變分同化、變分最優(yōu)分析及流體動(dòng)力穩(wěn)定性中的若干問(wèn)題的研究.pdf

1、上海大學(xué)博士學(xué)位論文變分同化、變分最優(yōu)分析及流體動(dòng)力穩(wěn)定性中的若干問(wèn)題的研究姓名：滕加俊申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：流體力學(xué)指導(dǎo)教師：黃思訓(xùn)戴世強(qiáng)20070501上海大學(xué)博士學(xué)位論文ABSTI認(rèn)CTInthisthesis，sometheoreticalproblemsarestudiedinthedomainsofvariationaldataassimilation，variationaloptimizationanalysisandt

2、hefastgrowthofdisturbanceenergywithinfinintetimeintervalinatmospherescienceandhydrodynamicsThreemainpartsareincludedinthisworkFirstlytherelationbetweenthevariationaldataassimilationandregularizationisanalyzedandtheerrore

3、stimatesofvariationaldataassimilationmethodsforsomespecialmodelsaretheoreticallyresearchedSecondlyanimprovedvariationaldataassimilationmethodispresented，whichcombinestheoptimizationanalysiswiththeregularizationmethodandi

4、snamedasthedeneralizedvariationaloptimizationanalysismethod(GVOAM)，andthenusedintheanalysisof2Dand3Dwindfields；Thirdlythegrowthofdisturbanceenergyofalinearmodelwithinafiniteperiodoftimeistheoreticallyandnumericallyinvest

5、igatedwiththepresentedmethodTheobtainedresultsareofsignificanceinthedisasterweatherforecastingInthefirstpartofthisthesis，onconditionthattheglobalobserveddatahavebeenobtained，theinitialconditionsandtheparametersforadiffus

6、ionequationareoptimallymodifiedbyusingthevariationaldataassimilationmethod，andtheestimatesofpredictionerrorsaregivenTheimpactsoftheparameterandboundaryerrorsaswellasoftheobservationalandmodelerrors，onvariationalassimilat

7、ionanalysisareinvestigatedforthediffusionequationSomemathematicalmethodsareusedtodeterminetheconvergenceandtheconvergenceratesoftheassimilatedinitialvaluesandthepredictionsolutions，andthevariationalassimilationmethodisth

8、eoreticallyprovedtobeaneffectivemethodForgivenlocalobserveddata，inordertoovercomethedifficultiescausedbytheillposednessofinverseproblems，theTikhonovregularizationmethodisintegratedintothevariationaldataassimilationmethod

9、，resulinginanimprovedvariationaldataassimilationmethodTheconvergenceandconvergenceratesoftheassimilatedinitialconditionsandthepredictionsolutionsoftheimprovedmethodareanalyzedinthesamewayByintroducingtheappropriateregula