Study of the Geometry of Flow Patterns in Compressible Isotropic Turbulence

The geometry of flow patterns in numerically simulated compressible isotropic turbulent flows for high r.m.s. Mach numbers was studied using three-dimensional critical point theory. The solution trajectories for three first-order linear differential equations are used to classify the elementary three-dimensional flow patterns defined by instantaneous streamlines. Fluid motions characterized by high rates of kinetic energy dissipation and / or high enstrophy are of particular interest. It is found that motions corresponding to high rates of dissipation are characterized by a 3-D rate-of-strain topology which is of the saddle-saddle-unstable node type, similar to the compressible mixing layer. Fluid motions corresponding to a high rate of dilatation dissipation are characterized by a topology of the node-node-node type in particular. The influences of Mach number on the geometry of flow patterns are described.