3国家重点基础研究发展规划项目(G1999032801)

3(G1999032801),(49825109)(49975020)3(,100029)(200218;2002322),,,,,.,,,Hamilton,P4331,.,.,,,.[1],,,.,,.,[2];,,.,.,,,3[35].,.,,().,[511].,Hamilton.Hamilton,[2].,,[12,13].,()().,,.2,:20120033JournaloftheGraduateSchooloftheChineseAcademyofSciencesVol.20No.1Mar.2003©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=-1acos99+u9u9+v39u9+f3v,9v9t=-1acoscos99+u9v9+v39v9-f3u,99t=-1acos99(u)+99(v3),(1)u,v,,,,a,,t,Ú3=2sin+utg/a,v3=vcos,=,U=u,V=v,ŽL1=u99+9u9,ŽL2=v399+9v39,ŽLŽL1+ŽL2,(1):9U9t+ŽLU=-1acos99+Ú3V,9V9t+ŽLV=-1acoscos99-Ú3U,99t+1acos99(U)+99(V3)=0,(2)F=(U,V,)TJ=ŽL-Ú31acos9.9Ú3ŽL1acoscos9.91acos9.91acos9cos.90,(3)(2)9F9t+JF=0.(4):J,(JF,F)=0,(3).(,,t),=h1,=h2,t=,FnijF(,,t)ij,,j,nt.F,G,ŠF=Fn+1+Fn2,F+t=Fn+1-Fn,ŠFtt=Fn+1+Fn-12,ŠF=Fi+12,j+Fi-12,j2,ŠF=Fi,j+12+Fi,j-122,F=Fi+12,j+Fi-12,jh1acosj,F=Fi,j+12+Fi,j-12h2acosj,(2):U+t+LU=-1acos+Ú3V,V+t+LV=-1acoscos-Ú3U,+t+1acos(U…)+(V3Š)=0.(5)LU=(uU)+uU+(v3U)+v3U,LV=(uV)+uV+(v3V)+v3V.(6)(5)9820©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(F)+t+JF=0.(7)J=L-Ú31acos()Ú3L1acoscos()1acos()1acos(cos)0.(8):(1)J,(7).(2)J,J.(5),,.,,(5):U+t+LU=-1acos…+Ú3V-RUn,V+t+LV=-1acoscos…-Ú3U-RVn,+t+1acos(U)+(V3)=-Rn(9)RF=ntBF,n,B.(9)(F)+t+JF=-RF.(10)==280,t=360s,Rossby2Haurwitz,.50,,,602.1En=12Ii=1Jj=1nijcosj(unij)2+(vnij)2+nijMn=Ii=1Jj=1nijcosjn,,n0.5.1/(m4/s4)/(m2/s2)n17618457506323.48175248645.43234900.4999947211492460107618457506323.46175248645.43234820.4999982754695059207618457506323.45175248645.43234960.4999984729997765307618457506323.46175248645.43234760.4999986031557488407618457506323.48175248645.43234850.4999988702854861507618457506323.46175248645.43234780.4999988239316499607618457506323.48175248645.43234950.4999988731868850707618457506323.43175248645.43234860.4999989734865475807618457506323.47175248645.43234790.4999990292554586907618457506323.51175248645.43234990.49999907868416241007618457506323.51175248645.43234830.4999912757234123,(1).1,:99©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=12sin+1acos9v9-9ucos9,(11)(1):9u9t+1acos9912(u2+v2)+-v=09v9t+1a9912(u2+v2)+-u=099t+1acos9u9+9vcos9=0.(12)Js:Js=01acos99-0-1a99-1acos99-1acos99cos0,(13)F=(u,v,)T,(12):9F9t=JsG.(14)G=u,v,12(u2+v2)+.H(F):H(F)=2-2cosd2012(u2+v2+)a2=12(u2+v2+)ds,(15)(12)9F9t=JsHF.(16)Js,J3s=JTs=Js;(16)Js,:dH(F)dt=H(F)F,9F9t=H(F)F,JsH(F)F=0.(17){T,S}=TF,JsSF,(18)Jacobi,(16)Hamilton,H(F)(16),(16)4,.(16),dFddt=JshHd(F)hFd.(19)10020©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=0d-¨-d0-¨¨T¨T0,(20)¨¨-1acos99-1a99.(19),,,Euler:Fn+1s-Fnst=Jn+12shHn+12shFn+12s.(21)Jn+12s=0n+12s-¨-n+12s0-¨¨T¨T0.n+12ij=1n+12ij2sinj-¨Tvn+12ij+¨Tun+12ij,Hn+12s=Hs(Fn+12s)=2ni=12n+1j=012un+12i,j2+vn+12i,j2+n+12i,jn+12i,ja2j2Rossby2Haurwitz(21)120(240s).2,().2/(m4/s4)/(m2/s2)/(1/s)17618457306235.04175248643.1728687-0.00000000000000001207618457306244.33175248643.17286790.00000000000000009407618457306240.22175248643.1728706-0.00000000000000008607618457306237.16175248643.17286920.00000000000000008807618457306244.37175248643.1728689-0.000000000000000091007618457306230.20175248643.1728696-0.000000000000000031207618457306238.05175248643.17287000.000000000000000214(1),,.(2),Hamilton,,Hamilton.,.(3),(4)J,F1F2:(JF1,F2)+(F1,JF2)=0.,.[14],.1,:101©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[1].,.:,1979[2],.HamiltonHamilton.,1991,1(2):102112[3],,.,,2001,18(1);5965[4],,..,2000,18(4):390394[5],,..,2002,19(4):362365[6],,..:.:,1980.300313[7],,..(),1988,166175[8]..:.:,1982[9],..,1987,11(2)[10]JiZhong2Zhen,WangBin.AFurtherDiscussionontheConstructionandApplicationofDifferenceSchemeofEvolutionEquations.Chi2neseJournalofAtmosphericSciences,1991,15(1):7281[11]WangBin,JiZhong2Zhen.HarmoniousDissipativeOperatorsandtheCompletelySquare2conservativeDifferenceSchemeinanExplicitWay.ScienceinChina,SerB,1994,37(4):462471[12]MZQin,WJZhu.ConstructionofSymplecticSchemesforWaveEquationviaHyperbolicFunctionsinh(x),cosh(x),tach(x).ComputerMathApplic,1993,26(8):111[13],,.Hamilton.,2001,18(4):289297[14],,..,2002,19(1):8285OntheTotalEnergyConservationandtheSymplecticAlgorithmJIZhong2ZhenWANGBinZHAOYingYANGHong2Wei(LASG,InstituteofAtmosphericPhysics,ChineseAcademyofSciences,Beijing100029,China)AbstractBasedonthetotalenergyconservation,twoimportantalgorithms,thetotalenergyconservationalgorithmandthesymplecticalgorithm,areestablishedforthesphericalshallowwaterequations.Also,therelationoftwoalgorithmsisanalyzed;andthenumericaltestsshowtheefficiencyofthealgorithms.Keywordsatmosphericandoceanicequations,conservativesystem,totalenergyconservation,Hamiltonian,symplecticscheme10220©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.