Quasi-geostrophic Wave-CISK in an Unbounded Baroclinic Shear

Chris Snyder Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Richard S. Lindzen Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Abstract

In this study, the free-shear problem, a minimal version of baroclinic, quasi-geostrophic wave-CISK, is analyzed. The basic state consists of a zonal flow, unbounded above and below, with constant vertical shear and Brunt-Väisälä frequency and zero meridional gradient of the potential vorticity; and convective heating is parameterized in terms of the convergence below an arbitrary level. Because of the sensitivity to the vertical distribution of the parameterized heating typical of wave-CISK models, a simple thermodynamic constraint on the heating profile is used to broadly identify appropriate parameter regimes. The unstable waves in the free-shear problem grow rapidly and share many structural characteristics with dry baroclinic waves, although the dynamical process associated with dry baroclinic instability is absent; consideration of the potential vorticity dynamics of the unstable modes illustrates how heating may act as a dynamical surrogate for potential vorticity gradients. Although highly idealized, the free-shear problem also explains much of the behavior of more general wave-CISK models.

Abstract

In this study, the free-shear problem, a minimal version of baroclinic, quasi-geostrophic wave-CISK, is analyzed. The basic state consists of a zonal flow, unbounded above and below, with constant vertical shear and Brunt-Väisälä frequency and zero meridional gradient of the potential vorticity; and convective heating is parameterized in terms of the convergence below an arbitrary level. Because of the sensitivity to the vertical distribution of the parameterized heating typical of wave-CISK models, a simple thermodynamic constraint on the heating profile is used to broadly identify appropriate parameter regimes. The unstable waves in the free-shear problem grow rapidly and share many structural characteristics with dry baroclinic waves, although the dynamical process associated with dry baroclinic instability is absent; consideration of the potential vorticity dynamics of the unstable modes illustrates how heating may act as a dynamical surrogate for potential vorticity gradients. Although highly idealized, the free-shear problem also explains much of the behavior of more general wave-CISK models.

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