Baroclinic Instabilities of a Deep Fluid

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  • 1 Geophysical Fluid Dynamics Program, Rutgers University, New Brunswick, N. J. 08903
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Abstract

An analytical study is made of the baroclinic instability problem for a zonal wind U (z), by modifying the Eady model through relaxation of the shallow-layer approximation. The linearized perturbation equation is derived, including the mass-divergence effect in the continuity equation and the non-hydrostatic effect in the vertical momentum equation.

When U (z) = constant, the non-hydrostatic effect decreases the effective propagation speeds of wave having short horizontal wavelengths.

Assuming that the zonal current velocity profile is linear, two limiting cases are treated (i.e., the geostrophic-type instability limit and the symmetric-type instability limit). For the case of the geostrophic-type instability limit, the mass-divergence effect seems to reduce primarily the wave propagation speeds, while the unstable wave growth rates are decreased by both the mass-divergence and the non-hydrostatic effects. However, for the case of the symmetric-type instability limit, the mass-divergence effect is quite mild, but the non-hydrostatic effect strongly affects the unstable wave growth rates.

Abstract

An analytical study is made of the baroclinic instability problem for a zonal wind U (z), by modifying the Eady model through relaxation of the shallow-layer approximation. The linearized perturbation equation is derived, including the mass-divergence effect in the continuity equation and the non-hydrostatic effect in the vertical momentum equation.

When U (z) = constant, the non-hydrostatic effect decreases the effective propagation speeds of wave having short horizontal wavelengths.

Assuming that the zonal current velocity profile is linear, two limiting cases are treated (i.e., the geostrophic-type instability limit and the symmetric-type instability limit). For the case of the geostrophic-type instability limit, the mass-divergence effect seems to reduce primarily the wave propagation speeds, while the unstable wave growth rates are decreased by both the mass-divergence and the non-hydrostatic effects. However, for the case of the symmetric-type instability limit, the mass-divergence effect is quite mild, but the non-hydrostatic effect strongly affects the unstable wave growth rates.

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