Introduction

Abstract

Among the three ways to compute turbulent flows, namely O. Reynolds’ statistical approach, the large-eddy (LES) and the direct simulation (DS) approaches, the latter is the most attractive because it dispenses with models and solves the unfiltered Navier-Stokes equations for suitable initial and boundary conditions. Since in a DS all turbulent length and time scales are resolved — from the largest down to the smallest scales, which decrease rapidly with increasing Reynolds number — its application is limited to low Reynolds number flow. There is at present only one possibility to study the instantaneous structure of a high Reynolds number flow, namely through large-eddy simulation. Its basic idea is to compute the large scale turbulence directly and to model the small-scale (sub-grid scale, SGS) part, which is supposed to behave universally, so that a small number of parameters are sufficient to describe its dynamics. Sophisticated SGS models have been proposed in the past, based on modern statistical theory of isotropic turbulence; however, simple models of the gradient- diffusion type were used and tested more extensively. The review articles of Ferziger (1983), Rogallo and Moin (1984) and the monograph of Lesieur (1987) provide comprehensive and deep insight into the state of the art and the theoretical background of SGS modeling. Reynolds’ statistical approach, on the other hand, which defines and calculates only mean values, involves a complete loss of information on turbulence spectra and provides therefore the most serious closure problem.