Linear Stability of Katabatic Slope Flows with Ambient Wind Forcing

TL;DR

This study analyzes how ambient wind forcing affects the linear stability of katabatic slope flows, revealing complex interactions that challenge traditional stability criteria based solely on the gradient Richardson number.

Contribution

We extend Prandtl's slope flow model to include ambient wind forcing and identify two key parameters governing flow stability, introducing the wind forcing number as a novel factor.

Findings

Ambient wind can both stabilize and destabilize slope flows.

Two dimensionless parameters suffice to describe flow stability.

Current stability criteria like the gradient Richardson number are insufficient.

Abstract

We investigate the stability of katabatic slope flows over an infinitely wide and uniformly cooled planar surface subject to an additional forcing due to a uniform downslope wind field aloft. We adopt an extension of Prandtl's original model for slope flows (Lykosov & Gutman 1972) to derive the base flow, which constitutes an interesting basic state in stability analysis because it cannot be reduced to a single universal form independent of external parameters. We apply a linear modal analysis to this basic state to demonstrate that for a fixed Prandtl number and slope angle, two independent dimensionless parameters are sufficient to describe the flow stability. One of these parameters is the stratification perturbation number that we have introduced in Xiao & Senocak (2019). The second parameter, which we will henceforth designate the wind forcing number, is hitherto uncharted and can be interpreted as the ratio of the kinetic energy of the ambient wind aloft to the damping due to viscosity and stabilizing effect of the background stratification. For a fixed Prandtl number, stationary transverse and travelling longitudinal modes of instabilities can emerge, depending on the value of the slope angle and the aforementioned dimensionless numbers. The influence of ambient wind forcing on the base flow's stability is complicated as the ambient wind can be both stabilizing as well as destabilizing for a certain range of the parameters. Our results constitute a strong counter-evidence against the current practice of relying solely on the gradient Richardson number to describe the dynamic stability of stratified atmospheric slope flows.