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On the relationships between local vortex identification schemes. (English) Zbl 1071.76015
Summary: We analyse the currently popular vortex identification criteria that are based on pointwise analysis of the velocity gradient tensor. A new measure of spiralling compactness of material orbits in vortices is introduced, and using this measure a new local vortex identification criterion and requirements for a vortex core are proposed. The interrelationships between different criteria are explored analytically and in a few flow examples, using both zero and non-zero thresholds for the identification parameter. These inter-relationships provide a new interpretation of various criteria in terms of the local flow kinematics. A canonical turbulent flow example is studied, and it is observed that all the criteria, given the proposed usage of threshold, result in remarkably similar looking vortical structures. A unified interpretation based on local flow kinematics is offered which allows to predict when similarities or differences can be expected in the vortical structures by using different criteria.

76D17 Viscous vortex flows
76B47 Vortex flows for incompressible inviscid fluids
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