Dissipation element analysis of scalar fields in turbulence

Abstract

The field of the fluctuating scalar obtained from Direct Numerical Simulation (DNS) in homogeneous shear flow is subdivided into finite size regions within which it varies monotonously. These regions are called dissipation elements and are identified by calculating trajectories normal to isoscalar surfaces starting from every grid point until a minimum and a maximum point is reached. Two parameters describe the statistical properties of dissipation elements sufficiently well: the linear distance between the minimum and maximum points and the absolute value of the scalar difference at these points. The joint probability density function of these parameters decomposes into a conditional pdf of the scalar difference and the marginal pdf of the distance between the minimum and maximum points, the latter being the object of this study. For the length scale distribution function a stochastic evolution equation was derived in a companion paper. It implies the cutting and reconnection of linear elements and the effect of molecular diffusion. The equation is an integral equation and must be solved numerically. In this paper we show how one-dimensional simulations of randomly generated scalar profiles would illustrate the cutting and reconnection processes as well as the drift and disappearance of small elements by molecular diffusion. The resulting distribution function from the simulation shows good agreement with the predicted distribution function. It is concluded that the mean distance between extremal points is of the order of the scalar Taylor length. To cite this article: N. Peters, L. Wang, C. R. Mecanique 334 (2006).