# Impact of the variations of the mixing length in a first order turbulent closure system

Françoise Brossier; Roger Lewandowski

- Volume: 36, Issue: 2, page 345-372
- ISSN: 0764-583X

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topBrossier, Françoise, and Lewandowski, Roger. "Impact of the variations of the mixing length in a first order turbulent closure system." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.2 (2002): 345-372. <http://eudml.org/doc/245830>.

@article{Brossier2002,

abstract = {This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity $\nu _\{t\}$. The mixing length $\ell $ acts as a parameter which controls the turbulent part in $\nu _\{t\}$. The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of $\ell $ and its asymptotic decreasing as $\ell \rightarrow \infty $ in more general cases$.$ Numerical experiments illustrate but also allow to extend these theoretical results: uniqueness is proved only for $\ell $ small enough while regular solutions are numerically obtained for any values of $\ell $. A convergence theorem is proved for turbulent kinetic energy: $k_\{\ell \}\rightarrow 0$ as $\ell \rightarrow \infty ,$ but for velocity $u_\{\ell \}$ we obtain only weaker results. Numerical results allow to conjecture that $k_\{\ell \}\rightarrow 0,$$\nu _\{t\}\rightarrow \infty $ and $u_\{\ell \}\rightarrow 0$ as $\ell \rightarrow \infty .$ So we can conjecture that this classical turbulent model obtained with one degree of closure regularizes the solution.},

author = {Brossier, Françoise, Lewandowski, Roger},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {turbulence modelling; energy methods; mixing length; finite-elements approximations; finite element approximation; turbulent eddy viscosity; uniqueness; convergence},

language = {eng},

number = {2},

pages = {345-372},

publisher = {EDP-Sciences},

title = {Impact of the variations of the mixing length in a first order turbulent closure system},

url = {http://eudml.org/doc/245830},

volume = {36},

year = {2002},

}

TY - JOUR

AU - Brossier, Françoise

AU - Lewandowski, Roger

TI - Impact of the variations of the mixing length in a first order turbulent closure system

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2002

PB - EDP-Sciences

VL - 36

IS - 2

SP - 345

EP - 372

AB - This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity $\nu _{t}$. The mixing length $\ell $ acts as a parameter which controls the turbulent part in $\nu _{t}$. The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of $\ell $ and its asymptotic decreasing as $\ell \rightarrow \infty $ in more general cases$.$ Numerical experiments illustrate but also allow to extend these theoretical results: uniqueness is proved only for $\ell $ small enough while regular solutions are numerically obtained for any values of $\ell $. A convergence theorem is proved for turbulent kinetic energy: $k_{\ell }\rightarrow 0$ as $\ell \rightarrow \infty ,$ but for velocity $u_{\ell }$ we obtain only weaker results. Numerical results allow to conjecture that $k_{\ell }\rightarrow 0,$$\nu _{t}\rightarrow \infty $ and $u_{\ell }\rightarrow 0$ as $\ell \rightarrow \infty .$ So we can conjecture that this classical turbulent model obtained with one degree of closure regularizes the solution.

LA - eng

KW - turbulence modelling; energy methods; mixing length; finite-elements approximations; finite element approximation; turbulent eddy viscosity; uniqueness; convergence

UR - http://eudml.org/doc/245830

ER -

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