Downslope Windstorms. Part II: Effect of External Wind Shear

Abstract

The nonlinear, two-dimensional, steady-state, mesoscale problem of a stable stratified airflow above a mountain ridge is considered. The influence of turbulence is disregarded. It is assumed that the atmosphere above this flow is neutral and perturbations of the pressure in it are small. Generalizing from Smith, with the aim of approaching observational data, we assume that wind speed in an undisturbed flow approaching the ridge increases linearly with height. The problem is solved analytically through the use of a graphical method. By some transformations, nonlinear equations of mesometeorology are reduced to a linear ordinary equation of the third order with constant coefficients and to some transcendental algebraic equation that can be solved graphically. As a result of the solution, the shape of the flow surface and meteorological fields in the flow can be obtained. We analyze only the solution that describes the flow with a zone of severe downslope storm winds. Criteria for the existence of such solution are found and formulas for evaluation of the maximal possible wind speed and drag are constructed. On the basis of the solution obtained, some physical conclusions have been drawn and an example of the flow with a storm zone (which was calculated on the basis of observational data) is presented.