The onset of separation in neutral, turbulent flow over hills

The onset of separation in turbulent, neutrally stratified, boundary-layer how over hills is considered. Since the flows are fully turbulent, the occurrence of intermittent separation, in the sense of any reversal of near surface flow, will depend strongly on the detailed structure and behaviour of the turbulent eddies. Very little is known about such intermittent separation and the phenomenon cannot be studied with numerical models employing standard turbulence closures; eddy-resolving models are required. Therefore, here, as elsewhere in the literature, the arguably less physically significant process of mean flow separation is studied. Numerical simulations of how over idealised two- and three-dimensional hills are examined in detail to determine the lowest slope, theta(crit), for which the mean flow separates. Previous work has identified this critical slope as that required to produce a zero surface stress somewhere over the hill. This criterion, when a mixing-length turbulence closure is applied, reduces to requiring the near-surface vertical velocity shear to vanish at some point on the hill's surface. By applying results from a recent linear analysis for the flow perturbations to this condition, a new expression for theta(crit) is obtained. The expression is approximate but its relative simplicity makes it practically applicable without the need for use of a computer or for detailed mapping of the hill. The approach suggested differs from previous ones in that it applies linear results to a non-linear expression for the surface stress. In the past, a linear expression for the surface stress has been used. The proposed expression for theta(crit) leads to critical angles that are about twice previous predictions. It is shown that the present expression gives good agreement with the numerical results presented here, as well as with other numerical and experimental results. It is also consistent with atmospheric observations.