Statistics of Coherent Fine Scale Structure in Turbulent Mixing Layer

Abstract

Fine scale structure in turbulence has been one of the most important subjects in turbulence research. Many theoretical works have been conducted to establish the theory of turbulence which can explain the intermittency in small scales (Townsend, 1951; Tennekes, 1968; Lundgren, 1982; Pullin and Saffman, 19893; Saffman and Pullin, 1994). Most of them are based on an assumption that turbulence is composed of randomly distributed fine scale eddies such as tube-like or sheet-like vortices, and each of those vortices is considered to be an analytical solution of Navier-Stokes equations. Recently, direct numerical simulations of turbulence have been conducted to clarify the structure of small scale motion in turbulence (Kerr, 1985; Sheet al.1990; Vincent and Meneguzzi, 1991; Ruetsch and Maxey, 1991; Ruetsch and Maxey, 1992; Jimenezet al.1993; Vincent and Meneguzzi, 1994; Tanahashiet al.1996). Our recent studies (Tanahashiet al.1997a; Tanahashiet al.1997b; Tanahashiet al.1998) showed that homogeneous isotropic turbulence consists of a lot of similar tube-like eddies and that mean azimuthal velocity profile of them can be approximated by Burgers’ vortex. Characteristics of these tube-like eddies can be scaled by Kolmogorov micro scale(71)and r.m.s. of velocity fluctuation(u _rn and mean diameter of these tube-like eddies is about 1071 and maximum of the mean azimuthal velocity is about 0.6 0.7u_rms(Tanahashiet al.1997b; Tanahashiet al.1998). These tube-like eddies can be called as `coherent fine scale structure of turbulence’ (Tanahashiet al.1997a). If turbulence has a universal fine scale structure, these coherent fine scale eddies will be observed in other kind of turbulent flow.