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Coherent structure detection and the inverse cascade mechanism in two-dimensional Navier–Stokes turbulence

Published online by Cambridge University Press:  19 May 2023

Jiahan Wang Open the ORCID record for Jiahan Wang [Opens in a new window] ,
Jörn Sesterhenn Open the ORCID record for Jörn Sesterhenn [Opens in a new window]  and
Wolf-Christian Müller Open the ORCID record for Wolf-Christian Müller [Opens in a new window]
Jiahan Wang
Affiliation:
Zentrum für Astronomie und Astrophysik, ER 3-2, Technische Universität Berlin, Hardenbergstr. 36a, 10623 Berlin, Germany
Jörn Sesterhenn
Affiliation:
Technische Mechanik und Strömungsmechanik, Universität Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany
Wolf-Christian Müller*
Affiliation:
Zentrum für Astronomie und Astrophysik, ER 3-2, Technische Universität Berlin, Hardenbergstr. 36a, 10623 Berlin, Germany
*
†Email address for correspondence: wolf-christian.mueller@tu-berlin.de
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Abstract

Coherent structures in two-dimensional Navier–Stokes turbulence are ubiquitously observed in nature, experiments and numerical simulations. The present study conducts a comparison between several structure detection schemes based on the Okubo–Weiss criterion, the vorticity magnitude and Lagrangian coherent structures (LCSs), focusing on the inverse cascade in two-dimensional hydrodynamic turbulence. A recently introduced vortex scaling phenomenology (Burgess & Scott, J. Fluid Mech., vol. 811, 2017, pp. 742–756) allows the quantification of the respective thresholds required by these methods based on physical properties of the flow. The resulting improved comparability allows us to identify characteristic relative differences in the detection sensitivity between the employed structure detection techniques. With respect to the inverse cascade of energy, coherent structures contribute, as expected, substantially less to the cross-scale flux than the residual incoherent parts of the flow although the energetically dominant coherent structures lead to an important large-scale deformation of the energy spectrum. This cascade inactivity can be understood by an increased misalignment of strain-rate and subgrid stress tensors within coherent structures. At the same time, the structures exhibit strong and localised nonlinear cross-scale interactions that appear to stabilise them. We quantify and interpret the resulting shape preservation of coherent structures in terms of a multi-scale gradient approach (Eyink, J. Fluid Mech., vol. 549, 2006, pp. 191–214) as the depletion of strain rotation and vorticity gradient stretching whereas the dynamics of the residual fluctuations are consistent with the vortex thinning picture.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A28
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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