A dynamic subfilterscale model for plane parallel flows
type de publication 
article dans une revue internationale avec comité de lecture 
date de publication 
2001 
auteur(s) 
Dubrulle Bérengère; Laval JeanPhilippe; Nazarenko Sergey V.; Kevlahan Nicholas 
journal (abréviation) 
Physics of Fluids (Phys. Fluids) 
volume (numéro) 
13 (7) 
 
pages 
2045 – 2064 
résumé 
We present a dynamic model of the subfiltered scales in plane parallel geometry using a generalized, stochastic RDT theory. This new model provides expressions for the turbulent Reynolds subfilterscale stresses via estimates of the subfilter {em velocities/} rather than velocity correlations. Subfilterscale velocities are computed using an auxiliary equation which is derived from the NavierStokes equations using a simple model of the subfilter energy transfers. It takes the shape of a RDT equation for the subfilter velocities, with a stochastic forcing. An analytical test of our model is provided by assuming deltacorrelation in time for the supergrid energy transfers. It leads to expressions for the Reynolds stresses as a function of the mean flow gradient in the plane parallel geometry and can be used to derive mean equilibrium profiles both in the nearwall and core regions. In the nearwall region we derive a general
expression for the velocity profile which is linear in the viscous layer and logarithmic outside. This expression involves two physical parameters: the von Karman constant and the size of the viscous layer (which can be computed via a numerical implementation of our model). Fits of experimental profiles using our general formula provides reasonable values of these parameters kappa=0.4 to kappa=0.45, the size of the viscous layer is about 15 wall units). In the core region, we find that the shape of the profile depends on the geometry of the flow: it ranges from algebraic in channel flow, to exponential in the bulk of boundary layers, and linear in plane Couette flow. This classification is consistent with Oberlack's system, which is based on symmetry arguments. Fits of boundary layer flows or channel flows at different Reynolds number over the whole flow region are performed using our results, and are found to be in very good agreement with available data. 
mots clés 
Turbulence model, Boundary Layers 
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