海岸动力学英文PPT课件Coastal-Hydrodynamics-2.4

CoastalHydrodynamics1.LinearizationofbasicequationsChapter2§2.3SmallAmplitudeWaveTheory2.Solutionofthelinearizedequations3.Dynamic&kineticcharacteristicsofsmallamplitudewaves4.Standingwaves2/37Chapter23.Dynamic&kineticcharacteristicsWaterparticlevelocitycomponentsWaterparticletrajectoryPressurefieldEnergyandenergypropagation3/37Chapter2Thevelocitycomponentscanbefoundbysubstitutingthesolutionofvelocitypotentialintothedefinitionofpotentialfunction.Velocitycomponents4/37Chapter2Velocitycomponentsareharmonicfunctionsofxandt.Thehorizontalvelocitycomponenthasthesamephaseastheelevationofthefreesurface.Thehorizontalandverticalcomponentsare90ºoutofphase.Velocitycomponentsdecreaseexponentiallywithdepth.5/37Chapter2Thedisplacementofthewaterparticlecanbefoundbyintegratingthevelocitywithrespecttotime.WaterparticletrajectorySquaringandaddingyieldsthewaterparticlepathas1)()(220220BzzAxx6/37Chapter2Thewaterparticlestravelinanellipticalpath.Theellipticalmotionbecomesflatterwithwaterdepth.Indeepwater,theorbitsbecometruecircles.Inshallowwater,themajordiametersofellipsesareconstant.7/37Chapter2ThepressurefieldassociatedwithaprogressivewaveisdeterminedfromtheunsteadyBernoulliequation.PressurefieldThepressureequationcontainstwoterms:thehydrostaticpressure(静水压强)&thedynamicpressure(动水压强)tkxkhzhkHggzpcoscoshcosh28/37Chapter2Thedynamicpressureisinphasewiththewatersurfaceelevation.ItispositivewherethefreesurfaceisabovetheSWL,andisnegativewherethefreesurfaceisbelowtheSWL.Indeepwaterdynamicpressureisverysmallatthebottom,whileinshallowwateritapproachesunity.Dynamicpressure9/37Chapter2Themaximumvalueortheminimumoneappearswhenwavecrestortroughreachesagivenpointrespectively.Hydrostatic&dynamicpressureatvariousphases10/37Chapter2ThetermKzisreferredtoasthe“pressureresponsefactor”(压力响应系数).khzhkKzcoshcoshThe“pressureresponsefactor”hasamaximumofunityatthemeanwaterlevelandaminimumatthebottom.Belowthemeanwatersurface,itisalwayslessthanunity.11/37Chapter2Acommonlyusedmethodtomeasurewavesineitherthelaboratoryorfieldbysensingthepressurefluctuationsisstatedasfollows.Ifthedynamicpressureisisolatedbysubtractingoutthemeanhydrostaticpressure,thenthefreesurfacedisplacementηishgKpzd12/37Chapter2Thetotalenergyconsistsoftwokinds:thepotentialenergy(势能),resultingfromthedisplacementofthefreesurface；thekineticenergy(动能),duetotheorbitalmotionofthewaterparticles.Waveenergy13/37Chapter2ThepotentialenergyperunitcrestwidthoveronewavelengthisThekineticenergyperunitcrestwidthofawaveisLgHxzzgELp16dd200LgHxzzxELhk022216dd2ThetotalenergyperwaveperunitwidthisLgHE8214/37Chapter2ForAirywavesthepotentialenergyisequaltothekineticenergy,whichischaracteristicofconservative(non-dissipative)systems.Itisworthwhileemphasizingthatneithertheaveragepotentialnorkineticenergyperunitareadependsonwaterdepthorwavelength,buteachissimplyproportionaltothesquareofthewaveheight.15/37Chapter2Therateatwhichtheenergyistransferredinthedirectionofwavepropagationiscalledtheenergyflux(波能流),anditistherateatwhichworkisbeingdonebythefluidononesideofaverticalsectiononthefluidontheotherside.EnergyfluxTherelationshipfortheenergyfluxisEcnkhkhEczuptTPhdT2sinh2121dd10016/37Chapter2Energyfluxhastheunitsofpower,andforthatreasonitisdenotedbyP;itiscommonlyreferredtoasthewavepower(波功率).Indeepwater,theenergyistransmittedatonlyhalfthespeedofthewaveprofile(n=1/2),andintheshallowwater,theprofileandenergytravelatthesamespeed(n=1).17/37Chapter2Conservationoftheenergyfluxwillbeusedlatertoexaminethewaveheightvariationsinshoalingwavesandtorelatetheheightofbreakingwavestothedeep-waterwaveconditions.Therateofsandtransportalongbeachesiscommonlycorrelatedwiththe“longshorecomponentoftheenergyflux”.18/37Chapter2Groupvelocity(群速)Iftherearetwotrainsofwavesofthesameheightpropagatinginthesamedirectionwithaslightlydifferentfrequenciesandwavenumbers,theresultingprofile,ismodulatedbyan‘envelop’thatpropagateswithspeedofgroupvelocity.tckkcxkktckkcxkka22cos22cos219/37Chapter2Itisclearthatnoenergycanpropagatepastanodeasthewaveheightiszerothere.Therefore,theenergymusttravelwiththespeedofthegroupofwaves.Characteristicsofagroupofwaves20/37Chapter2Theaveragerateofenergypropagationperunitcrestwidthoveronewaveperiodisseentobetheaverageenergyperunitsurfaceareaprogressingwiththegroupvelocity.Thespeedatwhichtheenergyistransmittedisequaltothegroupvelocity.21/37Chapter2ThegroupvelocityisdefinedasThisderivativecanbeevaluatedfromthedispersionrelationshipkkcCgddcnckhkhCg2sinh212122/37Chapter24.StandingwavesStandingwaves(立波)oftenoccurwhenincomingwavesarecompletelyreflectedbyverticalwalls.Ifaprogressivewavewerenormallyincidentonaverticalwall,itwouldbereflectedbackwardwithoutachangeinheight,thusgivingastandingwaveinfrontofthewall.Standingwavesarealsocalledclapotis(驻波).23/37Chapter2ThesurfaceelevationofstandingwavescanbeexpressedasItisseenthattheheightofthestandingwaveistwicetheheightofeachofthetwoprogressivewavesformingthestandin