TY - JOUR

T1 - Cancellation exponents in isotropic turbulence and magnetohydrodynamic turbulence

AU - Zhai, X. M.

AU - Sreenivasan, K. R.

AU - Yeung, P. K.

N1 - Funding Information:
The authors acknowledge helpful discussions with Kartik P. Iyer. The authors also thank the reviewers for their comments and suggestions. This work is supported by Grants No. 1036170 and No. 1640771 under the Petascale Resource Allocations Program, and Grant No. 1510749 under the Fluid Dynamics Program, both funded by the National Science Foundation (NSF). The computations and data analyses reported in this paper were performed using BlueWaters at the National Center for Supercomputing Applications (NCSA), University of Illinois at Urbana-Champaign, and the Texas Advanced Computation Center (TACC) of the University of Texas at Austin under the XSEDE program supported by NSF.
Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/2/7

Y1 - 2019/2/7

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevE.99.023102

DO - 10.1103/PhysRevE.99.023102

M3 - Article

C2 - 30934280

AN - SCOPUS:85062008059

SN - 1063-651X

VL - 99

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 2

M1 - 023102

ER -