Keylock, C.J. orcid.org/0000-0002-9517-9896 (2017) Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence. Physical Review Fluids, 2 (8). 084607. ISSN 2469-990X
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 American Physical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number LEVERHULME TRUST (THE) NONE |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 24 Aug 2017 13:54 |
Last Modified: | 24 Aug 2017 13:59 |
Published Version: | https://doi.org/10.1103/PhysRevFluids.2.084607 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevFluids.2.084607 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120521 |