# Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

Anne-Claire Bennis; Tomas Chacón Rebollo; Macarena Gómez Mármol; Roger Lewandowski

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 6, page 1255-1277
- ISSN: 0764-583X

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topBennis, Anne-Claire, et al. "Numerical modelling of algebraic closure models of oceanic turbulent mixing layers." ESAIM: Mathematical Modelling and Numerical Analysis 44.6 (2010): 1255-1277. <http://eudml.org/doc/250700>.

@article{Bennis2010,

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.
},

author = {Bennis, Anne-Claire, Chacón Rebollo, Tomas, Gómez Mármol, Macarena, Lewandowski, Roger},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Turbulent mixing layers; Richardson number; first order closure models; conservative numerical
solution; stability of steady states; tests for tropical seas; turbulent mixing layers; conservative numerical solution},

language = {eng},

month = {10},

number = {6},

pages = {1255-1277},

publisher = {EDP Sciences},

title = {Numerical modelling of algebraic closure models of oceanic turbulent mixing layers},

url = {http://eudml.org/doc/250700},

volume = {44},

year = {2010},

}

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

DA - 2010/10//

PB - EDP Sciences

VL - 44

IS - 6

SP - 1255

EP - 1277

AB -
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.

LA - eng

KW - Turbulent mixing layers; Richardson number; first order closure models; conservative numerical
solution; stability of steady states; tests for tropical seas; turbulent mixing layers; conservative numerical solution

UR - http://eudml.org/doc/250700

ER -

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