Baroclinic Waves and Frontogenesis. Part II: Uniform Potential Vorticity Jet Flows-Cold and Warm Fronts

Brian J. Hoskins U.K. Universities’ Atmospheric Modelling Group, Department of Meteorology, University of Reading, England

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Nigel V. West U.K. Universities’ Atmospheric Modelling Group, Department of Meteorology, University of Reading, England

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Abstract

The semi-geostrophic equations are used to study the baroclinic instability of jet flows having zero potential vorticity gradient. Normal modes of the linear problems are obtained and it is shown that the most unstable modes tend to tilt in the horizontal with the ambient shears of the basic zonal flows. These most unstable modes are used as initial conditions for integrations of the nonlinear equations. When an upper westerly jet is present, the slightly unrealistic frontogenesis in the Eady mode independent of y (Hoskins and Bretherton, 1972) becomes a realistic cold front development. As the wave grows further a warm front is produced. The same solution may be used for baroclinic growth on a flow with positive vorticity at the surface on the equatorial side of the mode. This exhibits the development of a very different sort of warm front. No cold front is produced. The three kinds of frontogenesis found in these models are analyzed, with emphasis being placed on 1) the ageostrophic horizontal advections implied by the coordinate transformation to semi-geostrophic space, 2) the deformation fields in semi-geostrophic space, and 3) the trajectories of air parcels in semi-geostrophic space.

Abstract

The semi-geostrophic equations are used to study the baroclinic instability of jet flows having zero potential vorticity gradient. Normal modes of the linear problems are obtained and it is shown that the most unstable modes tend to tilt in the horizontal with the ambient shears of the basic zonal flows. These most unstable modes are used as initial conditions for integrations of the nonlinear equations. When an upper westerly jet is present, the slightly unrealistic frontogenesis in the Eady mode independent of y (Hoskins and Bretherton, 1972) becomes a realistic cold front development. As the wave grows further a warm front is produced. The same solution may be used for baroclinic growth on a flow with positive vorticity at the surface on the equatorial side of the mode. This exhibits the development of a very different sort of warm front. No cold front is produced. The three kinds of frontogenesis found in these models are analyzed, with emphasis being placed on 1) the ageostrophic horizontal advections implied by the coordinate transformation to semi-geostrophic space, 2) the deformation fields in semi-geostrophic space, and 3) the trajectories of air parcels in semi-geostrophic space.

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