Numerical Study of Some Unstably Stratified Boundary-Layer Flows over a Valley at Moderate Richardson Number

Abstract

A two-dimensional numerical model is utilized to investigate steady-state, three-dimensional turbulent flow over a valley under unstable thermal stratifications. An eddy viscosity turbulence model is employed, in which the mixing length is a function of distance to the surface, shears of the mean velocity components, and a stability parameter involving Monin-Obukhov length. Three case studies are presented to show the effect of various surface temperature distributions on flow at bulk Richardson numbers in the vicinity of minus one. At such numbers the thermal effects of topography are of the same scale as the dynamic effects. Variables examined for each of the cases include the potential temperature and vorticity over the valley as well as the surface heat flux and shear stress. In addition, the shape and magnitude of the wind speed profiles over the two valley slopes are presented and discussed. Baroclinicity and thermally enhanced turbulent mixing are seen to play important roles. In all three cases the ambient momentum of the geostrophic wind is well-mixed down to the valley surface, preventing any local upslope flows over the windward slope from developing.