Air flow over a two‐dimensional hill: Studies of velocity speed‐up, roughness effects and turbulence

Wind tunnel measurements have been made of the streamwise mean and turbulent velocities over a rough, bell‐shaped, two‐dimensional hill, with height h and maximum slope 0.26, placed in a neutrally stable boundary layer of thickness 10 h and roughness length z o = 0.02 h. Close agreement is found between the mean velocity and predictions obtained from Taylor's (1977) computational model and Jackson and Hunt's (1975) analytical linearized model, for locations at or upwind of the hill top but not in the wake. Examination of the models shows that the shear stresses are only important in an inner region close to the hill surface, so that, as suggested by Jackson and Hunt (1975), the perturbation to the mean flow outside this region is essentially inviscid. the theory shows that over very rough surfaces, such as wooded or urban terrain, the height of this inner region can be of the same order as the height of the roughness elements (so that in our experiments no measurements could be made in this region). In a second experiment flow over a smooth hill on a rough surface was studied. the additional increase of wind speed over the hill top can be estimated by assuming a linear superposition of the velocity changes produced by the changes in elevation and in surface roughness (in this case rough to smooth). In the lee of a hill, however, the change in roughness significantly alters the flow with flow separation being suppressed and here a linear superposition is not appropriate. Finally we consider why observed changes in turbulence structure close to the surface differ from those well above the surface. Calculations of these changes based on the simple theoretical arguments of equilibrium shear layers and rapidly distorted turbulent flows agree well with turbulence measurements in wind tunnels and in the field.