The Instability of Long's Stationary Solution and the Evolution toward Severe Downslope Windstorm Flow. Part I: Nested Grid Numerical Simulations

Abstract

Through direct numerical simulation, the instability of Long's exact finite-amplitude steady-state solution to the problem of stratified flow over topography and the subsequent evolution towards severe downslope windstorm flow is investigated. The integrations are initialized with Long's analytical solution and are calculated in a model domain that employs three levels of interactive grid nesting. In this manner, the resolution achieved is approximately a factor of 10 greater than that previously employed. As a result of this increased resolution, three distinct stages of windstorm development are explicitly identified. In the first, convection acts to neutralize the region of overturned isentropes. During the next stage, a large-amplitude stationary disturbance develops above the lee slope of the topography. In time, small-scale secondary shear instability develops in local regions of enhanced shear associated with flow perturbations caused by the large-amplitude disturbance. In the final stage of development, these modes of shear instability evolve to larger spatial scale and come to dominate the flow in the mature windstorm state. In our analysis, it is furthermore demonstrated that these stages of development can be qualitatively and, to some extent, quantitatively reproduced in a parallel flow extracted from a cross section through Long's solution if a horizontally localized forcing, designed to enhance the vertical shear in the background wind field, is imposed.