Hierarchy of coherent vortices in turbulence behind a cylinder

To draw concrete pictures of the hierarchy of multiscale coherent vortices in turbulence behind a cylinder and to reveal their sustaining mechanism, we conduct direct numerical simulations of the turbulence at the Reynolds number, which is defined by the uniform inflow velocity and the cylinder diameter, 5000. The turbulence consists of three kinds of hierarchies of coherent vortices in three distinct regions: namely, the downstream region, the recirculation region just behind the cylinder and the separate shear layers. By tracking the temporal evolution of multiscale vortices in each of these regions, we demonstrate that, in all the three regions, smaller coherent vortices tend to align in the direction perpendicular to larger ones. This implies that smaller vortices are stretched and amplified in the strain-rate fields around larger ones. We also show the relevance of this observation to the energy cascade. Smaller-scale vortices receive the kinetic energy in the regions where they are stretched by larger-scale vortices; and, at the same time, they tend to compress larger ones, thus reducing larger-scale kinetic energy.