An Asymptotic Theory for the Flow over Heterogeneous Roughness

Abstract

The flow over arbitrary roughness changes is investigated, revisiting the analysis of Belcher et al. (Q J R Meteorol Soc 116:611–635, 1990) regarding surface-roughness heterogeneity. The proposed theory is restricted to steady neutral boundary layers over flat regions with changes of roughness sufficiently slow and mild to inhibit the growth of nonlinear terms. The approach is based on a triple-deck decomposition of the flow above the roughness, although only the first two layers are interactive at leading order. Two experimental datasets (one with a smooth-to-rough and the other with a rough-to-smooth transition) are used to validate the theory. The latter is further compared against two large-eddy simulations featuring chessboard patterns of alternating surface roughness with relatively short and long length scales, respectively. All the comparisons show that the proposed theory is able to reasonably assess the wind-field perturbation due to the roughness heterogeneity, supporting the use of the model to quickly assess the effect of roughness changes in the flow field.