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On the identification of a vortex. (English) Zbl 0847.76007
The objective definition of a vortex which should identify vortex cores in any flow is developed in the paper. It is shown by known examples that three common intuitive indicators of vortices – pressure minimum, closed or spiraling streamlines and pathlines, and isovorticity surfaces – are inadequate in detecting vortices in an unsteady flow, in general. Moreover, particular examples are given which show that recent Galilean-invariant definitions of a vortex (based on complex eigenvalues of velocity gradient tensor and on the second invariant of this tensor) are insufficient, as well. The authors propose a new definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor containing the sum of squares of the symmetric and antisymmetric parts of the velocity gradient tensor. This definition is found to represent correctly the topology and geometry of vortex cores for large variety of flows.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76F10 Shear flows and turbulence
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