Langmuir Circulations in a Surface Layer Bounded by a Strong Thermocline

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  • 1 Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York
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Abstract

Langmuir circulations reside in, and are responsible in part for the existence and maintenance of, the mixed layer. It is, therefore, typical for the water containing Langmuir circulations to be bounded below by a thermocline. When this bounding thermocline is strong, it may be expected to act as an effective “slippery bottom” constraint. Such an assumption has been invoked previously, but failed to predict a preferred spacing for the windrows produced by the circulations. This model assumed that the momentum transfers across the horizontal boundaries of the mixed layer were independent of the water motion induced by Langmuir circulation. Here, mixed boundary conditions are explored. Estimates of the transfer coefficients in these boundary conditions suggest that the revised model differs only slightly from the earlier one, but allows for a more general and realistic stress model. Incorporating these effects into the theory gives windrows with a finite separation, in accord with the observations. The windrow spacing emerging from this modified theory depends in a simple way on the layer depth and the constant of proportionality in the stress boundary condition when the latter number takes physically plausible values. The analysis allows the water layer above the bounding thermocline to be homogeneous or either stably or unstably density stratified. The stably stratified case permits oscillatory convection under certain restricted circumstances.

Abstract

Langmuir circulations reside in, and are responsible in part for the existence and maintenance of, the mixed layer. It is, therefore, typical for the water containing Langmuir circulations to be bounded below by a thermocline. When this bounding thermocline is strong, it may be expected to act as an effective “slippery bottom” constraint. Such an assumption has been invoked previously, but failed to predict a preferred spacing for the windrows produced by the circulations. This model assumed that the momentum transfers across the horizontal boundaries of the mixed layer were independent of the water motion induced by Langmuir circulation. Here, mixed boundary conditions are explored. Estimates of the transfer coefficients in these boundary conditions suggest that the revised model differs only slightly from the earlier one, but allows for a more general and realistic stress model. Incorporating these effects into the theory gives windrows with a finite separation, in accord with the observations. The windrow spacing emerging from this modified theory depends in a simple way on the layer depth and the constant of proportionality in the stress boundary condition when the latter number takes physically plausible values. The analysis allows the water layer above the bounding thermocline to be homogeneous or either stably or unstably density stratified. The stably stratified case permits oscillatory convection under certain restricted circumstances.

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