Local log-law of the wall: numerical evidences and reasons

Abstract

Numerical studies performed with a primitive equation model on two-dimensional sinusoidal hills show that the local velocity profiles behave logarithmically to a very good approximation, from a distance from the surface of the order of the maximum hill height almost up to the top of the boundary layer. This behavior is well known for flows above homogeneous and flat topographies (`law-of-the-wall') and, more recently, investigated with respect to the large-scale (`asymptotic') averaged flows above complex topography. Furthermore, this new-found local generalized law-of-the-wall involves effective parameters showing a smooth dependence on the position along the underlying topography. This dependence is similar to the topography itself, while this property does not absolutely hold for the underlying flow, nearest to the hill surface.