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Can vortex criteria be objectivized?

Published online by Cambridge University Press:  08 December 2020

George Haller Open the ORCID record for George Haller [Opens in a new window]
George Haller*
Affiliation:
Institute for Mechanical Systems, ETH Zürich, Zürich, Switzerland
*
†Email address for correspondence: georgehaller@ethz.ch
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Abstract

Several procedures have been proposed to modify non-objective (observer-dependent) local vortex criteria so that they become objective. These modifications are only justifiable if they are equivalent to applying the original criteria after a generalized (possibly nonlinear) frame change is performed on the flow domain; otherwise, the arguments used in deriving those criteria no longer apply. To examine the feasibility of available objectivization procedures, we derive here necessary and sufficient conditions for the existence of a generalized frame change prescribed pointwise through its Jacobian field. From these conditions we conclude that, of all proposed objectivization approaches in the literature, only the replacement of the spin tensor with the spin-deviation tensor is applicable to generic fluid flows.

JFM classification

Mathematical Foundations: Computational methods Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A25
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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