Wall-attached structures over a traveling wavy boundary: Turbulent velocity fluctuations

Abstract

The wall-attached structures of velocity fluctuations over a traveling wavy boundary are explored here by performing large eddy simulation (LES) at a moderate Reynolds number (Re-tau approximate to 1000). The wave slope is ak = 0.1, where a is the wave amplitude and k is the wave number. The prescribed wave age is c/u(*) = 2, where c is the wave phase speed and u(*) is the friction velocity. For comparison, the results of a LES over a smooth wall are also discussed. The wall-attached structures are self-similar with respect to their heights, and in particular the population density of their streamwise components scales inversely with their heights, which is reminiscent of a hierarchy of attached eddies. The wall-attached structures in the flow over the traveling wavy boundary retain geometric self-similarity; however, their streamwise length scale is decreased by the wavy boundary while their spanwise length scale is increased. By conditionally averaging the streamwise velocity fluctuations within the wall-attached structures, the reconstructed streamwise turbulent intensity was found to exhibit logarithmic behavior. The turbulent intensity carried by the small-scale wall-attached structures in the near-wall region is weakened by the traveling wavy boundary, while that of the large-scale wall-attached structures in the outer region is enhanced. The streamwise velocity corresponding to the highest uniform momentum zone for the large-scale wall-attached structures in the presence of the wavy boundary is larger than that for the smooth wall.