A semi-geostrophic model of frontal passage over topography was formulated to examine the effects of the interaction of a well developed front with isolated orography in idealized conditions. The choice of the semi-geostrophic framework is due to the ability it provides to represent a realistic front in all stages of development. In the linear formulation of the model an initial state, constituted of a uniform vertical shear and the two dimensional Eady wave of the desired amplitude, is perturbed by a mountain of small height located ahead of the incoming front. The interior perturbation is assumed of zero potential vorticity and the mountain appears in the boundary condition at the bottom boundary as a forcing of vertical velocity. Therefore the model lacks the blocking effect on the flow induced by mountains of finite height. More importantly, this representation of the mountain induces spurious fluxes of potential vorticity into the interior flow, making the zero potential vorticity problem inconsistent. The inconsistency is small enough that the problem can be solved within the numerical accuracy of a relaxation technique, producing a solution which can be viewed as a first-order approximation to the fully non linear, and provably consistent, problem of finite height mountain and terrain-following lower boundary condition. While the latter is being developed, we present a preliminary exploration of parameter space, with specific attention to varying intensity and orientation of the primary wave.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics