Coriolis effects on orographic and mesoscale flows

A perturbation theory is developed for the effects of rotation on stably stratified flow over mountains at low Froude number, F = U_O/(N H) where N is the buoyancy frequency, U_O is the wind speed and H is the mountain height. The Rossby number, R_O = U_O/(f D) where f is the Coriolis parameter, and D the along-wind length of the mountain, is assumed to be a large number. The mountain width, β D, is assumed to be larger than D. Typically R_O is found to lie in the range 3-10. The results are compared with the recent numerical simulations. It is found that as the flow impacts on the mountain, in the northern hemisphere it turns to the left (with your back to the wind); also wave activity over the top of the mountain is greatest on the left side but the pressure drop is greatest on the right in the northern hemisphere. Over the Rossby deformation distance, L_R, of the order of H N /f, e.g. 150 km for the Pyrenees, a new wake structure develops that can extend downwind over 1000 km (or a spin-down distance). There is a momentum defect within the wake but the wind speed increases either side of the wake. Coriolis forces induce a deflection upwards of the isopycnals (and hence more precipitation) on the left, and downwards on the right; this is consistent with some of the differences in mesoscale weather and climate phenomena that are observed on the different flanks of elongated mountains and between the different side of wide valleys, and also in the wakes downwind of mesoscale convection cells. The large perturbation pressure change predicted by the theory is of the order of ρ U_O²/F (where ρ is the density), which is consistent with the magnitude of the terms introduced into the recent European Centre for Medium-Range Weather Forecasts orographic parametrizations, but it should be noted that these large Rossby-Froude orographic effects on drag and wave flux are asymmetric with respect to the mountain's centre line. The theory shows how 'lift' forces on the mountain are caused, and how these are related to circulation in horizontal planes around the mountains.