Mesoscale elements description of turbulent flow

Abstract

• Description of turbulent flow as an ensemble of finite size, or mesoscale , Lagrangian elements is formulated. • Mesoscale element has no deterministic position but a probability of presence and a region of influence growing with time. • Consideration of finite size elements allows explicit account of molecular transport described through pairwise interactions. • The method applied to a mixing layer in grid turbulence yielded scalar statistics in quantitative agreement with experiments. This work proposes to describe a turbulent flow using a set of mesoscale elements, that is fluid elements of small, but finite, size the properties of which are representative of larger region surrounding them. Consideration of fluid elements of finite dimensions allows one to formulate a small scale mixing model with an explicit dependency on the molecular transport coefficients. The dimensions of a mesoscale element are determined from an evolution equation accounting for the molecular diffusion and the strain rate induced by small-scale turbulence while its position is determined by convection by large-scale velocity components. In addition to consideration of the fluid elements of a finite size, the second key new concept is the notion of radius of influence over which such an element contributes to the statistics of the flow; this radius grows with time. It is shown that the proposed method satisfies the mass conservation and normalisation of the probability density functions of scalar quantities . The proposed method is illustrated with simulations of thermal mixing layer in grid turbulence.