Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

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. 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.

Compressibility in turbulent magnetohydrodynamics and passive scalar transport: mean-field theory

“…1995, 1996, 1997, 2000, 2001; Pandya & Mashayek 2002; Reeks 2005; Amir et al. 2017). It has also been detected in the direct numerical simulations of Brandenburg, Rädler & Kemel (2012 b ), where the density stratification was caused by gravity.…”

“…2000, 2001; Amir et al. 2017), detected in direct numerical simulations (Haugen et al. 2012), different laboratory experiments (Buchholz et al.…”

“…2006, 2010; Amir et al. 2017) and atmospheric turbulence with temperature inversions (Sofiev et al. 2009).…”

Turbophoresis in forced inhomogeneous turbulence

“…In such cases, the HIPs are found to accumulate in the vicinity of the minima of mean temperature. This large-scale clustering phenomenon, which can be described by turbulent thermal diffusion, was predicted in an analytical study [18,[48][49][50][51][52] and detected in laboratory experiments [53][54][55], DNS [56] and atmospheric observations [57].…”

Transport and diffusion properties of Brownian particles powered by a rotating wheel

“…Note that the rotation of the wheel in the present system can create the turbulence and in the turbulent medium the effective coefficient of turbulent thermal diffusion [34]can be obtained from the approximate method. Here, we use an alternative approximate method to obtain the the bulk diffusivity of Brownian particles driving by the rotating wheel.…”