Shallow katabatic flow on a non-uniformly cooled slope

Abstract We examine katabatic flow driven by a non-uniformly cooled slope surface but unaffected Coriolis acceleration. A general formulation is given, valid for non-uniform buoyancy distributions over down-slope length scale $$L\gg \delta _0$$ L ? ? 0 , where $$\delta _0=\nu /(N\sin \alpha )^{1/2}$$ = ? / ( N sin ? ) 1 2 the slope-normal Prandtl depth, kinematic viscosity $$\nu$$ frequency N and angle $$\alpha$$ . demonstrate that similarity solution of Shapiro Fedorovich (J Fluid Mech 571:149–175, 2007) can remain quantitatively relevant local to end region. The usefulness steady determined spatial eigenvalue problem on L scale. Broadly speaking, there are also two modes temporal instability; stationary aligned vortices propagating waves. By considering limiting inviscid stability problem, we show origin vortex mode oscillation profile normal slope. This leads growth in region displaced from surface, at point inflection, just as owe their existence an inflectional velocity. Non-uniform flows detrain fluid ambient shown further destabilise whereas entraining lead weaker rates. Rayleigh waves dominate general, become more significant small angles quantify relative