The Role of Dissipation Mechanisms in the Nonlinear Dynamics of Unstable Baroclinic Waves

P. Klein IFREMER, Plouzane, France

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J. Pedlosky Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Abstract

The effect of three different parameterizations of dissipation on the nonlinear dynamics of unstable baroclinic waves is studied. The model is the two-layer f-plane model and the dynamics is quasigeostrophic. The dissipation mechanisms are 1) dissipation due to Ekman layers at the horizontal boundary surfaces, 2) the addition of interfacial Ekman friction, or 3) dissipation proportional to the perturbation potential vorticity.

We find, as anticipated by weakly nonlinear theory, a strong effect on the nonlinear amplitude dynamics for supercriticalities as large as four times the threshold value for instability. The use of interfacial friction or potential vorticity damping expunges the vacillating behavior common to the system with type 1 dissipation.

At high supercriticality a barotropic vacillation involving the mean flow and harmonics of the fundamental is superimposed on the basic baroclinic wave dynamics. Examination of the critical transition for the emergence of the barotropic oscillation reveals that the enhanced linear instability of the higher harmonics is responsible for the self-sustained vacillation.

Abstract

The effect of three different parameterizations of dissipation on the nonlinear dynamics of unstable baroclinic waves is studied. The model is the two-layer f-plane model and the dynamics is quasigeostrophic. The dissipation mechanisms are 1) dissipation due to Ekman layers at the horizontal boundary surfaces, 2) the addition of interfacial Ekman friction, or 3) dissipation proportional to the perturbation potential vorticity.

We find, as anticipated by weakly nonlinear theory, a strong effect on the nonlinear amplitude dynamics for supercriticalities as large as four times the threshold value for instability. The use of interfacial friction or potential vorticity damping expunges the vacillating behavior common to the system with type 1 dissipation.

At high supercriticality a barotropic vacillation involving the mean flow and harmonics of the fundamental is superimposed on the basic baroclinic wave dynamics. Examination of the critical transition for the emergence of the barotropic oscillation reveals that the enhanced linear instability of the higher harmonics is responsible for the self-sustained vacillation.

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