Baroclinic Instability of the Zonal Wind: Part III

Abstract

A zonal-wind configuration in which wind speed is proportional to pressure-altitude and stability is proportional to the square of the density is posed. A solution to the eigenvalue problem governing the stability of this configuration with respect to small disturbances is obtained in terms of hypergeometric functions. It is proved that one and only one (exponentially) unstable mode exists for each point in a wavelength, wind-shear plane.