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Turbulence at the Lee bound: maximally non-normal vortex filaments and the decay of a local dissipation rate

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posted on 2020-02-20, 13:16 authored by Chris KeylockChris Keylock
© 2019 Cambridge University Press. This paper uses a tight mathematical bound on the degree of the non-normality of the turbulent velocity gradient tensor to classify flow behaviour within vortical regions (where the eigenvalues of the tensor contain a conjugate pair). Structures attaining this bound are preferentially generated where enstrophy exceeds total strain and there is a positive balance between strain production and enstrophy production. Lagrangian analysis of homogeneous, isotropic turbulence shows that attainment of this bound is associated with relatively short durations and an upper limit to the spatial extent of the flow structures that is similar to the Taylor scale. An analysis of the dynamically relevant terms using a recently developed formulation (Keylock, J. Fluid Mech., vol. 848, 2018, pp. 876-904), highlights the controls on this dynamics. In particular, in high enstrophy regions it is shown that the bound is attained when normal strain decreases rather than when non-normality increases. The near absence of normal total strain results in a source of intermittency in the dynamics of dissipation that is hidden in standard analyses. It is shown that of the two terms that contribute to the non-normal production dynamics, it is the one that is typically smallest in magnitude that is of greatest importance within these filaments. The typical distance between filament centroids is just less than a Taylor scale, implying a connection to the manner in which flow topology at the Taylor scale explains dissipation at smaller scales.

Funding

Royal Academy of Engineering/ Leverhulme Trust Senior Research Fellowship LTSRF1516-12-89.

History

School

  • Architecture, Building and Civil Engineering

Published in

Journal of Fluid Mechanics

Volume

881

Pages

283 - 312

Publisher

Cambridge University Press

Version

  • AM (Accepted Manuscript)

Rights holder

© Cambridge University Press

Publisher statement

This paper was accepted for publication in the journal Journal of Fluid Mechanics and the definitive published version is available at https://doi.org/10.1017/jfm.2019.779

Acceptance date

2019-09-17

Publication date

2019-10-24

Copyright date

2019

ISSN

0022-1120

eISSN

1469-7645

Language

  • en

Depositor

Prof Chris Keylock ( Deposit date: 19 February 2020