Synoptic Development in a Two-and-One-Half-Layer Contour Dynamics System

Abstract

Synoptic development is studied using a two-and-one-half-layer contour dynamics model in full spherical geometry. The model has three isentropic layers: two lower layers that are dynamically active and one upper layer that is kept motionless. The isentropic layers cover the whole sphere and are confined in the vertical direction by two rigid horizontal boundaries. The model is assumed to be in hydrostatic and geostrophic equilibrium; forcing/friction and diabatic heating/cooling are neglected. In both active layers, the horizontal structure is represented by a piecewise-uniform distribution of potential vorticity with a single front in each layer. The potential vorticity front in the upper active layer can be associated with the tropopause or, to be more specific, with the sudden change in height of the tropopause at the jet stream. The potential vorticity front in the lower active layer enhances the baroclinicity of the system and may be associated with the polar front. Because of the assumption of hydrostatic and geostrophic equilibrium, the model atmosphere is completely defined by the instantaneous positions of the contours and can be integrated in time using the technique of contour dynamics. It is shown that realistic zonal flows can be obtained by a suitable choice of parameters. A linear stability analysis reveals that small-amplitude perturbations of given planetary wavenumber may grow for only specific latitudinal positions of the potential vorticity fronts. The maximum growth rates and highest planetary wavenumbers are found for potential vorticity fronts that are located at approximately the same latitude. Because of the conceptual simplicity of the model, in which the potential vorticity structure is represented by only two contours, the instability mechanism expresses itself in a clear way. The contour dynamics model also captures the nonlinear stages of cyclogenesis remarkably well, as is evident from the time evolution of the fronts and the time evolution of a passive tracer in a numerical simulation of a cutoff cyclone.