The Spatial Structure of Isotropic Turbulence and the Related Three-Dimensional Graphics Problems

Abstract

Vorticity tubes are observed with great details in data processing from direct numerical simulations of homogeneous turbulence at resolution 240³ (R _λ ≈ 140 with an inertial subrange extended over more than one decade). These tubes correspond to the regions of strongest vorticity as well as regions of lowest pressure. Their width is of the order of a few dissipation scales, while their length can reach the integral scale of the flow. The large velocity regions are sheets located near and parallel to the axis of the tubes but directed perpendicularly to it. The maxima of both the compressive (negative eigenvalue) or extensive (positive eigenvalue) part of the rate of strain tensor are located near the tubes and oriented perpendicularly to their axis. Further, the eigenvector associated with the intermediate eigenvalue is most of time a stretching (positive eigenvalue) and oriented along the axis of the tube. These results are in excellent agreement with recent laboratory measurements (Tsinober et al. 1990).