By Marcel Lesieur

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Another problem concerns the macropressure that has been introduced, for it contains the unknown trace of the subgrid-stresses tensor. This is fine if one is not interested in the exact value of the static pressure. If, however, the latter is needed,3 then it is necessary to model the trace Tll . A similar problem arises in LES of compressible turbulence, for which the same type of macropressure will be introduced (see Chapter 7). Notice finally that the use of subgrid models in a rotating frame poses realizability problems; these are discussed by Horiuti [127] and Domaradzki and Horiuti [71].

U = 0. Then ρ may either be uniform or have a mean variation taken into account through Boussinesq’s approximation (see Lesieur [170], Chapter II). 1 LES equations for a flow of constant density To begin with, let us consider a numerical solution of the Navier–Stokes equations with constant density ρ0 carried out in physical space, using finitedifference or finite-volume methods. Let x be a scale characteristic of the grid mesh. To eliminate the subgrid scales, we introduce a filter of width x. 1) and the subgrid-scale field is the departure of the actual flow with respect to the filtered field: f = f¯ + f .

Advanced multifractal studies of three-dimensional isotropic turbulence are presented in Frisch [103]. The multifractal character of turbulence might be at the origin of departures from Kolmogorov’s 1941 laws [145] concerning the velocity structure functions of high order. 9. Schematic view of the backward-facing step. 2 Backward-facing step We now present LES results of a uniform-density flow above a straight backward-facing step. The code used is TRIO-VF, a tool developed for industrial applications of turbulence modeling and LES by the Commissariat a` l’Energie Atomique (CEA) in France.

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