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 found in the presence of non-flat surfaces, where it governs the dynamics of the areally-averaged velocity and involves renormalized effective parameters. Here, we analyze wind profiles over two-dimensional sinusoidal hills obtained both from numerical simulations performed with a primitive equation model and from wind-tunnel measurements. We show that also the local velocity profiles behave to a very good 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 a local log-law-of-the-wall involves effective parameters smoothly depending on the position along the underlying topography. This dependence looks very similar to the topography itself.