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An objective definition of a vortex

Published online by Cambridge University Press:  17 February 2005

G. HALLER
G. HALLER
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Rm 3-352, Cambridge, MA 02139, [email protected]
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Abstract

The most widely used definitions of a vortex are not objective: they identify different structures as vortices in frames that rotate relative to each other. Yet a frame-independent vortex definition is essential for rotating flows and for flows with interacting vortices. Here we define a vortex as a set of fluid trajectories along which the strain acceleration tensor is indefinite over directions of zero strain. Physically, this objective criterion identifies vortices as material tubes in which material elements do not align with directions suggested by the strain eigenvectors. We show using examples how this vortex criterion outperforms earlier frame-dependent criteria. As a side result, we also obtain an objective criterion for hyperbolic Lagrangian structures.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 525 , 25 February 2005 , pp. 1 - 26
Copyright
© 2005 Cambridge University Press

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