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

Abstract

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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.

How to cite

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Bennis, 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 -

References

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