Thin Shear Layers in High Reynolds Number Turbulence—DNS Results

Abstract

Using direct numerical simulation of turbulence in a periodic box driven by homogeneous forcing, with a maximum of 40963 grid points and Taylor micro-scale Reynolds numbers Rλ up to 1131, it is shown that there is a transition in the forms of the significant, high vorticity, intermittent structures, from isolated vortices when Rλ is less than 102 to complex thin-shear layers when Rλ exceeds about 103. Both the distance between the layers and their widths are comparable with the integral length scale. The thickness of each of the layers is of the order of the Taylor micro-scale λ. Across the layers the velocity ‘jumps’ are of the order of the rms velocity uo of the whole flow. Within the significant layers, elongated vortical eddies are generated, with microscale thickness lv ~10η ≪ λ, with associated peak values of vorticity as large as 35ωrms and with velocity jumps as large as 3.4uo, where η is the Kolmogorov micro scale and ωrms the rms vorticity. The dominant vortical eddies in the layers, which are approximately parallel to the vorticity averaged over the layers, are separated by distances of order lv. The close packing leads to high average energy dissipation inside the layer, as large as ten times the mean rate of energy dissipation over the whole flow. The interfaces of the layers act partly as a barrier to the fluctuations outside the layer. However, there is a net energy flux into the small scale eddies within the thin layers from the larger scale motions outside the layer.