Effective Drift Velocity from Turbulent Transport by Vorticity

We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length-scales larger than $\mathrm{\ell }$ 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 $\mathrm{\ell }$. 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 $\mathrm{\ell }$ 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, ${\text{bv}}_{\ast }$, 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, $\text{OL}{\text{bu}}_{\mathrm{\ell }}$, but by the effective velocity, $\text{OL}{\text{bu}}_{\mathrm{\ell }}+{\text{bv}}_{\ast }$, the physics of which may improve commonly used LES models.