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Mixing driven by vertically variable forcing: An application to the case of Langmuir circulation
Anand Gnanadesikan
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 modesl of the instability. Given a particular horizontal wavelength for the disturbance, the strength of the forcing on the ceels, and thus the growth rate, is determined by a tradeoff between maximizing 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 2-1/2 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.