Local law-of-the-wall in complex topography: a confirmation from wind tunnel experiments

It is well known that in a neutrally-stratified turbulent flow in a deep constantstress layer above a flat surface, the variation of the mean velocity with respect to the distance from the surface obeys the logarithmic law (the so-called “law-ofthe-wall”). More recently, the same logarithmic law has been found also in the presence of non flat surfaces. It governs the dynamics of the mean velocity (i.e. all the smaller scales are averaged out) and involves renormalized effective parameters. Recent numerical simulations analyzed by the authors of the present Letter show that a more intrinsic logarithmic shape actually takes place also at smaller scales. Such a generalized law-of-the-wall involves effective parameters smoothly depending on the position along the underlying topography. Here, we present wind tunnel experimental evidence confirming and corroborating this new-found property. New results and their physical interpretation are also presented and discussed. PACS: 83.10.Ji – 47.27.Nz – 92.60.Fm Boundary layer flows, Near wall turbulence In the realm of boundary layer flows over complex topography, much effort has been devoted in the last few years to investigate both the detailed form of the surface pressure perturbation arising from the interaction between the shear flow and the underlying topography (see, e.g., Refs. [1, 2, 3]) and its link with the effective parameters describing the large (asymptotic) scale dynamics (see, e.g., Refs. [4, 5]). The latter regime is selected by observing the flow far enough from the surface and, furthermore, considering solely the mean velocity. It is thus clear that with this approach all information on the dynamics at smaller scale becomes completely lost.