Vortex criteria can be objectivized by unsteadiness minimization

Holger Theisel, Markus Hadwiger, Peter Rautek, Thomas Theussl, Tobias Günther

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Reference frame optimization is a generic framework to calculate a spatially varying observer field that views an unsteady fluid flow in a reference frame that is as-steady-as-possible. In this paper, we show that the optimized vector field is objective, i.e., it is independent of the initial Euclidean transformation of the observer. To check objectivity, the optimized velocity vectors and the coordinates in which they are defined must both be connected by an Euclidean transformation. In this paper, we show that a recent publication applied this definition incorrectly, falsely concluding that reference frame optimizations are not objective. Furthermore, we prove the objectivity of the variational formulation of the reference frame optimization that was recently proposed and discuss how the variational formulation relates to recent local and global optimization approaches to unsteadiness minimization.
Original languageEnglish (US)
Pages (from-to)107115
JournalPhysics of Fluids
Issue number10
StatePublished - Oct 22 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-11-11
Acknowledgements: As a final example, we compute an objective version of the λ2 criterion following Gu€nther et al.10 to a rotating mixer flow. This is a numerically simulated flow with a bulk rotation that is stirred by three rotating paddles in a cylindrical container. While the left-hand side shows the standard λ2 criterion, the objective version on the right-hand side better reveals weaker vortex structures that are located closer to the rotation center. The work was supported by Grant No. DFG TH 692/18-1 and ETH Research Grant ETH-07 18-1. It was also supported by King Abdullah University of Science and Technology (KAUST). This research used resources of the Core Labs of King Abdullah University of Science and Technology.

ASJC Scopus subject areas

  • Condensed Matter Physics


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