDdthreemod~ls:a study-st atehomogeneoU3mod~l, a time-dtl'endent homegeaeousmodeleed a rime-dependenttw()olayer model. A windset- up lastingfor four daysisused torthetillie-dependenthomogeneousmodel and cee ofa single dayfor'

"

.

thetwo-Iaye;model.Typic~lIy,thi, wind period forms a 'tandi ngwave calleda'!~iche' whichdecaysdue.~frictionale~ecuafterthewiodis,witchedoff.

.~--.

wiad-l ndueedcirculatio o in ,ballow, yomogeoeou,basio, i,goven ed by depth uriatioo,withthewatertransport rUD Dinl'inthe directionof the wind io

sha"~w ~as

andagainstthewind indeeperareas.ICsaDady ,

1082).

A,steady-sta te model i! useful beeeuseit i,the easie, fobe'lO impl;ment and. theresultilli: circulationpatterolives a good iducf tbe mean dyoamic state ofthe lakeillresponsetcbbea!erage wind regime.

Becausetbe,windvelocityvarie,MllDewbat00a day to day basis,itispossibletbat attady ••tat eis DOtalwan ~e~ h ed ,thoul buponaclose'examinationtheelimatologinl .aod oCCJl,nog rapbitrecordsusually sbowquite'COll,istClltmunwiod compOllcnts ead

/

•

-15-

Homogtlleous time-dependtllt circulalion mooels are also all'«ltd 5tronsly by the bathymetry,and are probablymo~realistictbans~tady-stateones. Alt houSb applin- bleto mallY la1r.n (especially the GrnL La!:") during the late tall, iee Iree periodsin

",inLer andtat ly spring, tbeee rj-pes or modelsanthe nu tuep up iDterms orrc m plex- ity.

A tWl>l:l.yer modelor LakeMelvilleis by far, the mostreali~ti eoneecueideeed here,eed else the m05t difficult alit to implement.,Sincerirtul~tionill 5tratiRcd bMin is affcCLedbythe presenceof internalwavnlike Kelvinwavn alonphore and stnndins. Poincare waves offsbore (Simons, 1080)"ce.rtainbumeriuli~!ta.bilitie5tanbe Indeeed wbicheaueeadegree or uncert aintyin thesimulat ion,

1.&,Reaultuttbo Work

Thereis a largeamount or coo5i5tfllCYin tbe rn u lt5 or the homogeneousmodelsof Lake Melville:A,

i~

sbo"'l1in ehapten three and four, the circulationpattern

re,ulti~p; t

from tbe;,t eady-st a teand time-deptlldentsimulati ODs,of'the homogeneous model :l.pptan to bein agreement wit b the physin or tbeproblem~tnd.The homogellfO':" /

• . I

,models are,very sensit ive to the botLom stress,pcci6c3t ions an the topography ,(:l.r:;

tonwbicb appear tobethe mostimport3Dt indeterm~niog circulat io npalleru~i"o"~

homcgeuecuslekea.

Tbe two-layermodel or Lake MelVille.dbeussedin chapterfive i, by rar,tbe most realisticODt. The simulations indieate that tb.e_ba~clinictll"ect sto~allydominate tbe dyoll;minor the 5ystim,.The elIeChof the tOPDsraphyof the lakeappeal'to

II;

'mall in determining thcfba.racteri5iit, oft be(utrtll t , in mo,tof the lak e:

hi,probableth at ill view of tbe la.elr. of eurreermea'u~meDtifrom the &lea, nOlle of the model, un heralib ralt da~tu.ntel'ytIlouSb to reprtHntthe masnitude of the

-16-

cunnls (ou odat~arioU5poiDt!io tbe lake.Themai o obje1:ti'torthi,thesisat tbis tilDe therefore,i.todewo r minttbe cireulat ioopatternrOtLab MelTilleby \PiD!hom~

it Oto!U,lidt.~I" ermodeb la dma keaDa1ttm~tlodeducetbeappro ximate ordtr

o r

- mal oiLudeortbeCUl1TO~tbal. malberO~ Ddthert.

.'

·'i.

CHAPTER. ,THEHYD RODYN AMIC ALEQ UATION S

OF MOTIONAND CONTINU ITY

2:1•.Gener a lEquUfo n.fo rBarotropl~Mo de l. -

• Therollo ~i D gequationsdesenbetbe -time-averagedturbulent-motionorl\1"'attr bOdy00arot at ing eart h(PrGudman.1953;Ddant.1961)

whereII, V and" arethevd o city component'in the x, y and~'dircrtiob~rr~pt'rtiv('ly with.xpos~tiveCasl W3 r<h,y positive"oorl h'nrdsandl;po,iti~('upward'andUfOnrrhe SUrfllCCorthe lake;tisthetime :pi~the10(31pr('~,urc:fis rbeCo~ioli'parameter : pis the8uid deDllity:k isthe verueeteddy viseeeity ;Iti,the acrt!e ratioQ due to

#

gravity;Aisthethe horboD-ta leddy

vi,(o.(iDde~nd(,llt O~,iLiool

^{and '172is the}

"' .

' .

'. ,

t"l'o-d imeo' ion al l.ap laciao. Byc'on,ideringthe waterinthe.bMinto be inromprr"ibll', we usetbeco nt ibui ~yeqaattcn ibtberor lb

/

--18-

12.4)

; '

laltbeb,.dro,~alicapproxilllaUoD applin,

'l b) tbe wavelfartluort hematioDaN!larlecompued...t iwlaeavtraredepth so

tbattbe verticalacceltn.~iollSanamall it hi, follo.,-fromCa )abovc},'

(el the-ooll·linr :ir.accelerative-tu m,a~,mallt.e."t heRo"byDumber

a.

-c

~(seeSimo ns(1980).Pl.~J ,

ld) tbeCorio~i':~lIra~cterandthe horiwotalaDdv~rtiuledd y viiKo,i tinare-.

COD'ta'DtOvti'i~.f3.k.t.

simplifiesC'qu:lolion(2.1) to1'2.~)to

(2051

lUI

l'l·il

.r:

(2.8)

whr~ttbeDoo-lille3.fud theboriloo b ldiffusivetu m,havebeeeeegleeted.These df'5(ribe mot ioo in tbrborizolli alpl~Dc :~lYi~'ll'C,imp lirytqu~tioD-12.3)~thebyd""~

tat ic'ap p":ximati oD.(~uatiOIl^(2.8))~bicb^{nqui ,,"obly t ht} ~«

•.

IOtr-KT;2otiollof ... fqllat iob12.8)illthe~ertinl

Ii ,,,,

abcxprn5io.1lrorthe treenrrxepeessueeas

p(KJ ,t) - p.IKJ.t)+1'1111-'1

r

lUI

.heref.(X".. I)istbe"atm~pberic.•prns llle 20t tbeai,,'aU,iolur.:t.C" r-andIJi'tbrsur- rac!elevatioll.

i":

. , . .

" t.~.)-

L"d'. h.tu')-:L" d a ,

tbccomponellt",ortbc"crtically iotceratc d "flod ty ;lo$

aDdthrcom polH'Dt,of,tfTUatabonloot&!,urracriU

1:!.I 0)

1:1.111

(:1.1:1)

.IfwedillcfTotimcquatioD(V~ ).itbrnpC(ttotbcspatial coordilluu,.".r-I;r-llb..

"

form,

r

c

"bicbcan beU5rdto repleee thep,eu~ictcrm rrom rqualioas(2.S)and12.01.

f':'.

-'20-

Ifweiotegrauequation,(2.5)to 12,7)inthe vertical(~eSimon,(1980),pg.13)' andusetbe deliniLioo,(2,11Jand (2,12),we get theequa t iOIDI ofvolumetra nsport

(2.14)

,( U S)

(Uli)

aflerusingthein'comp ressibilit y condition,Thedeepwaterassumption

1l+Il""H

is used:ISwell.Interms ofthe depthavera gedcurrent,equa t ions (2.14)to ('l,lli) beeeme

!!

+

(U --I~+~ - 'T~111

tiL iJy .pH pH

('l.17)

(2.181

('l.19)

As indicatedin section L3,t.be surface,tres,i,computedilleeeeedeeeewiththe qua- .~' draticdrasllw, equ at ion (tAltee alltbree modelsconsideredhere.The bottom ,t ress

~

.-'

-21-

.rollo.,trop!the c:ogYclltioDo(Simons (l9ao):Itwe ue depth llonralcd,.eloeitydistri·

bution,rheeit ispossible to write thebottomalms"

~_KM

_{p .}

wherethe various d"igaationsror K are (Simoos,1080)

(3) llonlioear:,K_iiI~I IH',Ii.::::<0.002$

.ir"-

('2.201

Forall model,

o r

Lake"Melville ecualdeeedhere,thelio~l\I'defiaitioD

o r

boltom etreee

. I

WMused only sinceit'11'33establishedrram te,t run,(00<,bown herelthatth$ejreula- uceis relativelyunaffectedby the

~ther

^{bott om,tftU}sptLficatioDs.

a.a.'Gene,,'EqU •• ::.rot.be B ..

ndl~le

^Mndel

^I

. The equatioD5or bydrodyumicsrora two-layertime,.depe od cntsyst emrollowtro m .eqaetic ue (2.5)to ('2.7). Let 11aDd II'-denotethe

d~'p!h"or

^the.upperand tbe lower"

laycra resp ectively eed ,"ume that the dCllSitiesere(OD,t,n1in eeehlaytr.The hor- izoDt alpressuregradieDt!:uoe110'

un~fo~1Il

withill each13rlet:lndare givenby

VP-PSVII. vp^l-PIVII'-II -, ,,Vb . lUI)

.... .wherethe ueprimed aadtheprimt'dqu.aDtitie!pertai to the upper aDd the lower

layel"llrespeC'tivelf' Itfolio"'!rrow equatioD.s (2. S) to (2.8) tbattbev-ert1eallyaver- 'agedeqUatiOM for the up perlayer [theepiliwo.ioo.)are

(2.22)

. ' (2.23)

(2.2~I.

and tbeequatiOn!fortbelower layer [tb ehypolimD.i~o)are

(2·" 1

(2.201

(2.27)

wbere tbeiot erf'acialandtbebottomerressC'oelJieient!eregivento afil"llt approximation by (Beonett, IQ78)

<.

12.281

{2.2QI

..

-23-

reJp~t i Yel,..Inorder to Jimplifythe allaly, is;it has beee MSumed th&ttbe!.urfaf'f'and .t heint erfacedb plact men tJ'lIaod.'1' aresmall compared'to bothdepthJ baed b' ')

such that the approximatiolls

b'

+.,.

^::o<b'...

hold feiu ooabl,. weil

i~

accordanc ewith deep wate rtbeo;":

2.3••Finite'Dlffere neeForm•.ofDe riva t ives

Fillitedifferellc~1I.PP~xim1l.tion,to the deriv atives were used tosolve theequcvioas ofJ~tio us2.1and 2.2numerically.Thue,the equat jons werereducedto theirfillite differenceformJ consist ing of astandard'fjl'e-pointreprt Jf'ol1l.tion ofthederiYatins wbichfollow fromthf'Tuylcr Ser iesexpan, iolls (S mith,1005)

(2.30) (2.31)

(

The centr al differenceapproxim a~,ontothespa t ialderivative'11"33obta ined by slIb t ra rt·

ing NtuationI 2.31)(romequat io n 12.30) wit h theres ult

!"'"

Rurra ngemf'lIh ofe(ju1l.liollS1'2.010 ) and

.

(VB) ylelded-t beforwardaud hckw"rd

-24- dill'ercoce,cbemes.,ivcDby

(2.33)9'

(2.34)

" ,. ,

respectively.Thcse approximation!h~vean errorterm _.b.ichis an orderor.:111; higher t.hiDt~e ce~traldi8'ereDce approximatioll! ortquatioD(2:32 )•.

A~oximatloll!

^toeeeced-eeder derivativesrollow by

addill~

cquatioDs (2.30) and

. .

^{' .}

.

^~

.

":"'-'(2:31)eadsolviD(rortbe term~xl wit h the ftsultiD(eX" ftnioli

rI

~

^-

(.:1~13

^{(F(x+'.:1x)-2F(x,+Fjx-.:1xll (2.35)}

"'-.

...

; ^{' ,) ."}

Tbe time derivativeswere evaluatedsimilarly rorec rnputa t jonalpurpcees.Foruueeei•.

calstability, dj8'ereDtdilJercocillgeebemeawereused aoa the,relevaqt.5cbem~~willbe Doted as they occur.

.~

\

"

'.<

, -25-

" ^\

~~".C~PTER3I THEST~ADY.STATEMODEL'OF

LAKE MELVILLE

3.1.De'rlv_tloDotth; StreamFu nftloQEqu'at lon

' . ' "

Forth~stea.dy.'statemodel, DO time-d,epeadelltteflDs'are~~llilled\'Dthe,'tqu~tioll:S:• orvo]tJ;;etrillaport(2,14);0(2.161 IRam miIlXandh:o 'll'alik,.

1 980~

·'II'h iCh:uo. lnoeo llle··

.~

lJ TCo) .TCoj

_r~t"l.__gH...2..+~_....!:....

II< , , (3.1)

\

rM(Or:" J'IH~ '+ T:~l

c

Tb171

< ' .

^~(3.2)

8M(ol 8110tJl

~'+"'"Ji'"-~r:.

.. .

~

i9'...bich rberigid.lidappr~J{imation.is"inmr~aleeetb~·tUnr:drprlldellttr.~;

'*

^nil_.

isbesrrom equa.lioll(3.3). , _. ' ', ~ ' "

:rbe

'spedG~alions

^{Jsrd rOfthe'll'iud,}

stfe~s

^f.::lld.l.he

'bottom', st~" ^{1 \} ·lU'~. lllI

gtvr nby f'qu3t iou(1,3) and ('l.20 1respectivet,..

l\ .'

Sincethe cOlll inuiLyequation(3:3:1 require,'thatlbe diverl!:eaeeor thelIet'horiloll~

t'alvolumeBux vanish"MI» andt-t\11e3D berepresellte(l iD termsot..stream tUDetioll' t(lI,y )suchthllo t

\

,.

•

·26·

(3.41

.

,~

Equat ions (3.4)were usedtoeliminat e M-) andM'-"J (rom'equations (3.J )~ (3.3).

Mtercross·dillert ntillt iog~Ua.tiOD~(3.!) and (3.2) and eliminating the'Iterm s,an ..~uatioDrepresen tingthe sln dy-st at e dynamicsofLake~e1vi1leand incorporatin gthe Hourbouomstressformul ation(equ.atioD (2.20))wa,.,arrived atatterusing the eon- tinuiyequetieu13.~)(Simoo"1980)a

where

13.7)

In('q~lIotion13.5)abov t;,thela.titudinal variat ioninthe Ccrlells parameter (,h'en by

'.buWD

-iglttttd.

^Itispouible

't~

^{do thi,}if ,b'c bor izoot al

~im('nsioo, ^{o r} ~

^{la ke'are}

muchsmalle; th:t.Dtberadius of the('i\rlb (Rooand Murty,1910) "bit his theease with

\ , .

..

TheeO~pODtDt'o~theveloeil)'fieldare eompu t edbyusiorthede6,oitioDS

"' ....

^13.81

.0

-27-

The..ind lIlru" ford ng

C

00theright haod ,ideor equation(3 .&)ap ~ a.niotbe r~rmor tbreeseparateterms.Thefin~tum00the rightband side.III (Qrlt,l.i, tbe vertic:al component01'CurlT, anddepends00lbecurlor rbe ..ledMreufield._The la,t t..oterm! ontheril!:bthand,ide7Ji-'T,t'laDd.;*'T.l1'lde~ndn~oLiallyOD thebot to m configu ra t ion or.th:basin and ma.y~rd elTe\to :;u tfle....boUo~\~!~peeempceem". staeethe problem at bandis linear interms'lr the str eamfunr tio Q

t.:

^{itmay he}

expresse das

r

(:\.0)

..here

~~

^i!

th~ront~ibuli~'n _..

·rrom tbe cur lofthe win(6;i d:'and

_">,

·'tltili the

cO~Lribution

from thebot t omelope part,Tberecan be ot4er fac lon.cont ribuLiogito '" eueb3S'pre- e

. _ . I

cipiiation.evaporat ion anddrainage eom pouect s .Such facLol"! will be'oel letted for the durati on ofthis work.

The appro priate boundary eonditioos followfromrberequirementthat theLotal tra.n!~t'ncr mal to the bounda ry01'the,perimeter of rbe lake vanis h lPedloslc.l'. IV70 1·

Tbi!

~dition

^of00 oo r mal.tra n5portimplie5 that... isacoo!lan t,or

<, i'{x,y)- O

\

.

on the bcuud aej-.

3.2.Metbod or Solution

l

^{Intbest eady}stat e st ream function equation (3 .05)

\

H~

^-r,

[~V~l

^{+tJ(IU J-}

.~T,C'I _ ~T,IJI

^{+!IlCurl'1'.1".}

the lut tum 00. tbe right handsidevanbhn for,.cou ta nt wind.treutha tillesed in

-28~

.all the simuJati oo!iotllis paptr. UsiDJ tile IiD!'arformulatiooof tlie bottom stress Cot!iCKotK

.

[seeKdio....2.11.we may write the lint tum

^.

of the leftb....dside of equa- t.ioa(3.")a.s

Equtioll 13..81~ow ~omts •

~ t · 8UTf.l 8H Till

Q~"-ij"QII.V'"+ -;J(II."'I- 8;.-;--

Ui"7'

13.10'

I~i '

Arter multip\yilllthrouSh bythesquareofthe aridspatioSIfJaDdexpending tbeJat'o-.

bia... tUIIlSend('oUtetias'tht·¥a.rioluteu lIs , .eeed upwit h the.form

/ ' ,

(-V:+ - 1-k6~ + r~~1~6-

~ - 1 ~6~ - t;~J~6

+

.f*t. trl- f~T.U' -

^o.

Itwedefio~tbe rollo. iog,

13.12)

t~.1 3J

. ^..

FI_.,I_

.f1tT. 111- ~PJ;T.I'l

'b" "'±'~3'12'

^m

~ ,.!;

nee ,m,, ;...',M

"

-29-

P v + - CCII,Y) 16~1

^{- DOII,y}}

16~1

⁺F'1l.7 l - o. 13.HI'

The pid used for

~omputatioo.,

^{inthi, modeli, •}single-leujeesymmttrinl

p~d ~re

Ra mmins andKowalik (1980),paleItS}, Alt houghit i, tODVeotionll1touse eeewel differellt n inna1 u ati n l su~ hequat ions, tbeae ortugive poor ecuvergeaees.In equetjcn (3.1-41,termslikeCelll,y) andDOll,, )seem to act like adveetioDtermslT ,J , Simon', pel'3Qul commu nicaliofl)andconvention al finitedifferenceeebemeeare oheniudequate in dellinl withtbeadye~lionor variable,thathave '.teepgradients, Tberefore,to belp tb'e.30lulionconverge,suchterms or equation(3.12')are treatedas rollowsintbe finite difference schemej

. . .

fOICClx,y )>0; 68 ; - +II,JI-+11.J- 1)

.. .

forCC{x-,y)<0;6a;-- +(I,J+II -+(I,J)

... 8 ""

tor OD(x,11~0;6-;;;"",'i'(T,J) -+ll-I,J)

tor DO(x,YI<0;6~_+11+t.Jl-+(I,J)

"where6"'S thf pid .!Ipacilll IUlliformin.botb theIIand )-

di~tion,)

andland J are tbe

spatialcoordinates in tbe ,eed x directionresp«t ivel,in tbe BTid,The otbu' deriv..

tivea wen: evaluatedUSinlceotraldiffereoce, andthe ecevergeaeew~eased by tbe pro- cess

ot

successivecvee-relsxeueeof the finile differencescheme (Simoo'"ItlBO),.

,

/

1.3.TheIop u\ Data

The

ba~h1metric/d.t.

^{ror'LakeMelvillewereobt aio'tdfrom Caudill!Hydro-}

Vapbte:Ser't'te:tchart.D';m~r5142 with~a1e1:100000.A'"~of mnh eieelotieeeueee- ttl'ScOI'l'"poodiolto • spuiOl of 1.833k:OIUctCrs 'II'as draWl!o'l', rthe cban~Ild.t~e dept hsf\,readOB"I 'all theilltuiorpoiolllofthelake. At tbebouodarylidlaa d poiOl!,HIJ . u Id equalto uro udthe lImallrslilld,atthelIol'\heasufD eedofthe lakewered('let~.,1.0ord~rto tlimiDIt.e(amp ul.tioaalinstabilities that~ill:htann r~om,hallowdepth!,',biDtbedoma inoriot.erntioll••11depthsthat .. ere~.tertba o letll,but 1t'U hiDt•Dly.five mdenwere~t^filualt~t.ell~1·11vt^meten.The.bol~

depth profile{Oll jeeee ted iuFis ure 1.1I'tl'a"tbeD 'll1oothed byusinsthe tor mula(Rao.

Thj~

,.-

proced ureleh moslor thl' rkpt hsOVl'r lhl' lakl'relativtl l Ulllll'ttttd.

.

Thl';moot htd.dt pl h prolilt or LabMelville ;,CivtD.in Ficun3~1aDdhasICOD_. louriou-rva!ortWtnll mdtn.The-dt'e-pnt part orthtlabisintheIlort bt asu-r llIt t-

..

po HIJ";'1"1J+1+HIJ-I+H"I-I"+H~IJ+.utI")/8. (3.1.5)

•

'ioD, wher l'utbe sballowntpar1.is·ontbl' wn u rnside.The dept b cradient.5 anmucb -create ralollCthe-northustull lowershortthanaDywhereelse,

lId

in ract tbe whole Ilortbe:u ler llbalrortbe Jake is quite deepwit b some dept h,ucetd iDl200 meten:It willbe

sbo~hat

^suchade°ptbprolilt."extfts a stro Dl ill8uellce OD

~be

eircula tiollpal_

~... '!':-....

. .

--

. 1 I

I

I

I·

·31·

).

J ....Tb.

R.~It.a

^or

&~

^{Mode l}

M~eoro&orieal.dat~^{'or tbeperiod19S5to1930'rom.GOO!lC!8a,}A~~I'\ io~itate thac.the&' 0mottcomPlOD';"'incb antbe.~wrlitsand the soutb.nl.erlin.10yit .of• theanilable meteorolOtin ldata,a.illdspeedofKyeDmetenper seeeedc~rrc:spolldine

. ;

to.iod'tm,.o( aboutoned'Deptr:tqulll"eccn~imeur.~chosen(oraWt be ,imul..- tiolP.

Fisure3.2sbo.stbe ,trea m 'uoctioD'cootGun for a !Out h' dterl(.indaodFie· . -\ -.

urn

^3.3to

.

'3.Sillustrate tbecireulalioll paUera.for

.

a.nterl,.iod.F~rthelaUleTalue

lofthe bottomstresscocl!icieDtK_0.025'IHtr<:-I,it isapparc~tfromFi(Q~3.2aed

.

. . . ' .

3..4 tha.t~t5et_o _ind,directionssire dxntialJy the same overallcirculationpauUlt. ,/'"

.10 ric.of tbis,a .esterl,~ill?.aschosen for~I~subscquCbtnlctrlatioD..!..

Tbebottom stress coefficientKrallIesio.ralue from0.01IH

»e- '

toO.~IHIIfC-- fOftheGreat L.kcs(Simons, 1980).Avalue~r^0.026

I

trace"'a'cbo:H'D as • rereeeeee

. . "" .

ioorder tosec .bat eflect.ifan,."as created aD thecireulat ioopaUenhydillereDt 1'&111"ofthi, ,kiDcodi cieDI.Asi,tlearTromFieUTcs 3.3to3.S,thedjlJCrcll~^-ulunof Khad 1"irtoal ly 00elfeet 00tbepositi~ooftheurn io La ke Melville,.Jtholllh·a

.

-

Chall~io tbenlueof tbi,bottom stresscocfl'icie ~tdidIfI"e<t thestreamfUllC'tion "alIICS and lance the

C~~Dt

^-ullin

dir«~IY.

^{T.ble-3.1Ibow,-thealI« t}of diRefu l nillnofK

o~the maximumC'~m p ll ~currco t

o.Ol/"

19.00

0.02S/H 14.06

O.OSH 0.37

.Tlble3.1:Muimumvalue ofcurrtnt~a function0'K ID ,iew0' the l.clt orGtld datarrom tbt area,Ip,rtkularnilleofKcab Dotbe deter- mlbed froIDtbesilo lllatioQ'fCS llltsaDd b'Dtt',thepreciH·~'eD.itudeoftbeeUll't'ots -C'~O

..Y .

-33-

\

..

-34-

· ¹

"!

j

"i

t •

~ .; =

~

~ · · _• .z ^{e ~ §}

~ t:

_j

; 'I

t _.. ^{, e ;}

..

_I

..

· ^{' '''} ~

-35-.

r 'I .

1

I

1-

I:

~".

,

'.AI'

, . _..

-36-

lil

, _·.'

~

·

Q

Ii!

i:l

~

·

..

..

Q

~

~

\

^-37-

lIot be tbeprimary concern.However,theseecedvalueinTllblc 3.1(above)tinsmax·

im umCUJTeDt.3ofaDorderormagnitude,imilar-tu"1 liose found intbeGft-at Laic" and maybe the mostapprop riateDOC.

The circu lationpatterneonsi, tsofODemiliac:e

c~VeriDlI:

^mostor

tL

laleeaDdIto smaller gyreinthe westero partwbicb isconsiderab lysmallerthan the maio one.Tbr re

\ _ is alsosome evldeeee ofIIthirdgyr~along the lower shoreofLake MelyillewhichisOM- rowandelongat ed.,T be maingyu rota te,dockwi, eu doe,t~eee e'inthe "ut ern end.

The gyre alollSthelower,horeoftbe lakehuananti·c1ock" i, esenseofrOt :t.tio D.Tbt 1",1e ofGeld~ata_donlIotallowanyverificati~HIofrbeeeresults, however co mmuo itatiooJ withIIloul fishermanindicatestbatthecUJ'~_~~lILakeJ, lel;ille:IUco~i,t~twitb tbel e°l'e!lulh(privat e communicationwit hMr.M.Best].

I Compari, onoCFigure3.1with Figure,3.2to3.5illu, tr ate::ju,t'h07 re,JIIlukahly thest reamlinepatt ern i, deter mined·by tbedepth profileelueetbertlativedi~«tio~^of tbe current, CollowCro m theapprexlm atebeleeeebeweeethe totalgravity force11111'1 duetothe ,ur raceelope aqd the local ",imJ,,trenbeeause rbeCori oli, termi,rdal inl y.

small.steeethelot al gravityIoreels direc t lyproportional totheloeel depttl. it i, small in,ha llow'areas ecm pare dtothewind ,t re"and thele,,-m:us here:toffectedby theume wied"""

;:.~.

^,h••

h>~.w

^{•• ",},.... . "tc h.

;i~h

.. ,h.. Ie deep. "...The

r

cr·

mationor the eeeve rgeeeeanddivergence~O lle,due to theEkm3ntran 'p~r tllear Ihe.

loweraad.rh e'upperahcreere,pecti~elyalsoeenrributeato tbi,.Howeverindeepwaler.

thepr}"ure'gradientdominat esbecause

0 t

tbeCorioli, termbeing,malland areturn 80wi,evident (Figure 3) rwbichis'lty p iullyweakertban tbecoa.stal

e~rttlit':

^Sucha

P~'Utegradientre,ulhabofromIhe~iJJd,etu~,,a~the downwind end or the'lake.a, / wellMrromsome accumulat ions rrom Ekma n't ra n,po rt ,tothe right or thewind lin Ibe non herohemisphere ).Thu'thecur rent,Me.larger aed ill the directionM..the windin"

,ballow areas,but,maller andagaln, t."tbewledin deep water (Figure3J~l"

t '

«: -38 ..

;.

I ] I

I

-}

\

^\

~

^-iii

~

L l i :

' . ^;;

~

11~

f .

.;; .

¹

~

ⁿ

,

e ^.

.~^."

1

^,I~~

~ ^~ :l • i

~ ^. ,

.. ^'j

" ^{. .}

\

y -

.'

-39-

CHAPTER.f, : THE TIME-DEPENDENT BAROTROPIC

MODEL OF LAKE MELVILLE

!

---

~4" 1••Introduction: ",,,..

A

tim~dependent homogelle~WI

model or l.akeitelvil1e is thenut

s~?'.,up- ~D

^terms

orcomplexity and"helpsolle' undeDtan dthetime resPllllseortb~la~easarUDc~iollor

", l •. , ' : ' .'

atmcepherie lorci':lg.For~bisplU'~i~model,~bestr eamCuncti onapproachwas Ieued topreseDt.Dumerical'd tffit-ultles[ikea 'numericaldrilt.'lo,t beGau".Seid~1iterationpro-

I . .,

eed ureused .Inorderto red uc\,sucb errop. a solln,ion basedontbe timeintep'ati~n01

~

the..6nite-dill'erenceforms01tbe

';timiti~e

equ atiollSwas.cbosen ,.Anexa minationor tbe

energe~ics

^{orthe sy5tem}

help~

in id\ntiryilll

tbe'dy~ic ~eehalli5m5 ,uPOD~.ibte ror'~he varia~IbDs

^aed8uetuatioll5

iD,~be la\e~perti" whic~ t~~1

^{us how.nd¥eDthe.model.}

epprcee beastea dy -st ate-.Tbi;mod$ areeesurraeeooe'whichmeaDStbalth esurrace . .wavt3.are:pre,entinlbi:model:;uopposed,to

~be sleiMJ~.stale

^{mode;'orChapter}

~b

^the,arenot.

~I'b/e~uatiollS

^ot,volume

:rau'~~~t

^forSIKh,a

~Om~gellt'Ous'3;.';.

temeregivenby<:quatiolls (2,1-4)to(2.I.ej. ' -, .'

4.2.TotalClrc ui..ttollEnergyror,Homoseneou.Buln•

.Motion5 in lak;, tanbe beuee.displayed if~beamouol01eoerD eeereteed in the '. circulatio nis invesligDted, 10'part icular,tbe3pi o';: up and spin·do,wD

~imu ~Il ~e

deducedfrom t" een~rgj-consideration, and'cutaia buie oscillatioDJ examined. ....

.\

.•.>

•

^·40-

,

The lol;tl potutillltDerC' ill a bomogcoeoU!buill isriveD

by

the ana ioterral ...

i

(4.1)

aDdI-be'tot alkinet

.

iccocrgyis given bythevolum e iDtc

v

(4.2)

The.

to~ tDer~

^{inthe lakemay beeipreuedallthelum}or tbe tot.alkinetieenergy and '\ the totalpOIC'lItialtnergy, 0.l. _

Total~tft[l)'-fAtlJ~ dA+

Ivtl lP

+V~

sv

..• .

^\

^.

whtre.',bur!~trgat,anevaluatednumerically.

•. 3.T.~eMethod erS,olution

!

c•

(4.3)

... -

.,

,

U.1.TheSt aggeredGr id

It .

The-uriablrs'arede6nedODa 'lBurredgrid_reprn cotatoionoftbeRichardson.type andtheir,rela tivepositi oosrercomputationalpurpmuare shownillFigure4.1'.The bydiocl)'Dl\

.

'miul equl t ioDS'ofvolu me lU lIsporl

^. a~e

evaluat edat timesteps TAtwhereT .- O,I .:l,3...and ~listhetiDleetep.For

' be

grid.tbe mesb aleeistakentobethe

Jo,-Joy_~_1,833kilom~tfll

•

. J

. .

^'

-41-

i

^{0 t 0 t 0 t}

^,.

⁰

~ ^{0 t 0 t} 0 t 0

J !

i ^{~ ~}

^{000 -ttt 000 ttt 000 ttt 000}

POSITIVEX- OIRECTION'(EAST)

---:,

^J..t,S2

0"11 poinU

t"M(x)

po!nt~

.""M(Y)..,o.i nt;

(a ) Staggered grid

H{Y)(J,J) H(t,J I,'n{I, J) , U(J,J)and V(I,JIdefi nedat point0 in grid \Quareabove.

- .. ..

Figure4.1:la)tbe51aggeu tlgridr~pre~I'Dt:lliD""Or Y:).ri:lb~~Ib):h~lttid~'I'lar...

.

-42- 4.3.2. The Boundary,and InitialConditions

The windilltW11edOD at time t - 0andthe initial cODditioD'

areused,Sincewe require thatthe component of volumetra ll..! pol11I0r mai to thebcun- d...,.~evani!lhilll,the boundary condition

f;l(l[,!l..~-ooll tbe boUlldary

i,wedfllrallt.

"

• " 4.3.3. NumericalSolution ofthe Equa. ioM

The~

^timestep in this

~odel

i, r.C3tricted

h~

^the

CO\U1lnt~Friedrichs

.Levy criterion whichrtquirn tbat tlie iDequality(SimolU,IGSO)

/

(' A )

\

be aati,fled for numericalstability.For LakeMelville,the

..

la.rl C3 ttime step

,

that un be^. usedi,about (ol1y eeeends.AsamaUer of convenience,Itime ,tepofthirty eeeeeds

r

wa.,,5Cleded. /

Allderivat ives are naluatedhereU,iOIforward differences. The time utrapollt ida...\

• ''' . I ' •

pfO(eedabypredittinlthe 'urface elevation" lint.and then the velocitycomponent!!by

,

.

utili&iDIthe mott reeeet prniou,l y computedvalueof each variable (Simons,IQ82).

.

^'

-43-

4.3.4.'Predict ion oftheSurfaceElevat ion

The fill.ite difference rorm. orthe con tinu ityequaLion(2:UI)113inll:forwud dilrereoce3 i, roundtobe

Rea rrangementorth i3equationyield,tbeIcr m

--¥1~~·~I.J+II·~~·~I.~) +W~I+ I.JI-"~~~I,JlI'

"hicb i,iter ablelnfime.

4.3 .5.Prediet.ice of the~\f~Tran, portComponent,

ThelIlome~tu m~quationinthes-direetic a,equaticn (t.H) unbewriUtll init~

finite-diD'ereoe erorma,

j

•

~l~~·'lI . JI'^+J.._"~·'I.JI'I-lr~111~I.J II' -~1~{I.J- lJ.~(I,JII'+~

-11i:~~·~ I. J)!:JIT.l'"

Upon re:lJ'rao s ement. tbi5equerioa bftome,

~1101(1.J)' +~...!o!I.l(I.JI'+~t[r~t'~l.J ll' +':U~lqU,J-II·llIl.JU'+ ~

.

.1tIK~t·~1.J1I'+

Atl T;'""

r

lUI

. .. -44-

.. ^{(' .}

A!i! clear from Figure4.1,the x eed,

compoD~ot!

of

VOIUlD~

trau ; ort are computed 00the adjacellt eldee of the grid equeee.10ord er to U3t equatioD(4.8),welOut 6.nt computethe 1 CbmPOllentof volumetrall5port.at thesamepoint by using thesimple averagiDc rorm ula

• ^W~I,')~

^-

+1~{l1~I,J~I)

⁺

~~(I

^{+I.J- I )}

, +Ml1^llJ.JI +MlT~ I+ 1,JW

(4.9)

before cllmputingAl he value,of,M'~l dt+Ill.

;he

r com~nent~t 'y~:lDe

^tranion.i, computed in a similar wa,.The Gnite differeneetormpfthe moment um eq uationinthe y-dleeetlee ,equat ion(2.15)i,found to b.

• \

'itrWl(I.Jf+0»._

~~I,JI~I_~ -i r M·~I.Jij'

⁺

~

-~IIl(l-I,JI-llll,JIlI+ ':»'

:"IK~P~I,JW+ IT,ll "

. ' e

Reatrangemt nt oftbi,fquatiolly ielde thl'"form

Ml'~I,JI'+.:».- MU'lll,JI' -~trrM(lIll,JlI'+~

" -~t~i'l(I-l,Jl-ll(I,J)l~+ .u

-~IIK·Ml1~l.JlI~+~IIT.I.J"

- \ (4.10)

(~ . II )

Beeauee the x compo nu tof volume tra ll' porti,evaluated at a differentpointrelativeto

\. the

y

co~ pollellt,¹¹¹¹averaging tormulll or thety p"

,(~.I~l

)

\ '"

-45-

must be used tocompute tbevalue orMJ'~I~l'tobe used in conjuoctionwith eqllltioD.

(4.11)above.

.'

••••Relultl at thll~ime-DCipendllllt-Model

4.4."1. Respcnaeor Lake MelvilletoWind Foreing

I

~

The c.urrentyectordiagrams.olLake Melville&l'esliown

~tPjth~'onset

^{01the willd}

attillle t_ 0to bear iu cut.-of[ alter

.

^. ninety-silthoun in Figute4.2.,The eUtR'lIt'pat-. te~nc10atlyrese iPble;'Figute3.6,especia llyItolllrorty houtS aDd onwarda.Frolll tbe dis- c'ussionipsectio n 3.4.2theo,ill'around ,lortyhou" the modelapprolchusteady.stlte where ;be depth eontoun.~etetill ine.the lIlagoitudeoftheclltfenu . M is'd earfrom -\Ihesefigures, the eireularien patt eee ehaogeslittlethroughout the fordng period.

Curre ntsare simulatedas rUDningdownwindaloDg theup~rand the lower ahoees and uPw,i11din theinterioral thr lake .The;rrspotlSr~f^theeurree u to thewindin the.shal- low reli oDs[l.e,aloog the ,hores)appearstobe laster than the respotlSe ill the deeper areM. For this time-de pendenthomogene?usmodel,-thecurrents nul' the shore (on-

. .

s'.ituti~g^a'(OlUtaljet' phenomena arepart 01wh~^{isknownlU the"}quasi.stat ic resp: nse' ora

~~

Row. This is especially

doinill.~t

eeeetheshore,dlltli g fcre- illg and isdue tothe formationl!.fthe convergenceand diver gencetonu due to Ekman lraDsport .

~nce

^ofthis

i~

found ill Pigutu 4.2(a)to 4.2(d)wherethe

cir~!Iatioll

^pat·

lerll adjusts towindforc ing in the inter ior or the lake[l.e. in the deeper'ah u l later .than it doesin!ballo~areas, ne.arthe fout.

" '.

. ^.

^{,," ' -}

Thcbasiccitc uli l ioll pattei'il cOll!istsoftwo maiDgyresjD,theupperIlld thelowr r part softhe lake . Theuppe~^gyrehas a tlockwj,e!Clue of rotatiollaDdcovenmoltor

r •

.

^'.