Issue |
ESAIM: M2AN
Volume 36, Number 2, March/April 2002
|
|
---|---|---|
Page(s) | 345 - 372 | |
DOI | https://doi.org/10.1051/m2an:2002016 | |
Published online | 15 May 2002 |
Impact of the variations of the mixing length in a first order turbulent closure system
1
IRMAR, INSA, Campus de Beaulieu, 35043 Rennes Cedex, France.
2
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042
Rennes Cedex, France.
Received:
3
October
2001
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 . The mixing length
acts as a parameter which controls the
turbulent part in
. The main theoretical results that we have
obtained concern the uniqueness of the solution for bounded eddy viscosities
and small values of
and its asymptotic decreasing as
in more general cases. Numerical experiments
illustrate but also allow to extend these theoretical results: uniqueness is
proved only for
small enough while regular solutions are numerically
obtained for any values of
. A convergence theorem is proved for
turbulent kinetic energy:
as
but for velocity
we obtain only weaker results.
Numerical results allow to conjecture that
and
as
So we can conjecture that this classical turbulent model obtained
with one degree of closure regularizes the solution.
Mathematics Subject Classification: 35Q30 / 76M10 / 76DXX / 76FXX / 46TXX / 65NXX
Key words: Turbulence modelling / energy methods / mixing length / finite-elements approximations.
© EDP Sciences, SMAI, 2002
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