Nature of Oscillations in Prandtl Katabatic Slope Flows*

Damped en masse oscillations have been observed in Prandtl slope flows. Here, we investigate katabatic Prandtl slope flows with a homogeneous negative heat flux and against a constrant prescribed stable stratification at dynamically unstable regimes for a range of slope angles. Numerical simulations confirm the existence of distinct primary and secondary flow instabilities creating aperiodic temporal and spatial oscillations in the flow. Stationary longitudinal rolls appear at shallow slopes. When the dimensionless stratification perturbation number π_s is increased slightly, stationary rolls meander as a result of  secondary instabilities. The average spacing between vortical rolls depends strongly on surface inclination for slope angles less than 35^?. Vortical rolls oriented in the spanwise direction emerge as travelling waves at very steep slope angles. Secondary instabilities causes these spanwise rolls to bend and bifurcate with increasing π_s. We compare the nature of en masse oscillations against the oscillations caused by the aforementioned flow instabilities. We find that in the dynamically unstable non-turbulent regime, en masse oscillations are insignificant, but its normalised frequency serves as a useful metric to discern the type of flow instabilities.