Experiments for a power law of near-surface mean velocity profiles in stratified boundary layers

Through a series of experiments in a wind tunnel, we study the near-surface profiles of the mean streamwise velocity in thermally stratified boundary layers. The surface is horizontal and is smooth or roughened by rods. We heat or chill this surface to achieve that stratification. Temperature-compensated hot-film anemometry is used to measure the mean streamwise velocity. Within the transition sublayer, lying in between the surface and the constant-flux sublayer, we find that the velocity profile is always a power-law function of the height from the surface. Its exponent ranges from 0.01 to 0.2 and increases with the surface roughness and the surface temperature. We summarize these findings in a formula and discuss its applications to the atmospheric boundary layer via the so-called Reynolds number similarity.