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New exact Betchov-like relation for the helicity flux in homogeneous turbulence

Published online by Cambridge University Press:  11 May 2023

Damiano Capocci Open the ORCID record for Damiano Capocci [Opens in a new window] ,
Perry L. Johnson Open the ORCID record for Perry L. Johnson [Opens in a new window] ,
Sean Oughton Open the ORCID record for Sean Oughton [Opens in a new window] ,
Luca Biferale Open the ORCID record for Luca Biferale [Opens in a new window]  and
Moritz Linkmann Open the ORCID record for Moritz Linkmann [Opens in a new window]
Damiano Capocci*
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Rome, Italy
Perry L. Johnson
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-2700, USA
Sean Oughton
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand
Luca Biferale
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Rome, Italy
Moritz Linkmann*
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, UK
*
†Email addresses for correspondence: capocci@roma2.infn.it, moritz.linkmann@ed.ac.uk
†Email addresses for correspondence: capocci@roma2.infn.it, moritz.linkmann@ed.ac.uk
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Abstract

In homogeneous and isotropic turbulence, the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (Johnson, Phys. Rev. Lett., vol. 124, 2020, 104501; J. Fluid Mech., vol. 922, 2021, A3). We extend the formalism to the transfer of kinetic helicity across scales, important in the presence of large-scale mirror‐breaking mechanisms, to identify physical processes resulting in helicity transfer and quantify their contributions to the mean flux in the inertial range. All subfluxes transfer helicity from large to small scales. Approximately 50 % of the mean flux is due to the scale-local vortex flattening and vortex twisting. We derive a new exact relation between these effects, similar to the Betchov relation for the energy flux, revealing that the mean contribution of the former is three times larger than that of the latter. Multi-scale effects account for the remaining 50 % of the mean flux, with approximate equipartition between multi-scale vortex flattening, twisting and entangling.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence theory
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , R1
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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