Analytical and Numerical Investigation of Two-Dimensional Katabatic Flow Resulting from Local Surface Cooling

摘要

The analysis of katabatic flows is often complicated by heterogeneity in surface characteristics. This study focuses on an idealized type of katabatic flow driven by a simple form of inhomogeneous surface forcing: a buoyancy or buoyancy flux that varies down the slope as a top-hat profile (cold strip). We consider the two-dimensional Boussinesq system of governing flow equations with the slope angle, Brunt-Vaisala frequency, and coefficients of eddy viscosity and diffusivity treated as constants. The steady-state problem is solved analytically in a linearized boundary-layer framework. Key flow structures are a primary katabatic jet (essentially the classical one-dimensional Prandtl jet), a rotor-like feature straddling the upslope end of the strip, and two nearly horizontal jets: an inward jet of environmental air feeding into the primary jet on the upslope end of the strip and an outward jet resulting from the intrusion of the primary katabatic jet into the environment on the downslope end of the strip. Next, the corresponding nonlinear initial value problem is solved numerically until a steady state is reached at low levels. The main features of the linear solution are seen in the numerical results, but with some notable differences: (i) the primary jet in the numerical simulation requires a longer distance to attain a one-dimensional boundary-layer structure and extends further downslope off the strip before intruding into the environment; (ii) the numerically simulated outward environmental jet is narrower and more intense than the inward jet, and has a pronounced wave-like structure.