A Predictive Analytical Model for Surface Shear Stresses and Velocity Profiles Behind a Surface Roughness Jump

Abstract

A simple analytical model is developed for the flow downwind of a step change of the aerodynamic roughness length in the atmospheric boundary layer. The region downwind of the roughness transition is assumed to be composed of two equilibrium layers, corresponding to the downwind and upwind conditions, and separated by a third, transition, layer. The key assumption in deriving the model is that the eddy viscosity in the transition region is composed of a linearly varying component and an augmentation, which is parabolic in the vertical coordinate. The model is fully predictive up to two parameters that need to be specified. The first parameter is the ratio between the equilibrium boundary-layer height and the internal boundary-layer height. The second parameter controls the degree of nonlinearity of the eddy viscosity augmentation. An empirical relation is developed for the first parameter, while a range of values (between 0.1 and 0.3) is recommended for the second. The model is tested with results from field observations, wind-tunnel experiments, and numerical simulations of the flow behind a sudden jump in surface roughness. These tests show that the flow field and surface stresses are predicted accurately for smooth-to-rough as well as rough-to-smooth transitions.