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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 ,
Tomas Chacón Rebollo ,
Macarena Gómez Mármol  and
Roger Lewandowski
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.

Keywords

Turbulent mixing layersRichardson numberfirst order closure modelsconservative numerical solutionstability of steady statestests for tropical seas
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 6 , November 2010 , pp. 1255 - 1277
Copyright
© EDP Sciences, SMAI, 2010

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