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Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

Published online by Cambridge University Press:  17 March 2010

Anne-Claire Bennis
Affiliation:
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France.
Tomas Chacón Rebollo
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numerico, Universidad de Sevilla, C/Tarfia, s/n. 41080, Sevilla, Spain. chacon@us.es
Macarena Gómez Mármol
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numerico, Universidad de Sevilla, C/Tarfia, s/n. 41080, Sevilla, Spain. chacon@us.es
Roger Lewandowski
Affiliation:
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France.
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Abstract

We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness of a simplified model, by application of the linearization principle for non-linear parabolic equations. We finally present some numerical tests for realistic flows in tropical seas that reproduce the formation of mixing layers in time scales of the order of days, in agreement with the physics of the problem. We conclude that the typical mixing layers are transient effects due to the variability of equatorial winds. Also, that these states evolve to steady states in time scales of the order of years, under negative surface energy flux conditions.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2010

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References

Blanke, B. and Delecluse, P., Variability of the tropical atlantic ocean simulated by a general circulation model with two different mixed-layer physics. J. Phys. Oceanogr. 23 (1993) 13631388. 2.0.CO;2>CrossRef
Bramble, J.H., Pasciak, J.E. and Steinbach, O., On the stability of the l 2 projection in h 1. Math. Comp. 7 (2001) 147156. CrossRef
H. Burchard, Applied turbulence modelling in marine water. Ph.D. Thesis, University of Hambourg, Germany (2004).
Gaspar, P., Gregoris, Y. and Lefevre, J.-M., A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: test at Station Papa and long-term upper ocean study site. J. Geophys. Res. 16 (1990) 179193.
Gent, P.R., The heat budget of the toga-coare domain in an ocean model. J. Geophys. Res. 96 (1991) 33233330. CrossRef
Goosse, H., Deleersnijder, E., Fichefet, T. and England, M.H., Sensitivity of a global coupled ocean-sea ice model to the parametrization of vertical mixing. J. Geophys. Res. 104 (1999) 1368113695. CrossRef
Jones, J.H., Vertical mixing in the equatorial undercurrent. J. Phys. Oceanogr. 3 (1973) 286296. 2.0.CO;2>CrossRef
Z. Kowalik and T.S. Murty, Numerical modeling of ocean dynamics. World Scientific (1993).
Large, W.G., McWilliams, C. and Doney, S.C., Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parametrization. Rev. Geophys. 32 (1994) 363403. CrossRef
G. Madec, P. Delecluse, M. Imbard and C. Levy, OPA version 8.0, Ocean General Circulation Model Reference Manual. LODYC, Int. Rep. 97/04 (1997).
McPhaden, M., The tropical atmosphere ocean (tao) array is completed. Bull. Am. Meteorol. Soc. 76 (1995) 739741.
Mellor, G. and Yamada, T., Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys. 20 (1982) 851875. CrossRef
Pacanowski, R.C. and Philander, S.G.H., Parametrization of vertical mixing in numericals models of the tropical oceans. J. Phys. Oceanogr. 11 (1981) 14431451. 2.0.CO;2>CrossRef
J. Pedloski, Geophysical fluid dynamics. Springer (1987).
Potier-Ferry, M., The linearization principle for the stability of solutions of quasilinear parabolic equations. Arch. Ration. Mech. Anal. 77 (1981) 301320. CrossRef
Robinson, A.R., An investigation into the wind as the cause of the equatiorial undercurrent. J. Mar. Res. 24 (1966) 179204.

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