Turbulent thermal diffusion in strongly stratified turbulence: theory and experiments

TL;DR

This paper develops a generalized theory of turbulent thermal diffusion applicable to strong stratification and validates it through laboratory experiments, revealing how particle velocities and diffusion coefficients vary with Stokes number and temperature gradient.

Contribution

It introduces a comprehensive theory of turbulent thermal diffusion for arbitrary conditions and confirms its accuracy with experimental data.

Findings

Effective particle velocity is less than turbulent velocity at high Reynolds numbers.

Inertial particle velocity and diffusion coefficient peak at small Stokes numbers.

Diffusion coefficient decreases with increasing temperature gradient.

Abstract

Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux. This non-diffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers (Phys. Rev. Lett. {\bf 76}, 224, 1996). In this study a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multi-fan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic vertical turbulent velocity for large Reynolds numbers is less than 1. The effective velocity of inertial particles as well as the effective coefficient of turbulent thermal diffusion increase with Stokes numbers reaching the maximum at small Stokes numbers and decreases for larger Stokes numbers. The effective coefficient of turbulent thermal diffusion also decreases with the mean temperature gradient. It has been demonstrated that the developed theory is in a good agreement with the results of the laboratory experiments.