The height of maximum speed-up in the atmospheric boundary layer flow over low hills

Abstract

In this paper, we study the height of the maximum speed-up, l, for atmospheric boundary layer flows over low hills in a neutral atmosphere. A recent analytically-derived expression for l is compared to the results of several other expressions available in the literature. A critical analysis of all these equations is presented and a new constant obtained from field data is proposed for one of them. We find that the new expression describes observational data better than the others. Through an order of magnitude analysis, we also show that the inner layer depth, calculated as the height where inertia and turbulent forces dominate the other terms and balance each other in the x-momentum equation, can also be used to estimate the height of maximum speed-up. Starting from four analytical speed-up profiles available in the literature, we calculate l by searching for the critical points of these speed-up functions, resulting in new equations for l. All these equations are analysed and our results suggest which one of them performs better when compared to field and wind tunnel data.