Oil Spreading on the Sea

7/31/2019 Oil Spreading on the Sea

1/28

Copyrigh Al ghts eeved

E E E

Maachu Inu f Thlg, ambdge, Maah

T ca f c a ca ra a

crag m ma a rgcmg c. W crag acv a f vma a gwg ccr a argca vrma amag ccrg wg acc r cc ar w ca va ar a mr w ra from r wr ar ca creasng. amage asoate w aca o wr cra vr ra ama am a cagc m fw cag ag. Bm 99 a ma a a am /1 of ee o al rc ra.

T gg arc cr a mva a cg a - acc a c W c a cr

a a mma m w ra wa a wr w g a gv m. Frrmr a ol tmia ad oo ol ri, attto hou b ve to vrma aar A wg wr g afr a ara cv a gv m m a a gg c ccrg m ag w crm

g r c f m ccg cracmm am T r a a c cc a a f an ck ma ama vw a cm

f w a cg cvc w a crra c ca aa f c f ra cam war

w ma ma argug a arr aw a war ac arma am ar a war w v m ac (a mr)av war rac r

PalrC,.aiUwnd = PH0C,H0U2ate

g

byUniversidadeFederaldoEspiritoSantoon05/15/12.

Forpersonaluseonly.


2/28

42 HOUL

ur assumpi implies at Cu C e it llws tat te rivelcity i te water is apprximately

P

r

Uw Uid 0.0 UwP We suppse a placig il a e aiwae ierace es t cage isresult is result is w t be csiset wit b abratry stuiesHiy & late 966, Brie 90 ver a 104 actr Reyls umbersbase waer ep wi spee, a iemaic viscsity e waera el bservatis Huges 1956 mit 196 e rit ue t tialcurrets is simply ae be te curret velcity. We bt wiriecurres a tial currets are prese it is suppse tat te w vectr

velcities simply a e ceer mass e il is tus suppse t mveaccrig a equati

= ur 005

were is te criae te ceer mass te il

(3)

e rit ue t wi-rive waes i quati 3 s presumably accute r i e term 0.035Uwd ere wul be aitial terms tatsul be iclue i waves but wi were preset suc a circumstac

e curret ca miy te waeel a, agai tis eect sul be iclue. But rm a practical pi view mst circumsaces i wic teil slic is grealy isplace amut eier srg wis a wea curresr example we a gale blws a sre il slic a beac r relaively strg tial cures as we a il slic is carrie u a arbrby te ugi ie.

urbule wis a curres i e ceas isperse as well as cvectparticles on te surface. It s expectd tat the large the ol ck, te morerapi tis ispersal is ue te results icars tmmel 1949 ur iscussi, tis ispersig ee is igre, because r a large spillat least up t times e rer a ew ays, te eects suc ispersalare muc slwer ta e teecy te il t sprea by itsel

We sall see i a mme tat tere are seeral pases il-slic spreaig, e rst beig a balace betwee ieria a gravity. accepig Equai e mig wer i e presece waves sul a least aect espreaig rae i tis rs pase. is questi is ureslve at te preseime, bu ere are reass believe ta suc a eect wul be smallirs, e verical accelerai ue waves is a ms 16 g; erwise, ewaves brea ppe 1966 ls, cea waves are early periic s at te

il is subject t a cyclic accelerati a ecelerai ue waves. erst apprimati we wul epect e il ave a early periic respset tis rcig ucti e becas te vertical accelerati s small w

Annu.Rev.FluidMech.1972.4:341368.Downloadedfromwww.annualreviews.org

byU

niversidadeFederaldoEspirito

Santoon05/15/12.

Forpersonaluseonly.


3/28

OIL PREADIN ON HE EA 343

mig expec a correspondng sma mdcaon n e moon To angete rate of spreadng apprecay woud seem o requre a cumuatve, secondorder eect, o sze 1/6)2

Wh hs dsusson we sha aep Euaon (3 and assume ha n

are onaned e ees of wnds waves and urrens e dea hen s odevelop a heory or how ol spreads n calm waer n order o predc henrease n area wh me of an o sc hs as was rs dea wh n aema wa b Fa 99 1971

In hs nroduon we sha dere how Fa deveopd order-omagnude emaes of he rae o pread of an o ck cam aer Laerecons w sho a ere re smlry souos he euaons ofmoon a predct e same resus Before dscussng a's resus smporan o reognze ta rtua a o scs are ue n typcal

on the order of 1/ nh or less n thcness s s hness aways muhess an e horontal sze of he sl or he waveengh of he wavesunderneah t s an eceen approxmaton to consder e o o e nhdrosatc eurum n he vetca

Another eneral dea s that he proeres o the o vary wth me hemos mporan ause of s varaon s he evaporaon o he lgher omponens o the o no the ar oer 1964 Hou e a1970) Oher ausesare dsouon of he oue omonens no sea waer Fa 171 and ehanges wroug y ologa degradaon Zoe hese hanges alend o mae he o densr and more scous here s also a cange n he

ne spreadng oecen due o surae ensonCrude o a mure of a vey are nume of omponens eah wh

s own proeres Wen s mure s modeed y a snge omponenud of onsan properes, a numer of appromaons are made learyhe process agng due to the causes mentoned aoe s ned s tederen omponens generall have ue deren spreadng coecentsdue o surace enson, n a regme wher he suracetenso eecs aremporan a u mode ma e a rather poor descrpon o e deals ohe ow

Fa assumes a u mode wh ostan properes s a s sep deelopng and undersandng he spreadng poess He denes our asores ha eher ause or reard preadng he o has a dens onghy deren from waer Poi=Pnl-, . Sne he o s n ydrosa eurum n he vera s hness s h, oas a heght haove e mean waer urface smple dosac cacuao hen sowsha tere s a pressure ac

"

(pg.h) 4

e he l pool ae a radus

ta aes wth me

e orce cor

repondn o hs pressure s

(p.)h 5

Annu.R

ev.FluidMech.1972.4:341368

.Downloadedfromwww.annualreviews.org

byU

niversidadeFederaldoEspiritoSantoon05/15/12.

Forpersonaluseonly.


4/28

44 HOULT

f a volum of oil is las fom s inia cs will n o ah moio h o o magi u of h iia m is

(6)

s h oi sis ov h sua of h wa h is a visous ag b h wa on h oil h iscous sss is coninuous a h oilwa ifac owv h oil is much mo viscous ha h wa incthe oi thikess s smalle ha h wa boua a w ca sablishha h voci ain in h oi i h vica icio is ii compa o ha i h wa h is a slu ow in h oil h ain ocu o viscous ag is

(7)

wh v is h wa bounala hinss is h viscosi of hwa an /uac nsio acs a h g o h oil sic h n spaing co

cin is as

w s awa iacia nsion 2 is h oil-wa inaciaso a 3 s h oa aca so h oc u o suacnsion is

(9)which ma b posiiv o naiv pni on h sin of o moscude oils s posve; a pica vu mgh b /m

Assume ha a volume o oi is las a a poi hn coniuiquis

now h vaious oomagniu simas a ompa is la

ha fo long ims wh h oil is v hin a O, h viscous focmu balan h sufac-nsion ocs n his suacnson gim ofspaig quai Equaions 7 a ils a pred lawP4 / / is impoan o no ha in his gim h a o oil spa is ipenden f he volume relesed.

o v sho mes, h siuaio is chag f h wo focs han o a h oi ia s ga bhav as

fo x imsios

whas h vscous ag bhavs as ov h oil s hic ough

Annu.

Rev.FluidMech.1972.4:341368.Downloadedfromwww.annua

lreviews.org

byUniversidadeFederaldoEspirito

Santoon05/15/12.

Forpersonal

useonly.


5/28

PDNG N J2h> pf

12

th ravt trm domat th urato drv or. or th

rtal rm o prad, quat Equato ad ad uEqato 1 yld aothr prad law I fV)1{t/2 (1)

whch hold hold or hort tm provdd Eato 1 mt tallyh val o u]2 tpcally 1 m

or trmdat tm, wh thr 1 bca th tm too loor 11 bca m too hort vald, thr a thrd rm that maybcom mportat. h rm ar w th vcou rtard orc

ratr tha th rtal rtard orc, that , wh < v2 )

bt wh th alty 2 tll mt. th vco rm th prad law drvd rom 7 ad 0

Equato 1 ad ar ay ma rult.

W ha atr that th mp ut act rprt maty

olto to th avr-to ato ubqt cto w dvlopth olto ad compar th thortcal rult wth both laboratoryxprmt ad ld obrvato. h a dco v o why a olc op prad whch a mattr ot arly o wll dtood a thprad law h papr cocld wth th applcato o th rlt topractcal ca

AL AA TR

W codr a ol layr, o thc

hld ovr a calm watr urac

h ol ha a dty f whch a actor o l tha tat o watr.cf typcally o th ordr o /1 w hal rta oy rtordr trm th olow quato

h ol uppod to b o vco that lar h a xclltapproxmato or ow typcally larr tha 20 dcrbd thtroducto th mp that vocty radt th vrcal th o armch tha tho th watr o th rao w am that th olocty dpdt o z th vrtcal drcto

th horzotal vlocty o th ol, th corvao o ma

rr + rn rnUh = r

6

Annu.R



byU


Forpersonaluseonly.


6/28

346 n uaton (1), s th sa oonat, O fo th onmnsonalmoon n a annl, an fo sa of an asmmt ool

assum that th hozontal nt of th ol s muh at than han tat t so ahjar s vw small I ths s tu thn th ol sn hostat ulum n th vtal hus th hht of th ol aovth man wat vl s h an th th low th man wat lvl s(1).

A sml hostat aulaton (Hoult 199) shows that th hozontalfo u to th fat that th ol oats on th wat s

In th ntal san m, ths avtatonal fo alans th

alaton of th ol

n ts uaton onl t lowsto tms n f av n tan Usnontnut, w ma smlf ths uaton to n

u u h-+ u- + gf = 0t r r

9)uatons (1) an (19) shoul b oma wth th uatons of a omssl, olto as f ths s on, t s fon that th moton o th olslk n ths m s analoous to that of a as, ov h nst of thas s assoat wth h, an s fat was onz Aott(19a, ) who stu th small amltu wavs n suh a sstm hwvs is [gh]

H w ons a nt olm. sf th volum of ollas at =O sn ths volm o ol s onsv

= (2r)nhdr = ostat (20)I a asnam analo s ons t mht thouht that suha on las o ol s analoous to a ont loson. In sh a asnamow, th nst os to zo t th on. Hoult & Suhon (1970) st oos suh a soluton, ut as w shall s, th sult s not n amnt wthmnt (Ston 2B)

In at qatons (6 (19, an (20) a nomlt, qn an atonal ouna onton to sf th soluton nul hs fat was

st onz annlo & alman (971), who oos tha thlan of t ol mov touh th wat wth a vlot of [fh]/wh hLB s th thknss of th ol at th lan of th wav.


byU


Santoon05/15/12.

Forpersonaluseonly.


7/28

347

a (1971) su annlo an Walmans ho an hn arguha h ol ang g a an nruon an aorng o von Krmn'(1940) amous alulaon h vlo of h lang g shoul [2gho] h ho h hkns of h ol som an from h langg. Fa ak h o h hknss of h ol a h ogn

= O 21)I oul rogn ha h h of h ouna onon hh

analogous o a RanknHugono laonh n gas nam s nonl la. Bnamn (1968) ha shon ha a sa-sa nruson muala ak so ha a s n gh]2an 2gDh /s ol. Hov n h rn olm h lang g lrang . sSon a h lraon ma un o rla h rag or

rur o salz h av aorng o Bnjamn's alulaonFo h raon w ha u a h ading-dg boundary ondiion

U= ghBI2 22)an hall lav h rmnaon of o rmn (f ha hans o osl)

hs olm ha a smlar soluon of h fom

U= Vt

h ha h orm

g3L23t23= D32

o n = 0 (odiiof n= sec

23)

2)hr a sml a o unrsan

Whn a onan

h ao of o h of h ool h n onn ha our n (2) ar fom

an orofmagnu anal a n (13), fo h o ass.n (23) an (24) L sans fo h lng sal aoa h h volum

rlas {3L= 2 o n= o n 0 25)Uon sutung (23) (24) an (25) no (20) on an rmn h

volum of ol rlas h onsran

26

Annu.R



byU


Forpersonaluseonly.


8/28

34 OULTEquaion (1 coninuiy, bcome

2-n

) H'+(vH' =03+nwhich may be ingraed o gie 2 -

H =3n (27)A 0 0 i ne nc he alue of h onan of neaoni zeo and 2n

28)=3+nI i worhwhile commenng ha h oil lociy n all ow coniddin hi pape beha a conX It independen of he ow regime in queionW hall alo ee h agumn 7 and 2 repead in ubqun cionon he icou and uface-nion rgime of padingo eemne h hicne iuon H we urn o he momnumequain (9) anfom od

H

=

2 -d " 3 n 3 nwhic inegra o giH 2n 2n+" 3 + n 3+n +

29

(30Now K i relad o he ra of prad of ol for i nonero ony in omrange of 0 T hu he conrain may be wrien

[2n 2 -nT

2nTn

K d = 3n 3n 2When h inega i eauaed i i found ha[ '!: 7 2)" K (1+ 2)2 n = 11n 23n (31

Clealy anohe equaion i rquid o pecify K or h purpoe w e22

which pci h yp of wave ha occu a he ladin dge of heoil lick In imilariy aabl hi boundary condiion become2 -n +- T =HT3n 2

Annu.R



byU


Forpersonaluseonly.


9/28

L SPRDING N S

'

PHCEL

OUT

Circu used to lnearze phoce uu.

n the as of one-mensonal sea t an b shown (0) that, fo uaton 2) 7 was o Fanno an Wamans hy, 1m8 19 In a as t san law s

YmAX = 1maxg-l/(3n)L-(2nf(3+n)t+(2-n/(3n)

B

(3)

he st emnts on te ntal san hase wee fom bAbbott (9b) wo sowe tat te lean of an ol slk tavellwth a velo of about [h EP/ that s, wth} 1 owve Abbott stuethe ow nea the ont o lease athe than the eleatn ow fa omth ont o elase whh was sb n Seton

hs latte oblem was th subjet of ements b Suhn (970)an Lan (197) oth mnts w on n a llass tank tw 7 fet lon an 1 oot e Lan measue th ol thknss b ahotoll mtho velo b L (197), shown n ues 1 an h

neal aaement of th aaatus s shown n u .al sults a shown n u 4. ae value th eemntavalu S on m woul sem to b n btte aemnt wth a's sut thanwth annel an almans Howv th stuaton s not so sml

Annu.R

ev.FluidMech.1972.4:341368.Downloadedfromwww.annual

reviews.org

byUniversidadeFederaldoEspiritoS

antoon05/15/12.

Forpersonalu

seonly.


10/28

mFGR cal calbratn cr r a htclllg crcut asmbl.Figure shows a photograph o the eading edge o the wave, as seen

through a gass window at the side o the channe. Figure 6 shows that thehca hkn rss h m th rgn t = thncras bng abut 0 rcnt th alu f th thcknss at th rgn

At = th thcknss ds arut t . al gu

shwsthat th actual wa thcknss dstrutn ars lttl rsmlanc t thsmld thrtcal ctur.Fgur 7 cmas th thrtcal thcknss dstrbutn nrmaldwih th ladngdg lct as a unctn j wth xrmntalrsults hs gur wuld sm t mply that Fay's bundary cndtn(labld 2) s a btr apprxmatn than Fannlp and aldmans (labld. h larg scatr s du t th gular lw surac th lay usng Equation ( dtrmnd th asmmtrc sradng ratto b 1.14

)

FGUR Experena n wh phe sans " X7 and h bef ea


byU


Santoon05/15/12.

Forpersonaluseonly.


11/28

D

I

4 des eh vs dese f ve sed

r = g-l/4L-3/41/2

3

e uue eeene h Fiue shws he neimensnl hinesssbu lule wh F's bud d.

F hs n he lwin sen i i neie nimesiizehe equs s flws is sie uwd):

h = L

y=-,

L

ri=-,

L [g J/ t

L

= / (3)hee e w ew feues f hs w s hee s Renlds umbe

bsed n he ees f we

(gL)I/2Lv (35)

h s ssumed be e R Sed hee s n dd em i hel mmeum equin h eeses he d due he we bude The ndmes mmeum equ hs he fm

Annu.R


reviews.org


antoon05/15/12.

Forpersonalu

seonly.


12/28

32 OULT

FGUR O ck prpgg o ll w a aO hU - fnhU + + h 0at f af R ay af (36)

W now rocd o m h cl o h r grdn Ug qo15 d omon logu w nd h nodmnol rdngw

(37)rom Eqon 10 w hv /( rom o con 1 whv "/(Rl/(Bn). h lcng h vco nd grvol

GUR Tc hck dru fr h - r

Annu.R



byU


Forpersonaluseonly.


13/28

33

< V [

IV I

V [

7.

em in Euion ie he cle of he dien, y"1j2, uggese uion 7) is, f we un o he euions in he we which e he vieSokeseuion, he moion will e of he oundlye pe whee ajaaja,Thi implie OR(5J> To hve he oil inei egligile

compe wh he gvonl vng foce,a jaaia,

This mplest

>OR(3-!(7-4n Hence, he lm pocess i R R5+n)>>OR(n)!(+4n s no supsn h n hs lim poces; fell me ws nonmensonlze wh nel vbles. Snce he vscousegme of speng lws follows he nel eme, s cle h shoul ecome e in he viscous spein eme. See Hou & Suchon1970The we coninu euon eemnes he mnue of he veclveoc n e we,

ne hese ccumsnces, he euons in he we ke he fom

Annu.R



byU


Forpersonaluseonly.


14/28

354 HOULT

a a fnU) + = 0fn af ay

U U U

2u

+u+v= at af ay R ayTh o momnum uaon ha h aoxma fom

1 au ok+hOR ay af

Th ol onnu uaon

ar o

fn +0af at

Fnall h amoun of o la

Th mla oluon n h a a h fom

ft-(?n8l8+4n

Z y/2t12 ftg'z =( + )2t-2Z)

= Hr-nh ounda onon a a a z=O,

y(z = 0 = 0

o( = 0 = the oand a = if h u s at rest far from te ol

g' 0

(38)

(39)

(4

(41)

42

43

4

45

can be sown a e o cnnuty equaon s dencally sasedand i s n a =0 and only

3 ro

"4

Equaon () mples tat

Annu.Rev.FluidMech.1972.4:341368


byU


Santoon05/15/12.

Forpersonaluseonly.


15/28

OL SPREDNG ON THE SE

3g'(O)=-

3

7

h o hon in (43) at th wat ontnty qaton dnta h at ont qaton

+ G ( + + 03

g'(O)

O = 0 g( 0 = 0Wih th ineial ems deleed Euain 6) nw akes he fm

_12Hg"(0)=

H['l-n+1)H]

whh ma ineae yid

H _(0) kw whn 0 the leadn ede o he slik eahed s ha k

J

/ "O

(8)

(9)

andk

s deemined b an u th inean (42 When his is dne s fund ha

= lg(0) f = 0 3//(0) (SO)

At th jnt t ght appa that th na oton to 48opt th pt ov t a hown ot & Shon 1970)that two ot of th th oton of 48 hav =0 and ( Th t happn that 48 do not hav nq ton

It an b hon tat na th adng ede i behaves ash )/ X ui ie 5)Hene he se / nne a th adn d o th k Th podt / has a nie va at th adn d o th k Th p thatth vo t als has a nie value a Sh a sess an be se pnl b a min useam f he leadi ede beause if hee n minin he wae a he leadin ede he veli wuld be ze hee and hesess eihe ze innie. We wuld exe his min exnd useam

a dtan he aeleains in his ein f size ae muhate than th dlaton f th o f z / beause Th

Annu.R


reviews.org


antoon05/15/12.

Forpersonalu

seonly.


16/28

FGUR 8. Sh o h adg dg o h o sc h vscous rg

he w ma be vewe lall as quassea skeh Fue ) henshws ha hee shu be a en f evese w n he buna laewnseam f he lean ee

In fa hs s a unvesa feue f a hsa ssbe suns f48) Furs 9 an 10 shw a numeal slun f 4) f =0 an = wih lue of ") eemne fm eemen ee ein 3.) Theeio o eee ow i.

ea he bunaae he s naabe he en ahea fhe lean ee. u hs n eemnes he nal sess n he Thsss s nal ") We beleve he ean ha he sluns

. 1

GUR h arc vo souo



byU


Santoon05/15/12.

Forpersonaluseonly.


17/28

x

The viscou oluton (one dimensona).

4 ae t el detemed s ta "O) s speed S "O)may not etermne from t onary-ayer ter sll appea texperment to eterne ts vae

Te la ea e leadg edge ll e te same te axsmmt nd oe-dimenion ce oy the eect crvture rem Te it oow tht "O the e ale t -dmesalad axsmm s e t ae O) s dtemd m oedmesal xmt its ae may be e to etermne te preangparameter n te axsmmt ae t way ee Seton 3B t fdtat O) =0.2 an

5x 2

n 0 from experment [om Equato 50]

B

52

Te expemetal med te same as a desed S BHe te wa w imuted wih yeriewter mxe. thia t ss ad eta gms d e sded te same apaas S 90). Fe ss t esls te onemenona

prea o o n te vo-gravtatona regme It een tat = 15.By appropratey oong te voty of te gyernewate mre,te vome of o eeae, an t ze of te tank, Sn ld y e-

Annu.R



byU


Forpersonaluseonly.


18/28

38 HOULT

VISCS SPREADNG

RP 1.5 '

R242719

(in)

22

1

L(in2)

183.6

viyic spreading.

emeta the e f tat fm the eta t u eme

Fue 12 hw thee eut f the edmea ae. me maed wth the etmated tme t the tat

Leth wee maed the etmated dae t the tat t

gL/3T/3The ta ul ha Th babl ue t the athe malhae the dtut that u fm e eme t theext I Fue the theeta the e hw h ehud e maed wth Fue

PG THRY

I th eme the the deeaed that avtata feae e mtat Refe t Equat ) we ee that f iOad the eta tem ae ed the

aUI =0y = (53)hu the w the wate uda ae mut have a waee haate

Annu.R



byU


Forpersonaluseonly.


19/28

OI SPRADING ON TH SA 359

'-

2 Trsin from nertal- ass sead

Thi wake i ae b the ation o a ine oe e to ae tenionThe oent in the bona ae t baane thi o:

.5

hr,

[f 0 f UdYd] maxnt _

ot

.

1.0 1.2FUR eea ness dsbus

fr edesa s spread

(54)

.5

Annu.R


reviews.org


antoon05/15/12.

Forpersonalu

seonly.


20/28

360 HUT

n h o on h o a bow h a n

y ) 0 n aon o h no nb h obl ha an aona

aa an o o h nondnona o o 4) U/pg6L2. How a ha h aa a a o ba h oon nnn o . oan o on ha h a aabha h a o n boh h ax an onnona a

6

Th han ba h a o o a n h nnn oh o o o la

Th qaon o oon a h na bona-a qaon )an 9). Th a oon ha h a o a n Eqaon 4)whh a b oa wn a

= i-1g'(z)v - 1)R-/2-/2g)z yl21

Th whn b no h on qaon

i' + " + ( l ' ') 0

(57)

58Ca h a olon o h ob on n bona onon o h o a

Uon bn h qaon no h o onn qaon w oban a h n a 7=0

g'O)

=! 59

Th o hn bon no n b h bona-a owTh ann bona onon a 5) 55) an no ow hoh

h a:

'(o) =0, "(O) 0, (O) 0 (0)Th an aw n b 54 Th nal a

an ha nal zo o r>max w max=7x(Ut3/pI4,Eqaon 54) bo a h nal a ala

6

In h a h a n bona onon o n h o


8.Downloadedfromwww.annua

lreviews.org

by

UniversidadeFederaldoEspirito

Santoon05/15/12.

Forpersonal

useonly.


21/28

OL PREDN ON HE E

z

GU he aeen oto n

6

to q F 14 a 15 ow g a a o o' o nO a n=1 vot po g a o go o v ow, a t vogavaoa ow at gg tat t oto o b qh ' h dpd

h h - d

.8

he mpd v mx

g"Z

{O.665mx

- -

n = O

he ee n

6



antoon05/15/12.

Forpersonalu

seonly.


22/28

362 HOUT

Sraetes sreadg

B e exeets wee de te sracetes ege te e

iesia case. ge 6 sws e est ee ( wc icaestat . te edmesal case Cmpare wt 0rm te tery

Te ata arrett & arger (190 are sw gre arretteasred te elty te spread ls wt ars Fgre swstat tese rslts are sstet t Lees data

gre ss Lees measremet te tkess dstrt aatty t predcted y te tery; h ares rgly as h1jr ad s tetkest ear te leadg edge We h s pltted smlar ty arales Leeds tat h vares rgly as

X L < mx 6

Tee a e lttle dt tat te as smlarty slt actally ccrs

Annu.R



byU


Forpersonaluseonly.


23/28

- -

OI SPRADING ON TH SA

OECAO - I OEY ALCOHOL

COOSEE OL+ CESYL POSPHAE

.-

:1

Q

Srcnon spradng

sonds

Meed te dr ree ee pe

363

Annu.Rev.F

luidMech.1972.4:341368.Do

wnloadedfromwww.annualreviews.org

byUniversidadeFederaldoEspiritoSant

oon05/15/12.

Forpersonaluse

only.


24/28

34

w:

g

Th x od wih d d

n th mnts. Bt th dsany btwn thy and mnt st ng t sms t n that th as axmatns madn t thy wd ad sh a ag dsany At ts wtng t s nt

a wy th dsany ass

T FAL AA F A Kt s knn tat at a tan m spd n t sa ass

sad Th sadng ss aays nds n a sfa-tnsn gm Tasn th -sadng ss sts s that th nt sadng nt (hangs fm st t ngat Ths th bm f dtmnng thna aa an s dnds n an stmat hw ady hangs

T fm s an stmat s nt a sm task Fst t a f sdtmnd by t y sma nntatn f sfatants n th nywth gad t u a ths mas mtant Snd d s mad f a y ag nmb f nsttnts a f whh has a dnt a f as as a dnt atty and sbty Thd th tmatsany and bga ts f sa wat dtmn t sm xtntt angs n t s nt nty a that th sd st n sma stmat f th na aa attand by an sk

Hw d t t ata sgna f ts stn tw dasa bn pt ft f stmatng t na aa f an sk Fst t sssd Bkk 94 An & Ests 90) that th sad ass aft

a tan mnmm thknss s ahd By ma atn f bsatn ths tknss s fnd t b h 0 nhsA hysay m asb da s t fth by ay (9) H ags


8.Downloadedfromwww.annua

lreviews.org

by

UniversidadeFederaldoEspirito

Santoon05/15/12.

Forpersonal

useonly.


25/28

u!j

.94

0

88

OIL SPREADING ON THE SEA

/

3

MTT MNNT l

OIL AGED ON IC } L AGED ON WATER FRM ASR VAN

ALUATED TIME ALE,tp R THIMPAN S:

k }* 12ft /sec SO THATt1 = 10 DAYT 3

4 . NN IMNIN IM

The chane n enty n he acc, a calculadusn an vapoave me

W N

0 103 10 0 0 10

Cmbn spreading laws.

Annu.R


reviews.org


antoon05/15/12.

Forpersonalu

seonly.


26/28

366

>

OL

I

/

/

f /0

()

22 Th uration of h raig rgmtat te satants sl dssle nt te ate and estmates te tmeat an appeale atn al s mpnents ntal n te lente te ate. Usng ts dea and te sae-tensn speadng teFa attans te lng slt te aea :

( V6 )1/8

pD86ee s s te slt and te dst te satants n ateFge 9 ss Fa's elatn empal data. Te t ntans neempal nstant eplaes , and .

Tee ae at least t te psal meansms tat ma ase t


byU


Santoon05/15/12.

Forpersonaluseonly.


27/28

L SPEDNG N E SE 367

a. e t te elete eaatn f te me late mnentf te de l (Ble 964 a ageement taned n t meanm f te eltn f l dent ee ge 0) A g etmate

tat fr a ta de l earan f te me latle mnent tee tme fate tan te dtn nt te ate eet agmet a ntng at te llt eaatn f fatanttat determne

e te al meanm s ga degadatn f l de tatera (Zel 99 ertan ll ange e prpere f te l

COCUSOS nme f atal elt ae fm te elt eented n te e

edng etn nde t te em f a age tanke nnng agndand eleang a lage lme If t e mdeled a a nt eleae ten gre te ee egme f eadng and dea esmae te area te sl as me rease gre 22 ss edratn f ea preadg regme as a fntn f lme released a estmated Fa (969

f an e l el ead a mall lea f a taner dage alas e rae-es preag l geerall e e l mpraspreag egme Fgre 2 ss e aea s a sl as a

w

X

[0

24 TONS OIL (TORREY CANYON)0 BBL OIL30 BBL OI

0 BBL OIl/WATR BB OIlWA BB OIlWAT X XXANTA BABARA

'

t ec

'

*x O,x

2 rea rea e sraees sprea

Annu.R



byU


Forpersonaluseonly.


28/28

68 me from releae compared w eld oervao (Fa 199 T cart conrced b ang tha e rea o e lck oe a wodmenonlpreadng law a decred n Secon 4 w e arrarl eqal o

ce te ate of read te aceeo reme deedet o tevome of ol releaed, meareme of e area of e lck wll ot ceo deermne e volme

Trnng o he cenc apec o ollck preadg we can make omegeneral aemen Fr ere are a ere of odarlaer pe problema are compng te c drag on a preadg ol lc. Te mpleorderof-magde rel of Fa (199 correpod o mlr oloof he bondarlaer eaton econd he preadng regme propoed ba are conen w expermenal obervaon

The mechanm b wch an o lc ceae to pread no enrel clear

at preent I ma e tat ere are evera mecam acg cocetat o modf te et peadg coecet tat readg ceae

Abbott M 1961a Houille Blanche 1

6225d 1961 1676

Allen, A. A, Estes J E. 1970 Detection andMasuremnt of Oil F Santa BarbaaOi Symposium, Uv of Caif Sanaabaa Cl, 1970

jam, T. . 968

Flud Mch.

9lokkr P. C. 964 Spadin and Evapr

ton of Ptroum roducts on WatrProc. t It. Harbour Cf., Antwer,Jn 22-27 1964, 91119

Bur, M. 1969 I Oil on the Sea, dD P Hoult, 51 Nw York Plu

anlop . K., Wadan G. 1971Th Dyamc of Ol Slcks-or Crpngrud. AIAA papr 71-14, AIAA 9thAerospac Scence Mt., Jn 1971

ay, 969 I Ol on th S, . out 33 ew York Peum

ay, J. A. 1971 Phyical Pocee in teSprad of Ol on a Wat Surfc Cof.on Pvenio nd Cool of Ol Splsponsord by AP, EPA, and US CoastGuad Wasigton, DC

Garrtt, W. D, argr, W. R. 1970 Envion Si Technol 41227

Hdy G M Plat, . 966 J FludMech 266517 (1 at)

H . P. 199 n Oil on the ea, . P Hout, 6580. w Yok Pu

out, . ay J. A, Mlgra J ,Coss R. H. 1970 The Speading and

ontnmnt o Ol Slcks AIAA D

lid Plasa Pys. Dynam. Conf., LoAgs, 1970

oult P uhon W 97 The Spreadof Oil in a Channel d Me. ab.,Dpt. M Eng, Ma Is o!.25 pp.

Hus P. 1956 Quart J Roy Meteorol.Soc 82 :494502

ppn A 1966 Estuay and astlineHydodynamic, 115 w York: MGawil

Lee R. A. S. 1971 A study of th uacetenion contolled egime of oil peadMS tsis (M. Eng) M

Liang L. S. 1971 Speading of oil on amWatr: netial phae, MS ess (M.g.). MI

O'Bi . A. 970 Wnd Tunnl Exprment n Oil Slik Tnpt. U NvCv gg Lab. ogs o, P , l.

Riardson L ., Stomel H 1949 Mtoo. 5 :40m J E (Ed), 19 "Toey Canyon

-Pollution and Maine Life CabidgEnglad Cbridge Univ Prss

Son W. 1970 An expeimental invetigation of oil peading oe wate MS tsM. g). MI

n Krm, 1940 Bull Am Math Soc453

Zobll C E. 1969 Mcrobal Modctonof rud Oil in the Sea, Proc. Jon .Prnton and Control of Oi Spills De.517 1969, pp 726


byU


Santoon05/15/12.

Forpersonaluseonly.

Date post:	05-Apr-2018
Category:	Documents
Upload:	maria-eduarda-torres-santos
View:	218 times
Download:	1 times

Oil Spreading on the Sea

Documents