  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.
