Time-resolved evolution of the wall-bounded vorticity cascade

Abstract

The temporal evolution of vortex clusters in a turbulent channel at Re τ = 950 is studied using DNS sequences with temporal separations among fields short enough for individual structures to be tracked. From the geometric intersection of structures in consecutive fields, we build temporal connection graphs of all the vortex clusters, and, from their properties, define main and secondary branches for each evolution. It is found that the average lifetime of the clusters within a branch is proportional to the cube root of their maximum volumes, and that they move approximately with the local mean velocity. Especial attention is paid to their wall-normal displacement. It is found that their probability of moving away from the wall is only slightly higher than that of moving towards it, and that this behaviour is independent of the wall distance at which the branch is initially created. Finally, direct and inverse physical cascades are defined, associated with the splits and mergers between structures. It is found that the direct cascade predominates, but that both directions are roughly comparable.