Table Of Content

II !I' ELLIHSO RWOODS ERIEISN SMeATEHrEtMdAioTIiAeCNrSD I sT:SA P PLICATIONS ProfesGsM.or. B ELLC,h elsCeoal lege, UnoifLv oenrdsoint y ·j ESitadttainOsdopt eircrasRti e:osne aalr ch !! ProfesBs.Wo .rC ONOLLYC,h elsCeoal lege, UnoifLv oenrdsoint y I BaldoGc.R k.&, BridgeTm.an , MathematicThaelo ryo fW avMeo tion deB arrGa., Measure Theorayn dI ntegration BerrJ.yS ,.B, urghDe.Ns .,,H untlIe.Dy .J,,a meDs.J, .G . & MoscarAd. ini, 0. TeachianngdA pplyiMnagth ematicMaold elling BurghDe.Ns .&, BorrM.i e, Modelliwnigt Dhi fferential Equations BurghDe.Ns. & , D ownAs.M,. Modern IntroductitoonC lassMieccahla niancds Control BurghDe.Ns .&, GrahAa.m ,I ntroducttiooC no ntroThle oryi,n cludOipntigm aClo ntrol BurghDe.Ns .,,H untlIe.& y M,c DonaJl. d, ApplyiMnagth ematics BurghDe.Ns .&, Wood,D . MathematicalM odelisn th e SociMaaln,a gement. A. andL ifSec iences ButkovAs.kG .i y, GreenF'usn ctionasn dT ransfFeurn ctionHsa ndbook ButkovAs.k G.i y, StructuorfeD istributed Systems CheritFo.n , TextbooofkD ynamic2sn,dE dition CheriFt.o n, Vectoarn dT ensMoerth ods Dunning-JD.a viesM,a thematicaMle thodsf oMra thematiciaPnhsy,s iSccaile ntists andE ngineers EasoGn.,,C o leCs.,W .& GettinGb.y , Mathematiancds Statistifcosrth e Bio-sciences ExtoHn., Handbooko fH ypergeomeItrnitce grals ExtoHn., MultiplHey pergeomeFtruincc tioannsdA pplications ExtoHn., q-HypergeomFeutrniccti onasn dAp plications FauIx.D, . & PrMa.t Jt., ComputatiGoenoamle tryf or DesaingnaM anufacture FirbP.yA ., & GardineFr., SurfaTcoep ology GardinFe.r , C. Modern Algebra Gass,Po C.nC.. Geometryo fS patiFaolrm s GoodboA.dM y., · CartesTieanns ors GoultR,.J . ApplieLdi neAalrg ebra GrahAa.m , KroneckPerro ducatnsdM atriCxa lculwuisth:A pplications GrahAa.m , Matrix Theorayn dA ppli· catifoonErsn gineanedr Msa thematicians GriffDe.!H ,. ApplieFdu nctionAanla lysis HanyAg.a , MathematicThaelo ryo fN on-linEelaars ticity HoskiRn.F s., GeneralFiusnecdti ons HunteSr.,C . Mechanicosf C ontinuoMuesd ia2,n d( Revised) Edition HuntlIe.& y J,o hnsRo.Mn ., Lineaanrd NonlinDeiafrf ereEnqtialu ations JaswoMn.,A . & RoseM;.A .· CrystSaylm metryT:h eT heoroyf C olouCrr ystallogr;�phy JohnsRo.Mn . ,L ineDairf fereEnqtuiaatli oanndsD iffereEnqcuea tioAn sS:y steAmpsp roach KimK,.H .& RoushF,.W . AppliAebds tracAltg ebra KosinWs.k i, FielSdi ngulariatinedWs a veA nalysiinCs o ntinuum Mechanics MaricheI.v , Integral TranosffH ioghrmesr T ranscendeFnutnacltio ns .MeeBk.L0, .. F & airthSo.rn e, UsinCgo mpute1r s, Muller-PfeEi.f fer, SpectrTahle oroyf O rdinaDriyf fereOnptiearla tors· .NonweTi.Rl .eF r., C omputatioMnaathle maticsA:n I ntroductitoonN umericAanla lysis OldknAo. w& ,S mitDh., LearninMga thematicwsi thM icros OgdeRn.W, . Non-linEelaars tiDce formations RankRi.n , ModulaFro rms RatscHh.e& kR,o knJeo,n Computer Methfoodrths e Rangoef F unctions ScorRe.Sr ., EnvironmeAnetraold ynamics SmitDh.K, . NetworOkp timisaPtiroanc tiAc eC:o mputatioGnuaild e SrivasH.tM .a &v aK,a rlsPs.Wo .n , MultipGlaeu ssiHaynp ergeomeStreirci es SrivasH.tM .a &v Maa,n ocHh.aL ., A TreatiosneG eneratiFnugn ctions S'\YeeMt., V . Algebra, GeoamnedTtr ryi gonomeitrnSy c iencEen,g ineerainndg Mathematics· TemperHl.Ne .yV ,.& TreveDn.Ha ., Liquiadnsd T heiPrr operties TemperHl.Ne .yV ,. GrapThh eorayn dA pplications ThornR,. MathematicMaold elosfM orphogenesis ThomaL.s , GamesT heorayn dA pplications TowneMn.cd S., t ewart Mathematicisn S port TwizEe.lH l. , ComputatiMoenthalo dsf orP artiaDli ffereEnqtuiaatilo ns WheelRe.F r., RethinkiMnagth ematicCaoln cepts WillmTo.Jr .e , TotaClu rvatuirneR iemanniGaeno metry WillmTo.Jr .&e ,H itcNh.i n, GlobaRli emanniaGne ometry 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 · HalsPtreedasd si:v iosfi on JOHWNI LEYS ONS NewY orCkh·i ch·eB srties·&rbT aonreonto First pu1b9l8ib4sy h ed in ELLHIORSW OOLDIM ITED MarkCertoH sosu sCeo,o pSetrr eCehti,c heWsetsSetur s,sP e0x1,19 BE,England Tphbuelc iooisrlnsheo efpporJrrhme'saGo ss mi'dd olsurnolf ctai ehwdei ng atnM caCirChrekionecsths e,s ter. Distributors: AulNisZeaatewlSo,r au aAnatsd:hi, - east JacarandLat-dJW.ai,cl aeryPa rnedsas , JOHNW ILEY SONISN C., & G.P..B Oox89 5,B risbQauneee,n s4l0a0n,0Ad 1u stralia Canada: JOHN WILEYS ONS CANLAIDMAI TED & E22Wo ourAcperRsfrioetaeRdcre,, x daaO lnet:,aC rai noa,.d a JOHN WILESYO NLSIM ITED & NBafaofLmaSsonnr Ceh,Aiu dtcrhmetWa hseitsteShetnu rr cs,hso dfeetaxe,w sh lE nogtedlarn :d. HalsPtreedas d si:v iosfi on JOHNW ILEY SONS & 60T5h iArvde enN,uewY orNk.,Y 1.0016,U S..A. G.D .C rapper/HEolrlwioso d Ltd. © 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. 84-20891 ISB0N- 83521-4-86.7 (EHlolwrioso Ldt d.) ISB0N-4 7-020122-(3H alsPtreeds s) TYPesePtr eRisonsm abnyE llHioswr ooLdt d. PrinitnGe rde Barti tbayiB nu tl& eTra nnFerro,m Seo,m erset COPYRIGHT NOTICE- RigthsR esveerdN.o p arotft h ipsu blicmaatyib oern e prodsutcoerdien,ad r etrieval Asllye smt,or t rsamnidt,tien afnoyro mrb ya nmye anesl,e ct,rm oencihcanpihoctalo,c ogp,y 'in recorodrio ntgh erwise,th ewp ietrhmoiusotsfE i lolnHi oswr oodLi imteMda,r kCerto ss 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 'Wassai gc dhe nvno mR ausche'nW?h daitId s aoyfr ippling? Daksa nkne iRna uscsheeinn : Thiisns o rti pptlhionugg h: Ess inwgoehndl iN ei xen Thwea ter-asrpseri intgeisn g Tieufn tiehnr Reeni hn'. Benetahtbehr oockl'eflsao rw '. FrobWmyei M ll'ritmah;Wi.r n oZJ.sChelaritanip?op'ner by M 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 menitts o d roapl arsgteoi nneta po o oolfw atWearv.se psr eoaudtw, i tchi rcular crecsetnst ornet dhp eo iantwt h itchhse t ohniett hsse u rfIantc eho.ec eaa n stogremn erwaatveweshs i cahl tghho umoirnoe n dei rectthiatonhn o msaed e byt hset one, ousitpn ra se iamdi larW efs ahsashleilteo h nat.th etyr aovveelr hundroefdk sio lmetorfeo sc eaTnh.e swea vreusn naiwnagfy r otmh wei nd whigcehn ertahteeamdr c ea l'lsewde Iltils s'w .ew lhli pcrho dubcreesa oknea r s beaocnhd aywsh efno lra cokfw inldo catlhlewyro eu bledn ow aveOsfc. o urse