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/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.

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