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Slow Instabilities in Tropical Ocean Basin–Global Atmosphere Models

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  • 1 Department of Meteorology, University of Wisconsin–Madison. Madison, Wisconsin
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Abstract

The effect of ocean boundaries on instability in coupled ocean-natmosphere models is determined. Eigenvalues and eigenvectors are calculated for coupled systems featuring an ocean basin bounded zonally by a flat continent. The atmosphere is periodic zonally about the globe. The oceanic and atmospheric dynamics are both represented by linear shallow water equations on the equatorial β-plane. The calculation involves latitudinal series expansion and longitudinal finite differencing.

Certain of the modes (i.e., eigenvectors) have amplitudes that grow with time, the growth being a direct result of the ocean-atmosphere coupling. Comparison is made to modes previously determined for the theoretically simpler case where the ocean is zonally unbounded. Growing modes in the bounded ocean case correspond in aspects of behavior and structure to particular modes of appropriate wavelength in the unbounded ocean basin. The basic mechanism of instability is the same in both cases. Growing modes in the bounded ocean case feature wavelike disturbances that propagate slowly across the ocean basin. The direction of propagation and period of the oscillation are very sensitive to the values prescribed for oceanic thermodynamic coefficients. The period is set by the 1ength of time that the coupled disturbance takes to propagate across the basin, and, for a 15 000 km wide basin, ranges from about a year to many years. Dependence of modal behavior on other parameters is also documented. Instability occurs for a greater range of parameters, and growth rates are larger when the ocean basin is wide (e.g., 15 000 km) than when it is narrow. The zonal width of the continent has little effect on modal behavior. The Kelvin and symmetric low-n long Rossby components of the oceanic and atmospheric motion fields are of primary importance in modal growth.

Abstract

The effect of ocean boundaries on instability in coupled ocean-natmosphere models is determined. Eigenvalues and eigenvectors are calculated for coupled systems featuring an ocean basin bounded zonally by a flat continent. The atmosphere is periodic zonally about the globe. The oceanic and atmospheric dynamics are both represented by linear shallow water equations on the equatorial β-plane. The calculation involves latitudinal series expansion and longitudinal finite differencing.

Certain of the modes (i.e., eigenvectors) have amplitudes that grow with time, the growth being a direct result of the ocean-atmosphere coupling. Comparison is made to modes previously determined for the theoretically simpler case where the ocean is zonally unbounded. Growing modes in the bounded ocean case correspond in aspects of behavior and structure to particular modes of appropriate wavelength in the unbounded ocean basin. The basic mechanism of instability is the same in both cases. Growing modes in the bounded ocean case feature wavelike disturbances that propagate slowly across the ocean basin. The direction of propagation and period of the oscillation are very sensitive to the values prescribed for oceanic thermodynamic coefficients. The period is set by the 1ength of time that the coupled disturbance takes to propagate across the basin, and, for a 15 000 km wide basin, ranges from about a year to many years. Dependence of modal behavior on other parameters is also documented. Instability occurs for a greater range of parameters, and growth rates are larger when the ocean basin is wide (e.g., 15 000 km) than when it is narrow. The zonal width of the continent has little effect on modal behavior. The Kelvin and symmetric low-n long Rossby components of the oceanic and atmospheric motion fields are of primary importance in modal growth.

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