An improved bound for the complex phase speed of baroclinic instability

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