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March  2010, 28(1): 227-241. doi: 10.3934/dcds.2010.28.227

Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases


Member of French Academy of Sciences, Laboratory for Geophysical and Industrial Flows, Grenoble, France

Received  September 2009 Revised  November 2009 Published  April 2010

This is the second of two articles dedicated to Roger Temam and Claude-Michel Brauner on turbulence large-eddy simulations using stochastic two-point closures. The first paper [31] has dealt with applications to isotropic turbulence. It has also discussed personal memories of Roger and Claude-Michel, and how we have collaborated on turbulence two-point closures applied to Burgers equation by studying the so-called Burgers-MRCM model. The present paper is basically a review of what can be done with the same models for LES of inhomogeneous turbulence (free-shear and wall-bounded flows) both in incompressible and compressible situations. It borrows results taken from Lesieur and colleagues [28][29][30]. We discuss also simulations obtained with the aid of dynamic multilevel methods (DML) of Dubois, Jauberteau and Temam [19]. Afterwards we consider the incompressible free-shear flows: temporal mixing layers, for which we review the helical-pairing phenomenon both numerically and experimentally, and mixing of a passive scalar in coaxial jets. We study the plane channel with LES and DML calculations. We look at passive control using longitudinal riblets and optimal control as developed by Temam and coworkers. We calculate with DNS and LES channels and mixing layers rotating about a spanwise axis, and demonstrate a universal character of the local Rossby number in anticyclonic regions. Finally we discuss compressible turbulence LES with applications to a subsonic (Mach 0.7) and supersonic (Mach 1.4) round jet.
Citation: Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 227-241. doi: 10.3934/dcds.2010.28.227

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