Improvement Of Nonlinear Stability Criteria Of The Eady Model

Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are im-proved by establishing an optimal Poincare inequality. In this thesis the Poincare inequality is improved by deriving it directly from the Arnol’d’s second stability theorem by use of the idea of Fourier series and use it to improve the nonlinear stability of the Eady model. From differential calculus we know that every differen-tiable function can be expressed in Fourier series. When applied to the Eady model in periodic channel with finite zonal length, we get an improved nonlinear stability criteria for Eady’s model..