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Mixing driven by vertically variable forcing: an application to the case of Langmuir circulation

Published online by Cambridge University Press:  26 April 2006

Anand Gnanadesikan
Anand Gnanadesikan
Affiliation:
Department of Physical Oceanography, Woods Hole Oceanographic Institution, MA 02543, USA Present address: Program in Atmospheric and Oceanic Sciences, Princeton University, PO Box CN710 Princeton, NJ 08540, USA. email:alg@gfdl.gov.
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Abstract

Two-dimensional mixing driven by an instability mechanism which is concentrated near one of the boundaries is considered, with particular application to Langmuir circulations driven by a wave spectrum. The question of how to define the equivalent of the Rayleigh number is attacked using the energy balance equations and simple truncated models of the instability. Given a particular horizontal wavelength for the disturbance, the strength of the forcing on the cells, and thus the growth rate, is determined by a tradeoff between maximizing the depth-averaged forcing and maximizing the depth of penetration. As a result of this tradeoff, long-wavelength cells grow more slowly, but penetrate more deeply and have a larger equivalent Rayleigh number. At finite amplitude, these long-wavelength cells come to dominate the flow field. The depth of penetration of, and density transport accomplished by, Langmuir cells is considered as a function of the mean stratification and diffusion. An application to oceanic mixed layers is considered assuming the Mellor-Yamada 2½-level turbulence closure model to define the background level of turbulent mixing. For many realistic cases, Langmuir cells are predicted to dominate the vertical transport of momentum and density.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 322 , 10 September 1996 , pp. 81 - 107
Copyright
© 1996 Cambridge University Press

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