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The Stability of a Steady Horizontal Shear Front with Uniform Potential vorticity

Alain JolyCentre de Recherche en Météorologie Dynamique, Paris

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Alan J. ThorpeDepartment of Meteorology, University of Reading

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Abstract

The stability of the steady two-dimensional horizontal shear front to geostrophic disturbances in the along-front direction is examined within the framework of semi-geostrophic theory. The basic state corresponds to the geostrophic along-front flow at any time during the nonlinear evolution of a two-dimensional Eady wave. The matrix resulting from the stability analysis can be transformed into a weakly nondiagonal form. Its structure shows that the selection of the most unstable along-front wavenumber is independent of the “intensity” of the front. The growth rate is a linear function of this amplitude. The most unstable along-front mode is a modified Eady mode stationary with respect to the front. It draws a fraction of its energy from the shear. For smaller along-front wavelengths, the solution is dominated by propagating modes near the boundaries. These are also baroclinic, with a larger contribution from the basic kinetic energy and much smaller growth rates. It is apparent that the existence of a vorticity maximum at fronts, however large, is not sufficient to produce the observed small scale of frontal waves. Anomalous potential vorticity at the front is necessary to provide a deep zone of large horizontal shear and hence the reduced horizontal scale of waves.

Abstract

The stability of the steady two-dimensional horizontal shear front to geostrophic disturbances in the along-front direction is examined within the framework of semi-geostrophic theory. The basic state corresponds to the geostrophic along-front flow at any time during the nonlinear evolution of a two-dimensional Eady wave. The matrix resulting from the stability analysis can be transformed into a weakly nondiagonal form. Its structure shows that the selection of the most unstable along-front wavenumber is independent of the “intensity” of the front. The growth rate is a linear function of this amplitude. The most unstable along-front mode is a modified Eady mode stationary with respect to the front. It draws a fraction of its energy from the shear. For smaller along-front wavelengths, the solution is dominated by propagating modes near the boundaries. These are also baroclinic, with a larger contribution from the basic kinetic energy and much smaller growth rates. It is apparent that the existence of a vorticity maximum at fronts, however large, is not sufficient to produce the observed small scale of frontal waves. Anomalous potential vorticity at the front is necessary to provide a deep zone of large horizontal shear and hence the reduced horizontal scale of waves.

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