Self-sustained Inertial Oscillations

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  • 1 Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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Abstract

The authors describe a self-sustaining baroclinic inertial oscillation whose energy source rests in a uniform horizontal temperature gradient. This energy is released through the agency of a stratification-dependent mixing law that is meant to crudely model the occurrence of enhanced mixing when the stratification weakens. The mixing is chosen to be negligible over most of the cycle and large only when the stratification is small.

Sustained inertial oscillations are shown to be the natural end state of the instability of possible steady solutions when the decrease of the mixing rate with temperature exceeds a critical value. If the variation of the mixing rate with temperature is abrupt, a finite-amplitude oscillation is sustained, although a possible steady solution is linearly stable.

Abstract

The authors describe a self-sustaining baroclinic inertial oscillation whose energy source rests in a uniform horizontal temperature gradient. This energy is released through the agency of a stratification-dependent mixing law that is meant to crudely model the occurrence of enhanced mixing when the stratification weakens. The mixing is chosen to be negligible over most of the cycle and large only when the stratification is small.

Sustained inertial oscillations are shown to be the natural end state of the instability of possible steady solutions when the decrease of the mixing rate with temperature exceeds a critical value. If the variation of the mixing rate with temperature is abrupt, a finite-amplitude oscillation is sustained, although a possible steady solution is linearly stable.

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