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Impact of the variations of the mixing length in a first order turbulentclosure system
Published online by Cambridge University Press: 15 May 2002
Abstract
This paper is devoted to the study of a turbulentcirculation model. Equations are derived from the “Navier-Stokes turbulentkinetic energy” system. Some simplifications are performed but attentionis focused on non linearities linked to turbulent eddy viscosity $\nu _{t}$ . The mixing length $\ell $
acts as a parameter which controls theturbulent part in $\nu _{t}$
. The main theoretical results that we haveobtained concern the uniqueness of the solution for bounded eddy viscositiesand small values of $\ell $
and its asymptotic decreasing as $\ell\rightarrow \infty $
in more general cases. Numerical experimentsillustrate but also allow to extend these theoretical results: uniqueness isproved only for $\ell $
small enough while regular solutions are numericallyobtained for any values of $\ell $
. A convergence theorem is proved forturbulent 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 obtainedwith one degree of closure regularizes the solution.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 2 , March 2002 , pp. 345 - 372
- Copyright
- © EDP Sciences, SMAI, 2002
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