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The Instability of Rossby Basin Modes and the Oceanic Eddy Field

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  • 1 Norwegian Meteorological Institute, Blindern, Oslo, Norway
  • | 2 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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Abstract

Low-frequency, large-scale baroclinic Rossby basin modes, resistant to scale-dependent dissipation, have been recently theoretically analyzed and discussed as possible efficient coupling agents with the atmosphere for interactions on decadal time scales. Such modes are also consistent with evidence of the westward phase propagation in satellite altimetry data. In both the theory and the observations, the scale of the waves is large in comparison with the Rossby radius of deformation and the orientation of fluid motion in the waves is predominantly meridional. These two facts suggest that the waves are vulnerable to baroclinic instability on the scale of the deformation radius. The key dynamical parameter is the ratio Z of the transit time of the long Rossby wave to the e-folding time of the instability. When this parameter is small the wave easily crosses the basin largely undisturbed by the instability; if Z is large the wave succumbs to the instability and is largely destroyed before making a complete transit of the basin. For small Z, the instability is shown to be a triad instability; for large Z the instability is fundamentally similar to the Eady instability mechanism. For all Z, the growth rate is on the order of the vertical shear of the basic wave divided by the deformation radius. If the parametric dependence of Z on latitude is examined, the condition of unit Z separates latitudes south of which the Rossby wave may successfully cross the basin while north of which the wave will break down into small-scale eddies with a barotropic component. The boundary between the two corresponds to the domain boundary found in satellite measurements. Furthermore, the resulting barotropic wave field is shown to propagate at speeds about 2 times as large as the baroclinic speed, and this is offered as a consistent explanation of the observed discrepancy between the satellite observations of Chelton and Schlax and simple linear wave theory. Here it is suggested that Rossby basin modes, if they exist, would be limited to tropical domains and that a considerable part of the observed midlatitude eddy field north of that boundary is due to the instability of wind-forced, long Rossby waves.

Corresponding author address: Dr. J. Pedlosky, Department of Physical Oceanography, Clark 363, MS 21, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

Abstract

Low-frequency, large-scale baroclinic Rossby basin modes, resistant to scale-dependent dissipation, have been recently theoretically analyzed and discussed as possible efficient coupling agents with the atmosphere for interactions on decadal time scales. Such modes are also consistent with evidence of the westward phase propagation in satellite altimetry data. In both the theory and the observations, the scale of the waves is large in comparison with the Rossby radius of deformation and the orientation of fluid motion in the waves is predominantly meridional. These two facts suggest that the waves are vulnerable to baroclinic instability on the scale of the deformation radius. The key dynamical parameter is the ratio Z of the transit time of the long Rossby wave to the e-folding time of the instability. When this parameter is small the wave easily crosses the basin largely undisturbed by the instability; if Z is large the wave succumbs to the instability and is largely destroyed before making a complete transit of the basin. For small Z, the instability is shown to be a triad instability; for large Z the instability is fundamentally similar to the Eady instability mechanism. For all Z, the growth rate is on the order of the vertical shear of the basic wave divided by the deformation radius. If the parametric dependence of Z on latitude is examined, the condition of unit Z separates latitudes south of which the Rossby wave may successfully cross the basin while north of which the wave will break down into small-scale eddies with a barotropic component. The boundary between the two corresponds to the domain boundary found in satellite measurements. Furthermore, the resulting barotropic wave field is shown to propagate at speeds about 2 times as large as the baroclinic speed, and this is offered as a consistent explanation of the observed discrepancy between the satellite observations of Chelton and Schlax and simple linear wave theory. Here it is suggested that Rossby basin modes, if they exist, would be limited to tropical domains and that a considerable part of the observed midlatitude eddy field north of that boundary is due to the instability of wind-forced, long Rossby waves.

Corresponding author address: Dr. J. Pedlosky, Department of Physical Oceanography, Clark 363, MS 21, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

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