Effective Drift Velocity from Turbulent Transport by Vorticity

TL;DR

This paper demonstrates that in turbulent transport, vorticity induces an effective advection velocity, distinct from the coarse-grained flow, which could enhance large-eddy simulation models.

Contribution

It reveals that subscale vorticity causes a conservative advection of coarse-grained quantities via an eddy-induced velocity, differing from strain effects and informing LES modeling.

Findings

Vorticity contributes to transport through a non-divergent eddy velocity.

Strain acts as an anisotropic diffusion or anti-diffusion.

Effective velocity for advection includes vorticity-induced eddy velocity.

Abstract

We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length-scales larger than $\ell$ by smaller scale (subscale) turbulence. %subscale flux/stress which appear in the evolution of coarse-grained (resolved) scalars/momentum account for the effect of (subgrid) scales smaller than the coarse-graining length $\ell$. We use the first term in a multiscale gradient expansion due to Eyink \cite{Eyink06a}, which exhibits excellent correlation with the exact subscale physics when the partitioning length $\ell$ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/anti-diffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced non-divergent velocity, $\bv_*$, that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity, $\OL\bu_\ell$, but by the effective velocity, $\OL\bu_\ell+\bv_*$, the physics of which may improve commonly used LES models.