广义 Eady 模型的非线性稳定性

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.

Nonlinear Stability of Generalized Eady Problem in Finite Periodic Channel

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/H are 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.