Stability of non-planar shear flow of a stratified fluid

Abstract

The linear stability of non-planar shear flow of a stably stratified fluid is investigated. Howard's (1961) semicircle theorem, which places bounds on the range of the complex phase speed c, is derived, although sufficient conditions for stability of the (x-directed) basic flow . The source of instability for each mode is examined by means of computed energy transformations. However, numerical difficulties prevent a detailed examination of these unstable modes for α > 0·2.