Large-eddy-simulation closures of passive scalar turbulence: a systematic approach

Abstract

The issue of the parameterization of small-scale (‘subgrid’) turbulence is addressed in the context of passive scalar transport. We focus on the Kraichnan advection model which lends itself to the analytical investigation of the closure problem. We derive systematically the dynamical equations which rule the evolution of the coarse-grained scalar field. At the lowest-order approximation in $l/r$, $l$ being the characteristic scale of the filter defining the coarse-grained scalar field and $r$ the inertial-range separation, we recover the classical eddy-diffusivity parameterization of small scales. At the next-leading order a dynamical closure is obtained. This outperforms the classical model and is therefore a natural candidate for subgrid modelling of scalar transport in generic turbulent flows.