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Nonlinear Equilibration of Two-Dimensional Eady Waves: Simulations with Viscous Geostrophic Momentum Equations

Noboru NakamuraDepartment of the Geophysical Sciences, University of Chicago, Chicago, Illinois

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Abstract

Equilibration of two-dimensional Eady waves is numerically investigated using the geostrophic momentum equations incorporating heat and momentum diffusion. Extended solutions are obtained beyond what would be the collapse of surface fronts in the inviscid theory, and are found to accurately reproduce the equilibration of baroclinic waves simulated with the primitive equations. Potential vorticity anomalies produced at the surface fronts are essential in the initial amplitude saturation and in the asymptotic behavior of the equilibrated flow. A supergeostrophic shear spun up nonlinearly in the zonal flow also plays an important role in causing the reversal of the tilt.

The zonal mean potential temperature profile in the equilibrium state is similar to the prediction by the adjustment hypothesis of Gutowski when only horizontal diffusion is present. However, it is closer to an Eady's basic state with enhanced static stability when vertical diffusion is also present.

The difference in the ageostrophic streamfunctions between the geostrophic momentum and primitive equations reveals rich features of inertia-gravity waves radiating from the surface fronts in the latter model. The role of the gravity waves in the equilibration process, however, is found to be minor.

Abstract

Equilibration of two-dimensional Eady waves is numerically investigated using the geostrophic momentum equations incorporating heat and momentum diffusion. Extended solutions are obtained beyond what would be the collapse of surface fronts in the inviscid theory, and are found to accurately reproduce the equilibration of baroclinic waves simulated with the primitive equations. Potential vorticity anomalies produced at the surface fronts are essential in the initial amplitude saturation and in the asymptotic behavior of the equilibrated flow. A supergeostrophic shear spun up nonlinearly in the zonal flow also plays an important role in causing the reversal of the tilt.

The zonal mean potential temperature profile in the equilibrium state is similar to the prediction by the adjustment hypothesis of Gutowski when only horizontal diffusion is present. However, it is closer to an Eady's basic state with enhanced static stability when vertical diffusion is also present.

The difference in the ageostrophic streamfunctions between the geostrophic momentum and primitive equations reveals rich features of inertia-gravity waves radiating from the surface fronts in the latter model. The role of the gravity waves in the equilibration process, however, is found to be minor.

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