Mathematical Modelling and Analysis of Water Wave Generation Due to Various Disturbances

Abstract

This thesisusesanalytictechniquestoanalyzeawiderangeofIVPthatmodelwavegeneration newlinebyarbitrarybottomandfreesurfacedisturbancesandtheirimpactonvarioustypesof newlinebreakwatersatlimitedorinfinitedepths.Theseissuesarisewithintherealmofocean newlineengineering. Thisworkpresentsamathematicalanalysisofvariousgenerationissuesofwater newlinewaves,assumingwatertobebothinviscidandviscous,aswellasincompressible,andofconstant newlinewaterdensity.Eachproblempresentedinthethesisisformulatedbasedontheassumptionof newlinelinearized theoryofwaterwaves.Oneofthekeyareasofstudyinwaterwaveproblemsfocuses newlineon thegenerationofsurfacewaves.Thewavemotionarisesprimarilyfromvariouskindsofinitial newlinedisturbances. Aninitialdisplacementofthefreesurfaceisthemodelforthecompleteeffectof newlinean explosionthathappensonorbelowthefreesurface,andaninitialimpulseatthefreesurface newlineis themodelforanexplosionthatoccursabovethefreesurface.Theinitialdisturbancescan newlinemanifest aseitheradepression(orelevation)ofthefreesurfaceoradistributionofimpulse,or newlineevenadelightfulcombinationofboth.Intheliteratureonthelinearizedtheoryofwaterwaves, newlinethe issueofwavemotioninthewatercausedbyanykindofinitialorgrounddisturbancein newlinethe fluidareaoratthesurfaceisprimarilyreferredtoasaCauchy-Poissonproblem.Theeffect newlineof wavegenerationduetobottomandfreesurfacedisturbancesisexaminedinthepresenceof newlinevariousconfigurationsatthefreeandbottomsurface,includingafloatingelasticplate,afloating newlineelastic membrane,currentatthefreesurface,aninertialsurface,porousslipperybottom,inertial newlinesurface andcurrent.Inadditiontohydrodynamicperformance,resultsonwavegenerationdue newlineto differentformsofbottomdisturbancessuchas:(a) G0(x) = eand#8722;x2 newline2 , (b) G0(x) = eand#8722;|x| and newline(c) G0(x) = and#948;(x) ,arealsodiscussed.Tounderstandandmonitorthewaterwavegeneration newlinecaused byatransientdisturbanceontheoceanbedformitigatingtheirpotentialimpactsand newlineensuring thesafetyofcommunitiesandecosystemsinaffectedregions.Theresultsofthisstudy newlinepresentanexcitingarrayofinformationonutilizingvarioussetups,includingfloatingelastic newlineplates, floatingmembranes,inertialsurfaces,wavecurrents,andporousslipperybot