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 : turbulent mixing layers, Richardson number, first order closure models, conservative numerical solution, stability of steady states, tests for tropical seas
@article{M2AN_2010__44_6_1255_0, author = {Bennis, Anne-Claire and Chac\'on Rebollo, Tomas and G\'omez M\'armol, Macarena and Lewandowski, Roger}, title = {Numerical modelling of algebraic closure models of oceanic turbulent mixing layers}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1255--1277}, publisher = {EDP-Sciences}, volume = {44}, number = {6}, year = {2010}, doi = {10.1051/m2an/2010025}, mrnumber = {2769057}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2010025/} }
TY - JOUR AU - Bennis, Anne-Claire AU - Chacón Rebollo, Tomas AU - Gómez Mármol, Macarena AU - Lewandowski, Roger TI - Numerical modelling of algebraic closure models of oceanic turbulent mixing layers JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2010 SP - 1255 EP - 1277 VL - 44 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010025/ DO - 10.1051/m2an/2010025 LA - en ID - M2AN_2010__44_6_1255_0 ER -
%0 Journal Article %A Bennis, Anne-Claire %A Chacón Rebollo, Tomas %A Gómez Mármol, Macarena %A Lewandowski, Roger %T Numerical modelling of algebraic closure models of oceanic turbulent mixing layers %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2010 %P 1255-1277 %V 44 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010025/ %R 10.1051/m2an/2010025 %G en %F M2AN_2010__44_6_1255_0
Bennis, Anne-Claire; Chacón Rebollo, Tomas; Gómez Mármol, Macarena; Lewandowski, Roger. Numerical modelling of algebraic closure models of oceanic turbulent mixing layers. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 6, pp. 1255-1277. doi : 10.1051/m2an/2010025. http://www.numdam.org/articles/10.1051/m2an/2010025/
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