Baroclinic Instability of an Unbounded Zonal Shear Flow in a Compressible Atmosphere

Abstract

The study assumes adiabatic, inviscid, hydrostatic and quasi-geostrophic motions on a mid-latitude β-plane. The domain is assumed vertically unbounded. The stability of a hyperbolic-tangent shear flow to small-amplitude disturbances is discussed. Negative shear zones (wind becoming stronger westward with increasing elevation) are unstable for weaker shears and the resulting instabilities have larger growth rates than in the case with positive shear zones (wind becoming stronger eastward with increasing elevation) and other conditions the same. Neutral solutions for the hyperbolic-tangent shear flow problem are found analytically, and growth rates and modal structure of unstable modes are found numerically. The unstable modes for a negative shear flow and for sufficiently small longitudinal wavenumber have the structure of vertically propagating Rossby waves. Thus, the shear zone can act as a source of Rossby waves which couple the zonal wind within the shear zone to the mean zonal wind many, scale heights removed from the shear zone.