Vortex definition and “vortex criteria”

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It is well known that the vorticity ω=▽ × u,where u is fluid velocity,has clear mathematic definition,but for viscous flow the definition of a vortex remains an open problem for long [1,2],which has now evolved to a big confusion after many "vortex identification criteria"("vortex criteria" for short) were proposed to identify various turbulent coherent structures observed experimentally and numerically.
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