An Improved Bound for the Complex Phase Speed of Baroclinic Instability

Abstract

An improved bound is obtained for the radius of the semicircle in the complex plane containing the complex phase speed of baroclinically unstable plane wave disturbances. In the limit of long waves, this bound contains a term increasing with β and decreasing with the mean stratification (i.e., decreasing with the baroclinic Rossby radius of deformation). An extension of the bound, valid for finite wavelengths longer than order (δu/β)1/2, where δu is half the range of velocities in the mean shear flow, is also obtained.