A Numerical Simulation of Barotropic Instability. Part I: Wave-Mean Flow Interaction

Mark R. Schoeberl Laboratory for Planetary Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, MD 20771

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Richard S. Lindzen Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139

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Abstract

A numerical model is used to study the evolution of the barotropic point jet instability as it interacts with the mean flow. The linearized instability solution agrees well with the recent analytical solutions of Lindzen.

Stabilization of the point jet instability occurs as the mean flow is modified by wave vorticity transport. Assuming stabilization occurs when the meridional gradient of the zonal mean vorticity is no longer negative, the maximum integrated wave enstrophy can be predicted. In addition, an estimate of the integrated wave enstrophy at steady state can be made by balancing the generation of vorticity against dissipation. These limits are found to be in good agreement with the numerical results.

Abstract

A numerical model is used to study the evolution of the barotropic point jet instability as it interacts with the mean flow. The linearized instability solution agrees well with the recent analytical solutions of Lindzen.

Stabilization of the point jet instability occurs as the mean flow is modified by wave vorticity transport. Assuming stabilization occurs when the meridional gradient of the zonal mean vorticity is no longer negative, the maximum integrated wave enstrophy can be predicted. In addition, an estimate of the integrated wave enstrophy at steady state can be made by balancing the generation of vorticity against dissipation. These limits are found to be in good agreement with the numerical results.

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