APPLICABILITY OF BOUSSINESQ APPROXIMETION TO THERMAL INSTABILITY IN A SHEAR FLOW

Abstract

The validity of the Boussinesq approximation is investigated by making use of numerical solutions of perturbation equations for an unstably stratified shear flow. Examinations of stability properties indicate that the Boussinesq approximation is applicable to perturbations in an atmospheric layer for which the Mach number, M, the relative range of the potential temperature, e, and the ratio of the depth of the layer to that of the isentropic atmosphere, o, are much smaller than unity. When the Richardson number is large, the Mach number is necessarily small under the condition of small values of e and o.