Eulerian Model for Mean Turbulent Diffusion of Particles in Free Shear Layers

Abstract

A simple Eulerian model is developed to determine the qualitative mean transverse diffusion in a free shear flow of a particle with a drag coefficient inversely proportional to the particle Reynolds number. The model is based on integrating the particle equation of motion within a single time-varying eddy to yield a closed-form analytic expression for the turbulent diffusion. The description is based on an average local length scale and an average local timescale of the turbulence similar to previous Lagrangian stochastic diffusion models. The resulting expression indicates three important nondimenslonal parameters: a local Stokes number (ratio of particle response time to eddy lifetime), an eddy Froude number (ratio of rotational acceleration to gravitational acceleration), and a drift parameter (ratio of particle terminal velocity to turbulent rms fluctuations), where the third parameter is simply a function of the first two. The model yields a particle diffusion greater than that of a scalar for a local Stokes number of order unity, the value of which depends on the eddy Froude number