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Can vortex criteria be objectivized?

Published online by Cambridge University Press:  08 December 2020

George Haller
Affiliation:
Institute for Mechanical Systems, ETH Zürich, Zürich, Switzerland
Corresponding
E-mail address:

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.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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