A Large Spectrum of Free Oscillations of the World Ocean Including the Full Ocean Loading and Self-attraction Effects

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 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. . . . .

Detailed overview of the effect of loading and self-attraction Tables of all gravitational and planetary vorticity modes Includes supplementary material: sn.pub/extras

Texte du rabat

The ocean tides are the most prominent forced oscillations in the global ocean. Recent research showed that tides play an important role for the earth's climate system and they are of considerable interest for the post-processing of satellite data. To understand these oscillations it is substantial to determine and analyse the free oscillations, which describe the oscillation behaviour of the global ocean. A highly efficient ocean model is developed to compute these free oscillations with explicit consideration of dissipative terms and the full ocean loading and self-attraction (LSA). The obtained spectrum of free oscillations enables e.g. an detailed analyses of the LSA effect on tides, the synthesis of tides by free oscillations and to show the existence of six long period planetary vorticity modes.

Résumé
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.

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