Study of the Geometry of Flow Patterns in Compressible Isotropic Turbulence.

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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.

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