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 $\ell$ by smaller scale (subscale) turbulence. We use the first term in a multiscale gradient expansion due to Eyink [ J. Fluid Mech. 549, 159 (2006)], 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/antidiffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced nondivergent velocity, ${\mathbf{v}}_{*}$, 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, ${\overline{\mathbf{u}}}_{\ell }$, but by the effective velocity, ${\overline{\mathbf{u}}}_{\ell }+{\mathbf{v}}_{*}$, the physics of which may improve commonly used LES models.