The Linear Stability of Nonlinear Mountain Waves: Implications for the Understanding of Severe Downslope Windstorms

Abstract

Two-dimensional vertically propagating steady state internal waves launched by the flow of stratified unboundedfluid over an obstacle of finite height are subjected to a linear stability analysis. Solution of the associatednonseparable boundary value problem reveals an abrupt change in the stability of small amplitude fluctuationswhen the obstacle is sufficiently high to cause streamlines to locally overturn. In addition to the convedvemode which is expected on the basis of even the simplest physical reasoning, a deep resonant mode is alsodiscovered. This resonant mode is, in fact, the dominant form of instability at small supercnticality, and it istrapped in the cavity between the ground and the level of maximum steepening of the streamlines, in which itgrows at the expense of the kinetic energy of the sheared flow which constitutes the finite-amplitude mountainwave. This trapped mode is instrumental in the transition which takes place in breaking mountain waves thatresults in the Occurrence of severe downslopc windstorms.