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On the Stability of a Fluid with Specialized Density Stratification. Part I: Baroclinic Instability and Constant Bottom Slope

D. G. WrightDepartment of Mathematics, University of British Columbia, Vancouver, BC Canada Y6T 1W5

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Abstract

A three-layer model is used to study the stability of large-scale oceanic zonal flows over topography. The mean density profile employed has upper and lower layers of constant densities ρ1* and ρ3*, respectively (ρ1*3*), and a middle layer whose density varies linearly from ρ1* to ρ3*. The model developed here includes vertical and horizontal shear of zonal flow in a channel as well as the effects of β and cross-channel variations in topography. In this paper (Part I) the effects of density stratification, curvature in the mean velocity profile, β, constant slope topography and layer thicknesses are studied. The following general conclusions with regard to the stability of the flow are made:

• Curvature in the mean velocity profile has a strong destabilizing influence.

• Density stratification stabilizes.

• The β-effect stabilizes.

• Topography stabilizes one of two possible classes of instability (a bottom intensified instability).

• Increasing either H1, or H3 relative to H2, stabilizes.

The model is compared with two-layer models and results clearly indicate the importance of having at least three 1ayers when curvature of the mean velocity profile is present or when H2 is significant.

Abstract

A three-layer model is used to study the stability of large-scale oceanic zonal flows over topography. The mean density profile employed has upper and lower layers of constant densities ρ1* and ρ3*, respectively (ρ1*3*), and a middle layer whose density varies linearly from ρ1* to ρ3*. The model developed here includes vertical and horizontal shear of zonal flow in a channel as well as the effects of β and cross-channel variations in topography. In this paper (Part I) the effects of density stratification, curvature in the mean velocity profile, β, constant slope topography and layer thicknesses are studied. The following general conclusions with regard to the stability of the flow are made:

• Curvature in the mean velocity profile has a strong destabilizing influence.

• Density stratification stabilizes.

• The β-effect stabilizes.

• Topography stabilizes one of two possible classes of instability (a bottom intensified instability).

• Increasing either H1, or H3 relative to H2, stabilizes.

The model is compared with two-layer models and results clearly indicate the importance of having at least three 1ayers when curvature of the mean velocity profile is present or when H2 is significant.

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