A Numerical Study of Barotropic Instability in a Zonally Varying Easterly Jet

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  • 1 Department of Meteorology, Naval Postgraduate School, Monterey, CA 93940
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Abstract

The structure and behavior of barotropically unstable and stable waves in the vicinity of a zonally varying easterly jet are studied numerically with a linearized barotropic vorticity equation on a β plane. The easterly jet is approximated by a Bickley jet with a slow zonal variation. The numerical results are also compared with a simple mechanistic analytical model using the local phase speed and growth rate concepts. In several aspects the results are grossly similar to that expected from the parallel flow theory of barotropic instability. However, in the unstable region the resultant structure of the waves causes a spatial growth rate greater than predicted by the local growth rates computed with a parallel flow model. In the stable region, the structure leads to a strong dynamic damping. When a uniform advective velocity is added to a variable mean flow, the difference between the magnitude of the growth rate of the computed waves and that implied by the parallel flow theory is somewhat reduced. However, in this case a stronger zonal asymmetry in the spatial growth rate curve with respect to the jet maximum occurs as a result of slower adjustment of the wave structure to the local stability conditions.

Abstract

The structure and behavior of barotropically unstable and stable waves in the vicinity of a zonally varying easterly jet are studied numerically with a linearized barotropic vorticity equation on a β plane. The easterly jet is approximated by a Bickley jet with a slow zonal variation. The numerical results are also compared with a simple mechanistic analytical model using the local phase speed and growth rate concepts. In several aspects the results are grossly similar to that expected from the parallel flow theory of barotropic instability. However, in the unstable region the resultant structure of the waves causes a spatial growth rate greater than predicted by the local growth rates computed with a parallel flow model. In the stable region, the structure leads to a strong dynamic damping. When a uniform advective velocity is added to a variable mean flow, the difference between the magnitude of the growth rate of the computed waves and that implied by the parallel flow theory is somewhat reduced. However, in this case a stronger zonal asymmetry in the spatial growth rate curve with respect to the jet maximum occurs as a result of slower adjustment of the wave structure to the local stability conditions.

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