Quasi-geostrophy and conservation of potential vorticity provide a simple explanation for the poleward deflection of flow as it passes over a mountain. Across the range from small-scales to mesoscales however, a much richer variety of flow patterns are observed for airflow over three-dimensional topography. Among these include effects of upwind stagnation (split flow & flow reversal) and gravity wave coupling (lee troughs & vortices) -- neither of which are explained within quasi-geostrophic theory.
Steady flows over weak topography are investigated using asymptotic intermediate models which incorporate the next-order physics beyond quasi-geostrophy: nonlinear inversion of PV, ageostrophic flow and vertical motion. These balanced corrections for finite Rossby number show that it is the feedback of vertical motion on horizontal winds which is primarily responsible for the tendency towards upwind stagnation. Predicated on the assumption of QG balance, these next-order effects prove insufficient to explain the development of lee flow structures. This issue is resolved through a hybrid asymptotic model, based upon small Rossby number and large Froude number (strong flow), which clearly demonstrates downwind generation of vorticity through the coupling to gravity wave action.
In a manner akin to surface quasi-geostrophy, these intermediate models reduce to a two-dimensional surface evolution for the fully three-dimensional flow when specialized to uniform interior potential vorticity. This reduction of computational dimensionality offers considerable advantage for time-dependent and parametric studies of topographic flows.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics