Unstable Waves on Oceanic Fronts: Large Amplitude Behavior and Mean Flow Generation

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  • 1 Department of Mathematics, University of Exeter, Exeter, U.K.
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Abstract

A primitive equation numerical model is used to study the large amplitude behavior of unstable waves on an oceanic density front, concentrating on a single wave mode corresponding to the fastest growing linear solution. At Small amplitude the model results agree well with linear theory, and at large amplitude “backward breaking” occurs and cortex pairs are formed, as have been observed in laboratory experiments. Vortex stretching due to advection across layer depth contours favors formation of the vortex pairs, with the result that the β effect is not necessary for vortex detachment, as it was in a previous quasigeostrophic study by Ikeda.

Examination of the energetics allows a life cycle to be identified for the waves, and shows that kinetic energy is fed into the mean flow through Reynolds stress. It is shown that the β effect is important in determining the precise form of the mean flow generated, and this is interpreted in terms of the deep potential vorticity fluxes. For realistic parameters the mean flows generated agree well with observations of deep mean flows near the Gulf Stream; in particular there is a counterflow (westward) directly below the original position of the front and a positive (eastward) flow displaced to the south. This pattern is not found in the results of eddy-resolving general circulation models and is qualitatively different from the three-jet structure found in Ikeda's study of a

symmetric, quasi-geostrophic jet.

Abstract

A primitive equation numerical model is used to study the large amplitude behavior of unstable waves on an oceanic density front, concentrating on a single wave mode corresponding to the fastest growing linear solution. At Small amplitude the model results agree well with linear theory, and at large amplitude “backward breaking” occurs and cortex pairs are formed, as have been observed in laboratory experiments. Vortex stretching due to advection across layer depth contours favors formation of the vortex pairs, with the result that the β effect is not necessary for vortex detachment, as it was in a previous quasigeostrophic study by Ikeda.

Examination of the energetics allows a life cycle to be identified for the waves, and shows that kinetic energy is fed into the mean flow through Reynolds stress. It is shown that the β effect is important in determining the precise form of the mean flow generated, and this is interpreted in terms of the deep potential vorticity fluxes. For realistic parameters the mean flows generated agree well with observations of deep mean flows near the Gulf Stream; in particular there is a counterflow (westward) directly below the original position of the front and a positive (eastward) flow displaced to the south. This pattern is not found in the results of eddy-resolving general circulation models and is qualitatively different from the three-jet structure found in Ikeda's study of a

symmetric, quasi-geostrophic jet.

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