. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 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.

Zusammenfassung

In this book, data from a model ocean developed to compute free oscillations is used to analyze the LSA effect on tides and the synthesis of tides by free oscillation. It is also used to show the existence of six long-period planetary vorticity modes.

Inhalt
Theory and Model.- The Free Oscillations.- Synthesis of Forced Oscillations.- Synthesis of Forced Oscillations.