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

Françoise Brossier; Roger Lewandowski

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 36.2 (2010): 345-372. <http://eudml.org/doc/194108>.

@article{Brossier2010,

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},

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

language = {eng},

month = {3},

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/194108},

volume = {36},

year = {2010},

}

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

DA - 2010/3//

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.; turbulence modelling; finite element approximation; turbulent eddy viscosity; uniqueness; convergence

UR - http://eudml.org/doc/194108

ER -

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## Citations in EuDML Documents

top- Tomas Chacón Rebollo, Stéphane Del Pino, Driss Yakoubi, An iterative procedure to solve a coupled two-fluids turbulence model
- Miroslav Bulíček, Roger Lewandowski, Josef Málek, On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions
- J. Lederer, R. Lewandowski, A RANS 3D model with unbounded eddy viscosities

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