We introduce a quasi-analytical model of thermally induced fl ows in valleys with sloping fl oors, a feature absent from most theoretical valley wind studies. One of the main theories for valley winds the valley volume effect emerged from fi eld studies in the European Alps in the 1930s and 1940s. According to that theory, along-valley variations in the heating rate arising from variations in valley geometry generated the pressure gradient that drove the valley wind. However, while those early studies were conducted in valleys with relatively fl at (horizontal) fl oors, valleys with sloping fl oors are ubiquitous and presumably affected directly by slope buoyancy (Prandtl mechanism). Our model is developed for the Prandtl setting of steady fl ow of a stably stratified fl uid over a heated planar slope, but with the slope replaced by a periodic system of sloping valleys. As the valley characteristics do not change along the valley, there is no valley volume effect. The 2D linearized Boussinesq governing equations are solved using Fourier methods. Examples are explored for symmetric (with respect to valley axis) valleys subject to symmetric and antisymmetric heating. The fl ows are 2D, but the trajectories are intrinsically 3D. For symmetric heating, trajectories are of two types: i) helical trajectories of parcels trapped within one of two counterrotating vortices straddling the valley axis and ii) trajectories of environmental parcels that approach the valley horizontally, move under and then over the helical trajectories, and then return to the environment. For antisymmetric heating, three types of trajectories are identified.
原文链接
分享
引用
