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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.

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