Dr. Alan Shapiro is Professor Emeritus at the University of Oklahoma’s School of Meteorology. He studies geophysical fluid dynamics.
Co-author: Matheus Gomes
We introduce a quasi-analytical model of thermally-induced flows in valleys with sloping floors, a feature absent from most idealized valley wind studies. Valley winds were studied particularly intensively in the 1930s and 1940s in major valleys in the European Alps. Because of the relative flatness of those valleys, the slope buoyancy effect could not explain the winds blowing through them. Modern theories for valley winds have focused on a valley volume effect in which along-valley variations in heating rates arising from along-valley variations in cross-sectional area generate the pressure gradient that drives the flow. However, valleys with inclined floors are ubiquitous and presumably affected by the slope buoyancy effect. Our model is developed for the Prandtl setting of steady flow of a stably stratified fluid over a heated/cooled planar slope but with the slope replaced by a periodic system of sloping valleys. As there are no along-valley variations, there is no valley volume effect. The 2D linearized Boussinesq governing equations are solved using Fourier methods. The structure of the wind and buoyancy fields are explored in several examples. Although the flow is 2D (Eulerian), the trajectories are intrinsically 3D. For the case of a uniformly heated symmetric valley, environmental air parcels approach the valley horizontally, move tangent to the valley slope near the surface, ascend a sidewall, turn back toward the valley center, and then return to the environment, while air parcels not originating in the environment are trapped in one of the two counter-rotating vortices straddling the valley center.