Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

Anne-Claire Bennis (1) , Tomas Chacon-Rebollo (2) , Macarena Gómez Marmol (2) , Roger Lewandowski (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 US.ES - Departamento de Ecuaciones Diferenciales y Analisis Numerico

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.

Mots clés: first order closure models; stability of steady staes; conservative numerical solution; Richardson number; turbulent mixing layers; tests for tropical seas

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Anne-Claire Bennis, Tomas Chacon-Rebollo, Macarena Gómez Marmol, Roger Lewandowski. Numerical modelling of algebraic closure models of oceanic turbulent mixing layers. ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44 (6), pp.1255-1277. ⟨10.1051/m2an/2010025⟩. ⟨hal-00548725⟩