Stability of a Continuous Baroclinic Flow in a Zonal Magnetic Field

Abstract

The properties of quasi-geostrophic, baroclinic flow in a zonal magnetic field, as formulated previously by the writer, are examined for a zonal flow profile of hyperbolic tangent form in the vertical coordinate. The stability problem is shown to be mathematically equivalent to a stratified shear flow problem considered by Drazin, with a magnetic Richardson number replacing the ordinary Richardson number of stratified shear flow. The marginal stability curve is found and indicates that, contrary to the two-layer case, there is a short-wave cutoff for unstable waves, and sufficient reduction of the channel width can render all waves stable. The hyperbolic tangent profile represents essentially a thin baroclinic layer in a vertically unbounded atmosphere. A layer qualitatively of this type might be produced in the convective zone of the sun through the influence of rotation on the supergranulation or granulation scale motions, in the manner suggested by the writer and other authors previously.