Effects of Topography on Fronts

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Abstract
The hydrostatic Boussinesq equations are used to simulate the passage of fronts over a two-dimensional mountain in a cyclic domain. The fronts are forced by a confluent, periodic deformation field that moves with the uniform mean flow over the mountain. The initial conditions are selected to give a cold front confined to the lower part of the domain. Fourth-order diffusion terms are included in the numerical model to control energy cascade to the grid size scale. A numerical frontogenesis experiment with no topography produces a realistic surface front in about two days. Numerical solutions for flow over the mountain with no front are found by integrating the equations from the initial conditions, which are semigeostrophic steady-state solutions. Various mountains are considered that have the same height but different widths. The numerical solutions for wide mountains remain close to the semigeostrophic initial conditions, while for narrower mountains vertically propagating waves and a hydraulic jump develop on the lee side of the mountain. The frontal solution and the mountain solution are combined to produce the initial conditions for the basic experiments. The numerical solutions show reduced frontogenesis on the upwind slope and increased frontogenesis on the lee slope. This behavior is caused by the mountain-forced divergence on the upwind side and convergence on the lee side in agreement with the semigeostrophic solution of Zehnder and Bannon. Further experiments with no deformation forcing are carried out to correspond to the semigeostrophic passive scalar studies of Blumen and Gross. A passive scalar that represents the perturbation potential temperature is advected with the mountain solution. The frontal scale, based on the tracer field, increases on the upwind side until it reaches a maximum at the top and then decreases on the lee side, back to its original value as the front moves away from the mountain. The numerical solutions for the interactive potential temperature field have a similar behavior, although some additional blocking effects are present. For the narrower mountains the frontal structure is distorted by the gravity waves on the lee side of the mountain. These solutions resemble those of Schumann for smaller-scale mountains.

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