This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.
ThisbookdependsonadissertationpreparedattheDepartementofGeosciencesat theUniversityHamburg. ItwasacceptedbytheDepartementwiththegradesumma cumlaudein2008. IwouldliketothankmyacademicadvisorProf. Dr. WilfriedZahelforhisconstant supportandforthelongandconstructivediscussions. Further,IwouldliketothankProf. Dr. Jur .. genSundermann .. forintroducingmeto theInternationalMaxPlanckResearchSchool. TheInternationalMaxPlanckResearchSchoolforMaritimeAffairsandinparticu larProf. Dr. Dr. h. c. Jur .. genBasedowandhisco directorsarethankedforgivingme theopportunitytoperformthisstudyinHamburg. IacknowledgethecomputationalsupportoftheDKRZandNEC,especiallythe helpfulcommentsofKlausKetelsenandJens OlafBeismann. LastbutnotleastmanythankstomywifeJanaSillmannandmysonDariusfor givingmethetimeIneededforthisstudyandprovidingajoyfulandlovinghome. ThisworkhasbeenfundedbytheInternationalMaxPlanckResearchSchoolfor MaritimeAffairsattheUniversityHamburg. Hamburg,August2008 MalteMuller .. Contents Abstract…1 1 Introduction…3 2 TheoryandModel …7 2. 1 Theory …7 2. 1. 1 SecondaryForces:TheLoadingandSelf AttractionEffect . 8 2. 1. 2 TheEquationsofMotionandtheEquationofContinuity…11 2. 1. 3 EnergyBalance…1 4 2. 1. 4 ParameterizationoftheLSA AnAnalyticalApproach …16 2. 2 Model…18 2. 2. 1 TheImplicitlyRestartedArnoldiMethod…19 2. 2. 2 TheParallelizationwithMPI …21 2. 2. 3 ThePerformanceoftheModel…21 3 TheFreeOscillations…23 3. 1 GravitationalModes…23 3. 1. 1 The? value…24 3. 1. 2 TheIn?uenceoftheLSA …25 3. 1. 3 TheAntarcticKelvinWave…30 3. 1. 4 NewModes…30 3. 1. 5 TheSlowestModes …31 3. 2 VorticityModes…32 3. 2. 1 TopographicalVorticityModes…32 3. 2. 2 PlanetaryVorticityModes…34 4 SynthesisofForcedOscillations…39 4. 1 TidalDynamicsandtheIn?uenceofLSA…40 4. 1. 1 TheProcedureofTidalSynthesis…40 4. 1. 2 LSA effectonForcedOscillations…45 4. 1. 3 TheSynthesisoftheSemidiurnalandDiurnalTides…50 xi xii Contents 4. 2 IntegrationoftheSolutionsofaTidalModelwithAssimilationof Data…55 4. 2. 1 NewExpansionCoef?cients…55 4. 2. 2 NewFrequenciesandAdjointEigenfunctions …59 4. 2. 3 Results…61 4. 2. 4 Summary…70 4. 2. 5 Discussion…71 5 Conclusion …73 Figures…75 Tables…101 Appendix…105 ListofSymbols …109 References…113 Index …1 17 Abstract AnewsetofbarotropicfreeoscillationsoftheWorldOceaniscomputedwithex plicitconsiderationofdissipativetermsandthefulloceanloadingandself attraction effect(LSA). Thissetcontainsfreeoscillationsthatdidnotappearinthespectraof previousstudies. Furthermore,theexpansiontowardslongerperiods(165hours) yieldsnewglobalplanetarymodes. Altogether169freeoscillationsarecomputed withperiodslongerthan7. 7hours. Ofthese,71aregravitationalmodes,92areto pographicallycontrolledvorticitymodes,and6areplanetaryvorticitymodes. The in?uenceoftheLSAisinvestigatedforallthreekindsofmodeswithrespectto changesintheperiodsandinthespatialstructureoftheseasurfaceelevationand thehorizontalmasstransports. Inparticular,formodesinthesemi diurnalanddi urnalperiodrange,theparameterizationoftheLSAisanalyzed. Forthefreeoscillationsintheperiodrangefrom9to40hoursthecorresponding adjointsolutionsarecomputedandusedtosynthesizesemidiurnalanddiurnaltides ofseconddegree. Sincethesefreeoscillationsaredeterminedwithandwithoutcon siderationofthefullLSA effect,thisstudyallowsforadetailedanalysisoftheLSA onthedynamicsofoceantides,e. g. anphysicalexplanationisgivenfortheinduced phasedelaycomputedbyoceantidemodels. Further,thesynthesisgivesaspectral compositionofcertainwellknowntidalfeaturesandpairsoffreeoscillationsare identi?ed,diminishingtheircontributioneitheronaglobalorlocalscale. Further,semidiurnalanddiurnaltidalsolutionsofatidalmodelwithassimilation ofdataareintegratedintheprocedureofsynthesizingtides.
