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stability of steady states

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Numerical modelling of algebraic closure modelsof oceanic turbulent mixing layers
Anne-Claire Bennis, Tomas Chacón Rebollo, Macarena Gómez Mármol, Roger Lewandowski
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 44 / Issue 6 / November 2010

Published online by Cambridge University Press:

17 March 2010, pp. 1255-1277

Print publication:

November 2010
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We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models foroceanic 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.