A Two-Dimensional Primitive Equation Model of Frontogenesis Forced by Confluence and Horizontal Shear

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Abstract
A two-dimensional primitive equation model of frontogenesis forced by a combination of confluence and horizontal shear is formulated for dry, nearly adiabatic and inviscid conditions. The frontogenetical forcing mechanisms are included by respectively specifying the cross-front and vertical variation of the cross-front geostrophic wind component. The results of three numerical integrations containing confluent forcing are analyzed and discussed in detail. The first is the case of pure confluence, in which the vertical shear of the cross-front geostrophic component is zero. The second and third cases respectively consist of negative and positive vertical shear of the cross-front geostrophic component, which correspond to cold and warm advection at upper levels for the configuration of the alongfront wind component. The above frontogenetical forcing and the resulting frontal structures are related to typical flow patterns occurring within midlatitude baroclinic waves during various stages in their life cycle. The simulated upper-level frontal structures in the pure confluence and warm advection cases resemble those of previous two-dimensional frontogenesis models. Development is maximized near the tropopause where frontogenetical confluence and convergence are maximized and the frontolytical tilting effects of vertical motions are minimized. Frontogenesis is enhanced throughout the troposphere in the warm advection case relative to the pure confluence case through differential thermal advection by the cyclonically sheared alongfront wind component. In contrast, in the cold advection case, a well-defined front evolves initially near the tropopause and eventually extends to the midtroposphere. The development is dominated by tilting, as effects associated with the horizontal components of the air motion are frontolytical. The frontogenetical tilting effects are a consequence of a lateral shift of the thermodynamically direct cross-front ageostrophic circulation far enough into the warm air to place the maximum subsidence in the midtroposphere within and to the warm side of the developing frontal zone. Numerous aspects of the above picture are shown to correspond closely to the observational findings of a number of synoptic case studies. A noteworthy result is that tropopause folding is reproduced, in which lower stratospheric air is advected downward to the 700 mb level. This behavior occurs despite the two-dimensional formulation of the model, which does not include the three-dimensional effects of curvature dynamics on the vertical motion field. Finally, several positive feedback mechanisms involving the vertical motion field are postulated and will be examined through a diagnostic analysis of the cross-front ageostrophic circulation in a companion paper.

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