Instabilities induced by variation of Brunt–Väisälä frequency in compressible stratified shear flows

Abstract

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible fluid in the presence of a lower rigid boundary are studied. A jump in the Brunt-Väisälä frequency at a level different from the shear zone is introduced and the variation of the Brunt–Väisälä frequency with respect to the vertical coordinate in the middle layer of the three-layered model is considered. An analytic solution in each of the layers is obtained, and the dispersion relation is solved numerically for parameters relevant to the model. The effect of shear in the lowermost layer of the three-layered model for a Boussinesq fluid is discussed. The results are compared with the earlier studies of Lindzen and Rosenthal, and Sachdev and Satya Narayanan. In the present model, new unstable modes with larger growth rates are obtained and the most unstable gravity wave modes are found to agree closely with the observed ones at various heights.