This video displays the surprisingly rich structure of instabilities of katabatic flows under the Prandtl model. Katabatic flows occur on mountain slopes during night time or over large ice sheets in Antarctica. They are important in numerical weather prediction models for regions with cold climate and complex topography, which in turn affects civil aviation, wind energy harvesting, and pollutant dispersion. Ludwig Prandtl originally derived an exact solution for gravity-driven flows over an infinitely wide inclined planar surface with a constant surface temperature. In our work, we discovered that this base profile is linearly unstable when the surface heat flux becomes sufficiently strong relative to the background stratification, as measured by a newly introduced stratification perturbation parameter. Two main modes of instability, namely a stationary longitudinal vortex mode as well as a traveling wave mode propagating in the slope direction, emerge. The slope angle determines which of these two instabilities is initially dominant. When the surface heat flux is strong enough, both instability modes become active and interact with each other in an intricate fashion. This rich palette of flow instabilities controlled by a few dimensionless flow parameters is reminiscent of the famous Taylor-Couette flow configuration, and a more thorough categorization of them may lead to an improved understanding of turbulent transition for katabatic winds.
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