A model study of pure katabatic flows

A time-dependent 2-dimensional model of pure katabatic flow over a simple finite-length slope is described. This numerical model, based on a turbulent kinetic energy closure, accounts for the effects of radiative cooling and turbulent friction at the surface, and entrainment of air aloft from a quiescent stably stratified ambient atmosphere. The model provides information on the temporal and spatial evolution and structure of katabatic flows. Numerical solution of the governing equations facilitates explicit determination of the coefficient of entrainment, slope Richardson number, profile-shape factors, and depth, velocity, and buoyancy-deficit scales of the flow. The steady-state results of the model, showing the variations of these parameters as functions of downslope distance, slope angle, and ambient stratification, are presented and discussed. For near-neutral stratification, the calculated entrainment coefficient varies as a function only of the slope Richardson number, in agreement with laboratory data. As ambient stratification increases, it profoundly affects the structure of the flow by reducing its depth, speed and entrainment rate. The results and parameterizations presented here can be used as inputs to hydraulic models of drainage flow and pollutant transport.