Stability of Theoretical Model for Catastrophic Weather Prediction
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摘要: 详细讨论、分析了涉及灾害性天气预报的理论模式的稳定性，这些模式包括：非静力完全弹性方程组、滞弹性方程组．证明了非静力完全弹性方程组在无穷可微函数类中是稳定方程；滞弹性方程组则因为对流体的特殊假设，改变了连续方程的形式，于是出现了“流体为粘性与不可压假设的匹配”现象，从而使在实际预报工作中占有重要地位的这一类重要方程组与Navier-Stokes方程呈现了相同拓扑性质的不稳定性，而这是在数值预报工作中首先应该避免的．据此提出了如何修改应用模式的参考意见．
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关键词:
- 非静力完全弹性方程组 /
- 滞弹性方程 /
- 不稳定方程 /
- 匹配
Abstract: Stability related to theoretical model for catastrophic weather prediction that includes non-hydrostatic perfect elastic model, anelastic model was discussed and analyzed in detail. It was proved that in infinitely differentiable function class non-hydrostatic perfect elastic equations set is stable. However, for anelastic equations set, its continuity equation is changed in form because of the particular hypothesis for fluid, so/the matching consisting of both viscosity coefficient and incompressible assumption-appears, thereby the most important equations set of this class in practical prediction shows the same instability in topological property as Navier-Stokes equation, which should be avoided first in practical numerical prediction. In light of this, the referenced suggestions to amend applied model are finally presented. -
[1] 张玉玲.中尺度大气动力学引论[M].北京：气象出版社，1999，1-16,291-298. [2] 沈桐立，田永祥，葛孝贞，等.数值天气预报[M].北京:气象出版社,2003,355-380. [3] 吕美仲,侯志明,周毅.动力气象[M].北京：气象出版社，2004,37-54. [4] 刘式适,刘式达.大气动力学[M].北京:北京大学出版社,1999, 1-33. [5] SHIH Wei-shu.Stratifications et Equations aux Derivees Partielles, Singularities of Maps,and Applications to Differential Equations[M].Collections Travaux en Cours.54.Paris:Hermann,1997, 95-124. [6] 施惟慧,陈达段,何幼桦.分层理论与非线性偏微分方程基础[M].上海:上海大学出版社，2001, 10-52，134-189. [7] Landau L,Lifchitz E.Mecanique des Fluides[M].Moscow：Editions Mir,1971,62-122. -
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