广义 Eady 模型的非线性稳定性

数学物理学报 ›› 2008, Vol. 28 ›› Issue (6): 1002-1014.

广义 Eady 模型的非线性稳定性

蔡景景|刘永明

(华东师范大学数学系上海 200062)

收稿日期:2006-10-28 修回日期:2008-06-10 出版日期:2008-12-25 发布日期:2008-12-25
通讯作者: 蔡景景
基金资助:
上海市重点学科项目和教育部博士点基金(20060269012)资助

Nonlinear Stability of Generalized Eady Problem in Finite Periodic Channel

Cai Jingjing|Liu Yongming

(Department of Mathematics, East China Normal University, Shanghai 200062)

Received:2006-10-28 Revised:2008-06-10 Online:2008-12-25 Published:2008-12-25
Contact: Cai Jingjing

摘要/Abstract

摘要：

对于广义 Eady 模型, 分别讨论了密度函数是常数函数与指数函数两种情形, 利用变分原理,
考虑到动量守恒的约束条件, 得到了优化的 Poincaré不等式, 从而得到了新的非线性稳定性定理, 并且得到了在径向长度分别不大于纬向长度的0.84402倍及 0.86068 倍时(这对于地球的实际情况是成立的), 非线性稳定性判据与线性稳定性判据是一致的.

关键词: 非线性稳定性, 准地转流, 广义 Eady 模型

Abstract:

Nonlinear stability criterion for the generalized Eady model is improved by
establishing an optimal Poincaréinequality. The inequality is derived from a variational calculation considering an additional constraint of invariant
of zonal momentum. Two cases that ρ(z)=ρ₀ and ρ(z)=ρ₀e-^z/Hare discussed, respectively, where ρ(z) is the prescribed reference-state density and ρ₀ is a constant. The improved nonlinear stability criteria are the same as the linear ones provided that the ratios of the meridional width to the channel length are less than or equal to 0.84402 for the case one and 0.86068 for the case two, respectively.

Key words: Nonlinear stability, Quasi-geostrophic flow, Generalized Eady model

中图分类号:

35A15

蔡景景|刘永明. 广义 Eady 模型的非线性稳定性[J]. 数学物理学报, 2008, 28(6): 1002-1014.

Cai Jingjing|Liu Yongming. Nonlinear Stability of Generalized Eady Problem in Finite Periodic Channel[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1002-1014.

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