Stability of shear flows with multilayered density stratification and monotonic velocity profiles having no inflection points

Abstract

The stability of stratified shear flows with multilayered density distributions and monotonic velocity profiles without inflection points is studied using a class of flows of an ideal incompressible three–layer medium as a model. The flow velocity is assumed to be increasing from zero at the bottom () to its maximum value (when ), with everywhere. It is shown that such flows have two modes of eigenoscillations, fast and slow, which are both unstable for all wavelengths when the bulk Richardson number is small enough, , and are stabilized at sufficiently high J. For each mode, the configuration of its instability domain and the growth rate behaviour are studied in detail, as well as their dependence on the wavelength, J, relative magnitudes of density jumps, and the distance between the jumps. Physical mechanisms of the instability and the possibility of extending the results obtained to flows with a greater number of density interfaces are discussed.