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Vortex stretching and enstrophy production in high Reynolds number turbulence

Dhawal Buaria1,2,*, Eberhard Bodenschatz1,3,4, and Alain Pumir5,1

  • 1Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany
  • 2Tandon School of Engineering, New York University, New York, New York 11201, USA
  • 3Institute for Nonlinear Dynamics, University of Göttingen, D-37077 Göttingen, Germany
  • 4Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
  • 5Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France

  • *dhawal.buaria@ds.mpg.de
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Phys. Rev. Fluids 5, 104602 – Published 9 October, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.104602

Abstract

An essential ingredient of turbulent flows is the vortex stretching mechanism, which emanates from the nonlinear interaction of vorticity and strain-rate tensor and leads to formation of extreme events. We analyze the statistical correlations between vorticity and strain rate by using a massive database generated from very well-resolved direct numerical simulations of forced isotropic turbulence in periodic domains. The grid resolution is up to 122883, and the Taylor-scale Reynolds number is in the range 140–1300. In order to understand the formation and structure of extreme vorticity fluctuations, we obtain statistics conditioned on enstrophy (vorticity-squared). The magnitude of strain, as well as its eigenvalues, is approximately constant when conditioned on weak enstrophy; whereas they grow approximately as power laws for strong enstrophy, which become steeper with increasing Rλ. We find that the well-known preferential alignment between vorticity and the intermediate eigenvector of strain tensor is even stronger for large enstrophy, whereas vorticity shows a tendency to be weakly orthogonal to the most extensive eigenvector (for large enstrophy). Yet the dominant contribution to the production of large enstrophy events arises from the most extensive eigendirection, the more so as Rλ increases. Nevertheless, the stretching in intense vorticity regions is significantly depleted, consistent with the kinematic properties of weakly curved tubes in which they are organized. Further analysis reveals that intense enstrophy is primarily depleted via viscous diffusion, though viscous dissipation is also significant. Implications for modeling are nominally addressed as appropriate.

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Phys. Rev. Fluids 5, 104602– Published 9 October, 2020
  • Received 1 June 2020
  • Accepted 16 September 2020
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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