| Stability of theoretical model for catastrophic weather prediction |
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| 作者姓名： | 施惟慧 王曰朋 |
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| 作者单位： | [1]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China [2]Department of Mathematics, Nanjing University of Information Science ＆ Technology, Nanjing 210044, P. R. China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006)，the Post-Doctoral Science Foundation of Jiangsu Province of China(No.0602024C) |
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| 摘 要： | Stability related to theoretical model for catastrophic weather prediction, which includes non-hydrostatic perfect elastic model and anelastic model, is discussed and analyzed in detail. It is proved that non-hydrostatic perfect elastic equations set is stable in the class of infinitely differentiable function. However, for the 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 the applied model are finally presented.
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| 关 键 词： | 灾难性天气 天气预报 理论模型 稳定性 非流体静力学理想弹性方程 滞弹性模型 |
| 收稿时间： | 2005-01-20 |
| 修稿时间： | 2006-12-12 |
Stability of theoretical model for catastrophic weather prediction |
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| Shi?Wei-hui,Wang?Yue-peng.Stability of theoretical model for catastrophic weather prediction[J].Applied Mathematics and Mechanics(English Edition),2007,28(4):553-561. |
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| Authors: | Shi Wei-hui Wang Yue-peng |
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| Institution: | 1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
2. Department of Mathematics, Nanjing University of Information Science & Technology, Nanjing 210044, P. R. China |
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| Abstract: | Stability related to theoretical model for catastrophic weather prediction, which includes non-hydrostatic perfect elastic model and anelastic model, is discussed and analyzed in detail. It is proved that non-hydrostatic perfect elastic equations set is stable in the class of infinitely differentiable function. However, for the 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 the applied model are finally presented. |
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| Keywords: | non-hydrostatic perfect elastic equations set anelastic equation unsteady equation matching |
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