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Baroclinic Instability and Thermohaline Gradient Alignment in the Mixed Layer

W. R. YoungScripps Institution of Oceanography, La Jolla, California

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Lianggui ChenScripps Institution of Oceanography, La Jolla, California

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Abstract

The density of the mixed layer (ML) is approximately uniform in the vertical, but there are dynamically important horizontal gradients. The subinertial mixed layer (SML) approximation is a small Rossby number filtering of the primitive equation that isolates the low frequency (ω ≪ f) dynamics.

A linear stability analysis based on the SML approximation shows that the horizontal density gradients within the mixed layer (ML) support baroclinically unstable waves with inverse wavenumbers in the range 1 to 10 km. This conclusion follows from both a slab ML model, in which the horizontal velocity has no vertical shear, and a geostrophic ML model, in which the horizontal velocity is sheared according to the thermal wind relation. In the geostrophic case the instability is identical to the long wavelength limit of baroclinically unstable Eady waves.

An interesting difference between the slab and geostrophic ML is the dynamics of thermal and saline anomalies. In the slab case, thermohaline anomalies are advected without shear dispersion, and the initial TS relation is preserved. In the geostrophic case, the shear dispersion associated with the thermal wind produces a flux of heat and salt orthogonal to the buoyancy gradient. This flux varies as the cube of the thermohaline gradients, and it acts so as to mix heat and salt while leaving buoyancy unchanged on fluid particles. The mechanism tighten an initially diffuse TS relation so that a cloud of points in the TS plane condenses onto a curve.

Abstract

The density of the mixed layer (ML) is approximately uniform in the vertical, but there are dynamically important horizontal gradients. The subinertial mixed layer (SML) approximation is a small Rossby number filtering of the primitive equation that isolates the low frequency (ω ≪ f) dynamics.

A linear stability analysis based on the SML approximation shows that the horizontal density gradients within the mixed layer (ML) support baroclinically unstable waves with inverse wavenumbers in the range 1 to 10 km. This conclusion follows from both a slab ML model, in which the horizontal velocity has no vertical shear, and a geostrophic ML model, in which the horizontal velocity is sheared according to the thermal wind relation. In the geostrophic case the instability is identical to the long wavelength limit of baroclinically unstable Eady waves.

An interesting difference between the slab and geostrophic ML is the dynamics of thermal and saline anomalies. In the slab case, thermohaline anomalies are advected without shear dispersion, and the initial TS relation is preserved. In the geostrophic case, the shear dispersion associated with the thermal wind produces a flux of heat and salt orthogonal to the buoyancy gradient. This flux varies as the cube of the thermohaline gradients, and it acts so as to mix heat and salt while leaving buoyancy unchanged on fluid particles. The mechanism tighten an initially diffuse TS relation so that a cloud of points in the TS plane condenses onto a curve.

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