A wind tunnel study of turbulent flow over model hills

Detailed wind tunnel measurements have been made of mean flow and turbulence over a two-dimensional ridge and a circular hill, both having cosine-squared cross-section and maximum slope about 15 °. The measurements were made in an artificially thickened neutrally stratified boundary layer, and have been compared with results from linear models and rapid distortion theory as appropriate.Our study shows that linear theory gives generally good predictions of the mean flow on the upwind side of the hills, and especially of the flow speedup at the hill top, but that the turbulence is less well predicted. In particular, the measurements show a major increase in the vertical component of turbulence and in the shear stress on the upwind slope of both the two- and three-dimensional hills which is not predicted by either equilibrium or isotropic rapid-distortion theories, although this may be partly due to the effect of streamline curvature. Rapid-distortion theory is successful only in describing the streamwise component of turbulence in the outer region of the flow, while in the upper part of the inner region of the flow, the turbulence measurements show disagreement with both the equilibrium and the rapid-distortion theories. Our experiments also confirm that the equilibrium region is a very thin layer close to the surface, while above this region and below the outer region, there is a transitional region where all terms in the stress equation are important.The measurements over the three-dimensional hill suggest that the mean flow and turbulence are broadly similar to those over the two-dimensional ridge, but with reduced perturbation amplitudes. The major differences between the two cases are found on the upwind slope and in the wake where, respectively, horizontal divergence and convergence of the three-dimensional flow are most pronounced.