Local Log-Law-of-the-Wall in Neutrally-Stratified Boundary-Layer Flows

It is well known that in a neutrally-stratified turbulent flow in a deep constant-stress layer above a flat surface,the horizontal mean velocity varies logarithmically with height (the so-called `log-law-of-the-wall').More recently, the same logarithmic law has also been foundin the presence of non-flat surfaces, where it governs thedynamics of the areally-averagedvelocity and involves renormalized effective parameters.Here, we analyze wind profiles over two-dimensional sinusoidal hillsobtained both from numerical simulations performed with a primitiveequation model and from wind-tunnel measurements. We showthat also the local velocity profiles behave to a verygood approximation logarithmically, for a distance from the surface of the order of the maximum hill height almost to the top of the boundary layer. Such alocal log-law-of-the-wall involves effective parameters smoothly depending on theposition along the underlying topography.This dependence looks very similar to the topography itself.