Stably stratified shear flow over low hills

An analysis is presented for the mean flow over hills with low slopes, for various kinds of stable stratification in the approach flow. (The Froude number F based on the height is always greater than unity.) The analysis is based on dividing up the flow into different regions with different dynamics. We concentrate on the flow in the inviscid outer region of the flow. It is shown that in the lower part of the outer region, the middle layer, where the shear is large, the upwind velocity profile and the shape of the hill, rather than the upwind density profile, largely determine the vertical perturbation velocity. In the ‘upper layer’ the structure of the flow depends largely on the form of the upwind density profile. For example, this largely determines the location of maximum surface wind. New solutions for stable conditions are obtained when there is a constant density gradient, when (N/UB) 2 ∞ z −2 and when there is an elevated inversion layer. In the first and third of these cases, we compare the results with the hydrostatic approximation, and also obtain new general formulae for the near‐surface winds. An approximate formula is developed for surface winds at arbitrary values of F (>1) for uniform stable stratification.