Cancellation exponents in isotropic turbulence and magnetohydrodynamic turbulence

X. M. Zhai, K. R. Sreenivasan, and P. K. Yeung
Phys. Rev. E 99, 023102 – Published 7 February 2019

Abstract

Small-scale characteristics of turbulence such as velocity gradients and vorticity fluctuate rapidly in magnitude and oscillate in sign. Much work exists on the characterization of magnitude variations, but far less on sign oscillations. While in homogeneous turbulence averages performed on large scales tend to zero because of the oscillatory character, those performed on increasingly smaller scales will vary with the averaging scale in some characteristic way. This characteristic variation at high Reynolds numbers is captured by the so-called cancellation exponent, which measures how local averages tend to cancel out as the averaging scale increases, in space or time. Past experimental work suggests that the exponents in turbulence depend on whether one considers quantities in full three-dimensional (3D) space or uses their one- or two-dimensional cuts. We compute cancellation exponents of vorticity and longitudinal as well as transverse velocity gradients in isotropic turbulence at Taylor-scale Reynolds numbers up to 1300 on 81923 grids. The 2D cuts yield the same exponents as those for full 3D, while the 1D cuts yield smaller numbers, suggesting that the results in higher dimensions are more reliable. We make the case that the presence of vortical filaments in isotropic turbulence leads to this conclusion. This effect is particularly conspicuous in magnetohydrodynamic turbulence, where an increased degree of spatial coherence develops along the direction of an imposed magnetic field.

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  • Received 7 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.023102

©2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid Dynamics

Authors & Affiliations

X. M. Zhai1, K. R. Sreenivasan2, and P. K. Yeung3

  • 1School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
  • 2Department of Mechanical and Aerospace Engineering, Department of Physics, and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA*
  • 3Schools of Aerospace Engineering and Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

  • *krs3@nyu.edu

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Issue

Vol. 99, Iss. 2 — February 2019

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