On the multi-scale mechanism generating enhanced particle settling speeds in turbulence: Part 2

Recent Direct Numerical Simulation (DNS) results in Ireland et al. (J. Fluid Mech., 796:659--711, 2016) for the modified particle settling velocities due to turbulence reveal behavior that is not accounted for by the analysis of Maxey (J. Fluid Mech., 174:441--465, 1987). In Part 1 of this talk we presented a new theoretical analysis of the problem that is able to explain the findings in Ireland et al., and here we supplement the analysis using DNS. The modified settling speeds occur because the average fluid velocity along the inertial particle trajectory is not zero, and to examine how this average is affected by different scales we post-process large DNS data sets where the fluid velocity in the average is subject to coarse-graining. Crucially, the particle trajectories are not themselves subject to the effects of coarse-graining, so that the average is only affected by coarse-graining through the range of scales available for the particles to preferentially sample. The DNS cover Stokes numbers $St\in[0,3]$, Taylor Reynolds numbers $R_\lambda\in[90,600]$, and Froude numbers $Fr=0.052,0.3$. The results confirm the theoretical findings and show how the scales responsible for the enhanced settling increase with increasing $St$, $R_\lambda$ and decreasing $Fr$.