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Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence

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journal contribution
posted on 2018-06-04, 09:04 authored by Chris KeylockChris Keylock
A method is presented for deriving random velocity gradient tensors given a source tensor. These synthetic tensors are constrained to lie within mathematical bounds of the non-normality of the source tensor, but we do not impose direct constraints upon scalar quantities typically derived from the velocity gradient tensor and studied in fluid mechanics. Hence, it becomes possible to ask hypotheses of data at a point regarding the statistical significance of these scalar quantities. Having presented our method and the associated mathematical concepts, we apply it to homogeneous, isotropic turbulence to test the utility of the approach for a case where the behavior of the tensor is understood well. We show that, as well as the concentration of data along the Vieillefosse tail, actual turbulence is also preferentially located in the quadrant where there is both excess enstrophy (Q > 0) and excess enstrophy production (R < 0). We also examine the topology implied by the strain eigenvalues and find that for the statistically significant results there is a particularly strong relative preference for the formation of disklike structures in the (Q < 0,R < 0) quadrant. With the method shown to be useful for a turbulence that is already understood well, it should be of even greater utility for studying complex flows seen in industry and the environment.


This research was supported by a Royal Academy of Engineering/Leverhulme Trust Senior Research Fellowship LTSRF1516-12-89 awarded to the author.



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Physical Review Fluids






KEYLOCK, C.J., 2017. Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence. Physical Review Fluids, 2 (8), 084607.


© American Physical Society


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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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This paper was published in the journal Physical Review Fluids and the definitive published version is available at https://doi.org/10.1103/PhysRevFluids.2.084607.




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