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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:[email protected].
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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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References

Cox, S. M. & Leibovich, S. 1993 Langmuir circulations in a surface layer bounded by a strong thermocline. J. Phys. Oceanogr. 23, 1330–1345.Google Scholar
Craik, A. D. D. 1970 A wave-interaction model for the generation of windows. J. Fluid Mech. 41, 802–822.Google Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulation. J. Fluid Mech. 73, 401–426.Google Scholar
Gnanadesikan, A. 1994 Langmuir circulations in oceanic surface layer. PhD Thesis, MIT/WHOI Joint Program in Physical Oceanography; WHOI Tech. Report 94-23, 354 pp.
Gnanadesikan, A. 1995 Effects of waves and heat fluxes on bubble patch structure and gas exchange. In Air-Water Gas Transfer (ed. B. Jahne & E. A. Monahan) pp. 313–323. Hanau, Germany, AEON Verlag.
Gnanadesikan, A. & Weller, R. A. 1995 The structure and instability of the Ekman spiral in the presence of surface gravity waves. J. Phys. Oceanogr. 25, 3148–3171.Google Scholar
Gottleib, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral methods: Theory and Applications. Soc. Ind. Appl. Maths, 170 pp.Google Scholar
Howard, L. N. & Krishnamurti, R. 1986 Large-scale flow in turbulent convection: A mathematical model. J. Fluid Mech. 170, 385–410.Google Scholar
Huang, N. E. 1979 On surface drift currents in the ocean. J. Fluid Mech. 91, 191–208.Google Scholar
Klein, P. C. & Coste, B. 1984 Effects of wind stress variability on nutrient transport into the mixed layer. Deep-Sea Res. 31, 21–37.Google Scholar
Langmuir, I. 1938 Surface motion of water induced by wind. Science 87. 119–123.Google Scholar
Leibovich, S. 1977a On the evolution of the system of surface wind drift currents and Langmuir circulation in the ocean. Part I. Theory and averaged current. J. Fluid Mech. 79, 715–743.Google Scholar
Leibovich, S. 1977b Convective instability of stably stratified water in the ocean. J. Fluid Mech. 82, 561–583.Google Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulation. Ann. Rev. Fluid Mech. 15, 391–427.Google Scholar
Leibovich, S., Lele, S. K. & Moroz, I. 1989 Nonlinear dynamics in Langmuir circulations and thermosolutal convection. J. Fluid Mech. 198, 471–511.Google Scholar
Leibovich, S. & Paolucci, S. 1981 The instability of the ocean to Langmuir circulations. J. Fluid Mech. 102, 141–168.Google Scholar
Li, M. & Garrett, C. 1993 Cell merging and the jet/downwelling ratio in Langmuir circulation. J. Mar. Res. 51, 737–769.Google Scholar
Li, M. & Garrett, C 1995 Is Langmuir circulation driven by surface waves or surface cooling? J. Phys. Oceanogr. 35, 64–76.Google Scholar
Malkus, W. V. R. & Veronis, G. 1958 Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260.Google Scholar
Mellor, G. & Yamada, T. 1974 A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806.Google Scholar
Pierson, W. J. & Moskowitz, L. 1964 A proposed spectral form for fully developed seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res. 64, 5181–5190.Google Scholar
Roache, P. J. 1977 Computational Fluid Dynamics. Hermosa.
Smith, J., Weller, R. A. & Pinkel, R. 1987 Velocity structure in the mixed layer during MILDEX. J. Phys. Oceanogr. 17, 425–439.Google Scholar
Terray, E. A., Donelan, M. A., Agarwal, Y. C., Drennan, W. M., Kahma, K. K., Williams, A. J., Hwang, P. A. & Kitaigorodskii, S. A. 1996 Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. (in press).Google Scholar
Thorpe, S. A. 1984a The effect of Langmuir circulation on the distribution of submerged bubbles caused by breaking wind waves. J. Fluid Mech. 142, 151–170.Google Scholar
Thorpe, S. A. 1984b On the determination of Kv in the near-surface ocean from acoustic measurements of bubbles. J. Phys. Oceanogr. 14, 855–863.Google Scholar
Thorpe, S. A. 1992 The breakup of Langmuir circulation and the instability of an array of vortices. J. Phys. Oceanogr. 16, 1462–1478.Google Scholar
Weller, R. A. 1981 Observations of the velocity response to wind forcing in the upper ocean. J. Geophys. Res. 86, 1969–1977.Google Scholar