Conditions for symmetric and nonsymmetric stability of geostrophic flows in a compressible atmosphere

The stability of zonal geostrophic flows in a linear approximation is studied. The quadratic conservation laws are used to find necessary and sufficient conditions for symmetric stability, i.e., stability with respect to perturbations independent of the coordinate along the flow. These conditions generalize those previously known to the case of a compressible medium. The generalized transfer equation for the potential vorticity (a linearized form) is formulated to describe the evolution of low-frequency long-wavelength perturbations. Within the framework of this equation, sufficient conditions for general (nonsymmetric) stability are found.