Baroclinic Instability in the Generalized Phillips’ Model Part I: Two-layer Model

By employing Arnol’d’s method (energy-Casimir), this paper has studied the nonlinear stability of the two-layer generalized Phillips’ model for which the top and bottom surfaces are either rigid or free, and obtained some nonlinear stability criteria. In addition, some linear stability criteria are obtained by normal mode method. The re-sults reveal the influences of the free surface parameter on the stability of atmospheric and oceanic motions