Effective Drift Velocity from Turbulent Transport by Vorticity in Compressible Turbulence

We analyze turbulence transport generated by strong shocks. Using a systematic non-perturbative expansion due to Eyink [1], we show that unlike strain, which acts as an anisotropic diffusion/anti-diffusion tensor, vorticity's contribution is solely a conservative advection by an eddy-induced non-divergent velocity, v_*, that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained (in a simulation) or under-resolved (in a lab measurement) quantities is accomplished not by the coarse-grained flow velocity, û, but by the effective velocity, û+v_*. The physics of this effective transport is missing from current turbulence models and may aid in the interpretation of data from experiments.

[1] Eyink, G. L., J. Fluid Mech. 549 (2006).