In the idealised problem considered, the upwind velocity profile is independent of height (above the boundary layer) and directed normal to an isolated two-dimensional ridge. The upstream stratification consists of a neutral layer immediately above the ground which is capped by a sharp temperature inversion. Above the inversion the flow is stably stratified and the Brunt-Vaisala frequency is independent of height. A range of inversion strengths (measured by the difference in potential temperature across the inversion) and inversion heights, some above and some below the mountain top height, are considered.
The dependence of the flow on the Froude number (defined in the same way as for a two-layer shallow water flow) and the ratio of mountain height to inversion height is investigated and presented in terms of a flow regime diagram. Linear theory is used in parallel to study the required conditions for different flow types.
The idealised numerical results are also compared to recent observations of near-surface flow across a mountain ridge on East Falkland (south Atlantic) where the presence of a strong temperature inversion influences the formation of rotors and strong downslope winds.