A Study of the Geometry of Flow Patterns in a Simulated Compressible Mixing Layer.

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  • 圧縮性混合層の位相幾何学（トポロジー）的構造
  • アッシュクセイ コンゴウソウ ノ イソウ キカガク トポロジー テキ コウゾウ

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Abstract

The geometry of flow patterns in a numerically simulated compressible mixing layer 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 incompressible mixing layer. The topolygy of the unstable focus compressing type is observed for helical pairing motions of the vortical structures. Fluid motions corresponding to high rates of dilatation dissipation are also characterized by the same topology as the solenoidal dissipation motions. Regions of high enstrophy are found to be characterized by the topology of the unstable-focus-stretching, type the topologies stable-focus-stretching, unstable-focus-compressing, and stable-focus-compressing types are also observed for these resions.

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