Introduction to Water Waves

219 Pages·1984·5.491 MB·English

by  Gordon David Crapper

II
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ELLIHSO RWOODS ERIEISN
SMeATEHrEtMdAioTIiAeCNrSD I sT:SA P PLICATIONS
ProfesGsM.or. B ELLC,h elsCeoal lege, UnoifLv oenrdsoint y
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ESitadttainOsdopt eircrasRti e:osne aalr ch
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ProfesBs.Wo .rC ONOLLYC,h elsCeoal lege, UnoifLv oenrdsoint y
I
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INTRODUCTIONT O
WATER WAVES
B.Sc.on.s)P,h .D.
G. CDR.A PPER, (H
ProfeosfAs poprl Miaetdh ematics
UniveorfLs iivteyr pool
ELLIHSO RWOOLDMI ITED
PubliCshhiecrhse ster
·
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JOHWNI LEYS ONS
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First pu1b9l8ib4sy h ed
in
ELLHIORSW OOLDIM ITED
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atnM caCirChrekionecsths e,s ter.
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© 1984
British LibCraaryt alogiuinPn ugb licaDtiaotna
CrpapeGr.D, .
Inrtoducttioow ant wearev s.
(ElHloirsw osoedr iinme ast hemaatniidct assp plications)
1.W atewra ves
IT.i tle
532'.59Q3C 157
Libraryo fC ongresCsa rNd o.
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HousCeo,o pSetrr eCehti,c heWsetseStru ,s sEenxg,ld a.n
Tabloef C ontents
AuthProerf'.asc. e. . 9
' . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ChaptBearsE qiuca antdiA opnpsr oximations
1
11. Introduction ,.. ................... .1.1. .
. . . . . . . . . . . . . .
12. EquatoifMo ontsi .o.n. .. . . . . . .............1...4.. ..
13. EnerEgqyu ation 18
. . . . . . . . . . . .. ... . . . . . . . . . . . . . .
An
14. Boundary C.o n.d i.t i.o n.s . . . . .1 9 . . . . . . . . . . . . . . . . . . .
.
15. Approximations 2 2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problems 2 7
. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chap2 tSeorl uftoSirmo aWnlaslv es
21. SeparSaobllueto ifLo anpsl aEcqeu'ast ion 29
. . . . . . . . . . . . . . . .
22. ProgrWeasvseisv e 32
. . . . . . . .... . . . . . . . .... . . . . .... . .
2.3S tandWianvge s 39
. . . . . . .... . . . . . . . . . . . ...... . . . . . . .
24. Non-lSionleuatrfi oPorrn osg rWeasvseisv e. :. ..4.1
. . . . . . . . . .
2.5C omplVeaxr iMaebtlheo ds 43
. . . . . . . . . . . . . . . . . . . . . . . . . .
26. PlaWnaev esW aavnoednsa C urrent 49
. . . . . . . . . . . . . . . . . . . .
27. CombinoaftW iaovneG sr:o uVpe locity 52
. . . . . . . . . . . . . . . . . .
28. CombinoaftW iaovneS sh:oC rrte sted W.aves 55
. . . . . . .. . . . . . .
29. ConserovfaWtaivoeGnsr :o uVpe locity 56
. . . . . . . . . . . . . . . . . .
2.01 SweAlplp roaacG heinntSgll yo pBienagc h 62
. . . . . . . . . . . . . . . .
Problems. . . 65
. . . . . . . . . . . . . . . . . . .·. .. . . . . . . . . . . . . .
Chap3 tWearvE en eanrdgyM omentum
31. ThEen erEgqyu at.ion . 69
. . . . . . . . . . . . . .... . . . . . . . . . . .
3.2 AveraUgniinfgWo:ar vmTe r ains . 72
. . . . . . . . . . . .. . . . . . . . .
33. TheA veraEgneedrE gqyu ation 77
. . . . . . . .... . . . .. . . . .. . .
6 TabolCfeo ntents
34. Mass aFnlMdoo wm entum Equations . 80
. . . .. . . . .. . . . . . . . .
35. MomentFulmui xnU nifWoarvme s 82
. . . . .. . . . . . . . . . . . . . . .
36. SurfTaecnes Eifofne c.ts . . . . 86
. . . . . . . . . . . . . .. . . . . . . . .
37. EnerDgiys sip.ation 89
. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .
Problems 92
. . . .. . . . . . . . . . . . . . . . . . . . . . . . ..........
Cha4p tWearvo enCus r reanndWt asvA ec tion
4.1M asMso mentaunmEd n ergy . 93
. . . . . .. .. .. . . . . . . . . . . . . .
4.2I nfinDieteWepal ty.e r.. .... . . . . . . . . .9.7. . . . . . . . . . . . .
4.3W avAec ti.on . .98
. . . .. . . . . . . . . . .. .. . .. . . . . .. . . . . . .
4.4T hCe urrEeqnuta tions . . 110
. .. . . . . . .. . . . . . .. . . . . . . . . .
4.5V ariaotfWi aovnAe c tiaolnoR nagy s :. .... . . .1.20. . . .
. . . .
4.6C urrweinttUshp welling . . 140
. . . . . . . . .. . . . . . . . . . . . . . . .
Problem.s . 160
. . . . . . . . . . . . . . . . .... . . . . . . . . . ......
ChaptAeprp lications
5
5.1S weAlplp roaacG heinntSgll yo pBienagc h . 170
. . . . . . . . . . . .. .
52. TheI niVtailaPulre o b.l.e.m. . .. .. . . . . . . . . . .. .. . . . .1 10
53. WavoensC urrents . 161
. . .. . . . . . . . . . . . . .... . . . . ..... .
54. ShiWpa v.es. . . .. .. .. .. .. . . . . . . ., 1.0.2. . . . . . . . . . . .
55. WavAepsp roaacC hiirncgIu sllaarn .d . . 132
. . . . . . . .. . . . . . . .
56. MorCeo mpliRceaftreadPc rtoibolne ms 138
. . . . . . . . . . . . . . . . .
5.7S hoWratv Reisd ionnLg o ngWearv es .142
. . . . . . . . . . . . . . .. .
58. RandoWma ves . .. . . 149
. . . . . . . . . . . . . . . .. . .. . . . . • • •
Problems i . ... 1 152
. . . . . . . . . . .... . . . . . . . . . . . . . . . . . . .
Chap6 tFeurr Stohleurft oSirmo aWnlaslv es
6.1W avemakTehre ory . 145
. . . . . . . .... .. . . . . . . . .. . . . . . . .
62. A SimpWlaevE en erMgayc hine . .1 59
. . . . . . . . . . . . . . . . ....
63. .WaRveefl exainoEdnd gWea ve.s . .1 26
. . . . . . . . . . . . . . . . . .
64. Diffor.na .c t.i . . . . . . . . .1 6.3 . . . . . . . . . . . . . . . . . . . . . . .
65. Wavoensa nI nterIfnatceeWr:an vaels . 166
. . . . . . .. . . . . . . . . .
66. Wavoensa T hiSnh eet. . 169
. .. . . . . . . . . . . . . . . . . . . . . . . .
Problems . 127
. . . . . . . . . . .. . . . . . . . . . . ...... . . . . . . . .
Cha7p tWearvi eSnsh aWlaltoewr
71. Equati.ons . . 174
. . . . . . . . . . . .. . . . . . . . . . . . . . .... . . .
72. LineSahra lWlaotwTe hre .o r.y . . . . . .1 87. . . . . . . . . . . . . . .
.
73. Non-lSihnaelaWlrao twTe hre ory . 180
. . . . . .. . . . . . . . . . . . . .
TabolCfeo ntents 7
74. SoliatnaCdrn yo iWdaavle s 191
. . . . . . . . . . . . . . . . . . . . . . . . .
75. WavoensB eac.he.s. . . . . . . . . . . .1.49 . . . . . . . . . . . . . . . .
Problems . . 169
. . . . . . . . . ..... . . . . . . .. . . . . . . . . . .. . .
SoluttProio obnls.e .ms.. ....... . . . ..................1.9.8. .
Bibliography 281
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Index ;. . .......2.22. .
. . . . . . . . . .... . .. . . . . . . . .... . . . .. . .

AuthorP'rsea fce
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Daksa nkne iRna uscsheeinn : Thiisns o rti pptlhionugg h:
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Tieufn tiehnr Reeni hn'. Benetahtbehr oockl'eflsao rw '.
FrobWmyei M ll'ritmah;Wi.r n oZJ.sChelaritanip?op'ner
by
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Schubiessr atit doh avbee efna scibnyar tuendnw iantge r. ceIrtt abciean nl y
heardt hrotuhgseho ng-'cDyicel esM cihiOln(leTeh rebi ena'u tdiafuulg hotfe r
all
thmei llteoMr u)l lpeore'msfs r,ow mh itchha eb oqvueo taitsti aoknea nni,dn
othfearm osuosn gosfw, h icthh bee st kinspo rwonb a'bDliFyeo re(lThlee '
Truot)I.na t extbwoeoc ka hna rdclayp ttuhrmeea giinct hsea mwea yb,u t
understtahnmede icnhga innivcosl ivnne owd a yr edutcheaest tracetvieno n,
ifw ee xcltuhdpeeo ssiboifwl aittseiprer si Htoepse.f, tu lolowy,es haalvlo id
thfea toeft hsei ngienSr c hubecrytc'tlshe r,o whiinmgs ienlttfoh set ream
anddr owning!
Thaei omf t hbeo okt opi rse stehbneat s tihce oorfwy a twearv ienass traight­
forwawarydu sidnigr ercatt htehras no phisticatedt emcahtnhieqmuaetsi.c al
A mimimoufmp revikonuosw leidsag ses umbeudst,o mfea milwiiatrthih tey
elemeonfft lsum iedc haannivdce sc taonra lwyisblielash elapst hdee rivations
oft hbea seiqcu ataironene sc esbsrairOeitflh.ye rtwhimeso esd ti ffciocnuclietsp t
thpea rtdiiaflf ereonfft uinawcttixwiohx(o2nin vacsrh.Qe, e kx pkz(tr,x1eixs2nt)s v)e,erd,m a d,si tfo1wf fe r jenta x
saejot1fnis n ad.epxev nadreinastbot l heast, but
= *
Wea lnseoe tdod ifferienntteiwgairttavehla sr ilaibmlTieht aesd .o ption
oft hdei raepcptr omaecahtn hsa sto moeft hdee rivaatrlieoo nnbgsu,m t u cohf
thlee ngijtsuh as tl geabnrndae eodnslp ye rsitsotf eonlclietot hw r oRuegfhi.n e­
menstusc ahst endsoourb slueb scnroitpatht aivonenob te euns eadg,am iank ing
theex preslsoinogNneosar t.t eimmspa td teod isctuhmseos r dei ffiacrueloatfs
theoirnpy a,r tiwcauvlgeae rn erbaytw iionngd e,n etrhaeloo rfdy i ffraorc tion
wave-breaking.
10 AuthoPrr'esf ace
To avuonidduc eo mptliioccnae,r tsaeicnt ciaobnne so mitotnea df irst
readiinnC gh:a pt3ae nr4ds elavoeu §t3 4.a fteeqru at(i33o.9n)§ ,§3 .,35 .,6
4.41.,42 .,44 ,.a 6n wdo rtkh ro§u§g4h4. .3p5,u tttihcneug r rceonmtp onents
Ut,U 2b otzhe rToh.ae l gehberriates h evne rmyu cshi mipelTidhf.e waacvtei on
equatdieornii vn§e 4d. i3ms o tsu sewfhuelcn u rraernpetr se sbeunttth ,ci asn
bea ssutmreufdroe t hsem aelflcf teisn§ 5 .a1n fdo §r§5 .,53 .,54 7..
Them ajoprh meoennaar ael ill luesdbt yrp ahtotogarsfa aparhsp s o isbsle
takienns i atituonwsh icarhme o slti kteolb yee ncounWtaetreerd .w aves are
eastyoo bseirnmv aen dyo messtiittciu aoanswse ,la ls roinsv le,ar ketsh seoe ra .
Iti hso ptehdat thi el sltturiaownisel nlc outrharege eat doel ro oaktw avienhs i s
ownen virotnoem xepnrlteto hceo nclusitohtnehs e oorfy .
Reeferncaensnd o tferosf ru threera daircneog l letcotgeeatdtth heeern odf
thbe ootkoa voiindt ruisnitveer riuntp htdeie ovne loopfmte hnmeta terial.
Thearrese o mgee nerrearflee ncaenssdo mree eldat stpoe cific sections of the
book.
Answearnsdi ,ns ome cfaluslse osl,u tairogeni svo ennl fyo r the most
diffoiftcuh plert o blseemts.
I indetbotm eadnp ye ople overf ormmaintnyhg e y eeiaxdrpesra esis ns ed
int ham beo oMko.r sep efcicailIlw yi sthot hapneko pilnev olinvt ehdae c tual
producmtyib orno:t herE-riiHnc-y ldMaew.,S, c R..,BI A...L,. R..S,Pf .ora ll
hihse lwpi tphh otognroaotpn hltsyh, o sspceei atlalkyae nnfd or mh icso llection
bualts por eoscsmiyno gw nD;rJ ohHno gfaonFr i 2g..;M7 rsH.e lPeons tlewhite
fohre arc cuarnapdta et iteynptia nngrd e -tyopfmi ynm ga nuscmryis potn;,
Mart,if nohri tsr atnisoolnfaM ullpeore'amsn; md y w i,fE eni,fd roe nucroaging
mea ndp uttuipnw gi tmhe d uritnhgwe r it.Pi hnogtogrnaopotht sh erwise
credairtmeey d own.
1
Basci equatainodn s
approximnast io
INTRODUCTION
1.1
Thee ndlseuscsc eosfsw iaovbner se akoinan b ge aicashs igthhtan te vert of ails
attrtahceety eT.h osoefu sw hol ibvyet hsee aar fea miwliittahhr v ea rious
moodrsa ngfirnocgma laml,m ogslta sss-elai,sk)mtetpi rlold uscmiabnlrgle akers,
tot hheo wlgianclgoe n diwthoentnsh w ea vaersse oh igthh awta tchbiencgo mes
dangeErvoeufsno. tr h onsoest o f ortuwnaavtpeeh ,e nomoenwn aat seurr faces
cabne o bserevveeddra yay t h omei,nt hbea tohrw asbha swihne,vr eer syh ort
'capiwlalvaemrsay'ka et tractive patterns.
Wavaetss eaar gee nerbaytt hewedi nads ,t atewmheinmctih g bhert e garded
ass elf-esviindocenewn itn,dd ya ytsh see iasr ougWha.v easrt eh ree sponse
madbey t hwea taesgr r avoirot,nya s maslcla sluer,ft aecnes tiroitneo,rs e store
thseu rftaoic teos r iglienvwaehlle t nh wei nddi stiutTr.hb ess i ozfet hwea ves,
botihnl engatnhdi nh eigihntc,r ewaisttehhs le e ngotfth i mfeo wrh itchhe
winhda bse ebnl owainntdg h lee ngotfwh a tseurr foar'c fee,t ocvhew'rh, i icth
habse ebnl owiTnhges. e coonfd tshteastee misee natseysn oufgohtr h ree ader
toc heocnka l imistterdeo tfwc aht seurc ahsa s mallo rrl easkeerU vsouiarl.l y
att heex truepmwei enndod f t hlea kweh etrhese u rfiassch ee lttehreaerrdee
now avaetsa laln,md o vianwga dyo wnwtihnfiedr swta vwehsi acphp ehaarv e
waveleonfgt thohers d oefr1 e ma nadr deu teo t heef foefcs tu rftaecnes ion.
Asw em ovfeu rtthhewera velegnrgatdhui anlclryea angsdre asv bietcyo tmhese
imporrteasnttof roirncge .
Whetnh wei nsdt obplso wtihnwega vdeosn ot disAa fpapmeiealxrip.ae rr i­
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