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1、ThispageintentionallyleftblankNon-lineardynamicsandstatisticaltheoriesforbasicgeophysicalflowsNon-lineardynamicsandstatisticaltheoriesforbasicgeophysicalflowsANDREWJ.MAJDANewYorkUniversityXIAOMINGWANGFloridaStateUniversitycambridgeuniversitypressCambridge,NewYork,Melbourne,Madri
2、d,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridgecb22ru,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521834414©CambridgeUniversityPress2006Thispublicationisi
3、ncopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2006isbn-13978-0-511-16813-0eBook(EBL)isbn-100-511-16813-6eBook(EBL)
4、isbn-13978-0-521-83441-4hardbackisbn-100-521-83441-4hardbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurlsforexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorap
5、propriate.ContentsPrefacepagexi1Barotropicgeophysicalflowsandtwo-dimensionalfluidflows:elementaryintroduction11.1Introduction11.2Somespecialexactsolutions81.3Conservedquantities331.4Barotropicgeophysicalflowsinachanneldomain–animportantphysicalmodel441.5Variationalderivativesand
6、anoptimizationprincipleforelementarygeophysicalsolutions501.6Moreequationsforgeophysicalflows52References582Theresponsetolarge-scaleforcing592.1Introduction592.2Non-linearstabilitywithKolmogorovforcing622.3StabilityofflowswithgeneralizedKolmogorovforcing76References793Theselecti
7、vedecayprincipleforbasicgeophysicalflows803.1Introduction803.2Selectivedecaystatesandtheirinvariance823.3Mathematicalformulationoftheselectivedecayprinciple843.4Energy–enstrophydecay863.5BoundsontheDirichletquotient,t883.6Rigoroustheoryforselectivedecay903.7Numericalexperimen
8、tsdemonstratingfacetsofselectivedecay95Referenc
