A Numerical Study of Frontogenesis

Stephen E. Mudrick Dept. of Meteorology, Massachusetts Institute of Technology, Cambridge

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Abstract

Fine-resolution, dry, inviscid, Boussinesq formulations of a quasi-geostrophic model and a primitive equations model are used in a study of frontogenesis. These three-dimensional models employ horizontal and vertical resolution on the order of 100 km and 1 km, respectively; an integration uses about 40 grid points in each horizontal direction and 20 in the vertical. The initial states consist of two baroclinic basic currents upon which are superimposed quasi-geostrophically balanced, small-amplitude perturbations corresponding to the most unstable mode in each case. In the second case, the wave grows by barotropic as well as by baroclinic processes.

The most rapid surface frontogenesis occurs where the synoptic-scale, quasi-geostrophic convergence contributes significantly to the pure deformational increase of the horizontal temperature gradient. In these integrations, this distribution favors formation of warm fronts. The frontal zones in the quasi-geostrophic and primitive equations models agree in structure with earlier theoretical solutions by Stone and Hoskins, respectively.

The horizontal deformation, as well as the “indirect” vertical circulation, is important in producing upper level frontogenesis. The two models generate similar patterns of vertical motion. A feedback mechanism relating the action of the horizontal deformation and the indirect circulation and leading to upper level frontogenesis is postulated.

Abstract

Fine-resolution, dry, inviscid, Boussinesq formulations of a quasi-geostrophic model and a primitive equations model are used in a study of frontogenesis. These three-dimensional models employ horizontal and vertical resolution on the order of 100 km and 1 km, respectively; an integration uses about 40 grid points in each horizontal direction and 20 in the vertical. The initial states consist of two baroclinic basic currents upon which are superimposed quasi-geostrophically balanced, small-amplitude perturbations corresponding to the most unstable mode in each case. In the second case, the wave grows by barotropic as well as by baroclinic processes.

The most rapid surface frontogenesis occurs where the synoptic-scale, quasi-geostrophic convergence contributes significantly to the pure deformational increase of the horizontal temperature gradient. In these integrations, this distribution favors formation of warm fronts. The frontal zones in the quasi-geostrophic and primitive equations models agree in structure with earlier theoretical solutions by Stone and Hoskins, respectively.

The horizontal deformation, as well as the “indirect” vertical circulation, is important in producing upper level frontogenesis. The two models generate similar patterns of vertical motion. A feedback mechanism relating the action of the horizontal deformation and the indirect circulation and leading to upper level frontogenesis is postulated.

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