Large-Eddy Simulation of the Up-slope Boundary Layer

Abstract

Large-eddy simulation (LES) is used to determine the turbulent structure of the steady-state up-slope boundary layer (UBL) which forms at a uniformly heated inclined or vertical plane surface below a stratified atmosphere at rest. At proper scales, the problem depends solely on the slope angle a and the surface roughness height z₀ a relative to a length scale H which is a function of stratification and surface heating. We cover 2° ≤ α ≤ 90° and 3 × 10^-5 ≤ z₀/H ≤ 3 × 10^-2 by a series of LESs. Simulations using different grids show that the results are only weakly sensitive to truncation errors. the UBL approaches a steady-state mean-profile by slowly decaying oscillations; its frequency equals the Brunt-Väisälä frequency times sin α. In the LES, convergence towards steady state has been enforced by adjusting the fields according to integral steady-state conditions. For α ≤ 10°, a well-mixed layer is formed which causes a strong temperature inversion and strong down-slope flow at the outer edge of the UBL. Large-scale coherence is weak with some indications of cross-slope rolls for small inclination angles and longitudinal rolls for steep slopes. Several mean quantities have been tabulated as a function of slope angle and surface roughness and approximating power laws are given. the dependence of mean quantities on the slope angle is difficult to explain with simple models, but the influence of surface roughness closely follows earlier results.