A scalar subgrid model with flow structure for large-eddy simulations of scalar variances

Abstract

A new model to simulate passive scalar fields in large-eddy simulations of turbulence is presented. The scalar field is described by clouds of tracer particles and the subgrid contribution of the tracer displacement is modelled by a kinematic model which obeys Kolmogorov's inertial-range scaling, is incompressible and incorporates turbulent-like flow structure of the turbulent small scales. This makes it possible to study the scalar variance field with inertial-range effects explicitly resolved by the kinematic subgrid field while the LES determines the value of the Lagrangian integral time scale TL. In this way, the modelling approach does not rely on unknown Lagrangian input parameters which determine the absolute value of the scalar variance.The mean separation of particle pairs displays a well-defined Richardson scaling in the inertial range, and we find that the Richardson constant GΔ ≈ 0.07 which is small compared to the value obtained from stochastic models with the same TL. The probability density function of the separation of particle pairs is found to be highly non-Gaussian in the inertial range of times and for long times becomes Gaussian. We compute the scalar variance field for an instantaneous line source and find good agreement with experimental data.