Scaling exponents saturate in three-dimensional isotropic turbulence

Kartik P. Iyer, Katepalli R. Sreenivasan, and P. K. Yeung
Phys. Rev. Fluids 5, 054605 – Published 15 May 2020

Abstract

From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the following (somewhat contested) results: the 4/5ths law holds in an intermediate range of scales and that the second-order exponent over the same range of scales is anomalous, departing from the self-similar value of 2/3 and approaching a constant of 0.72 at high Reynolds numbers. We compare to some typical theories the dependence of longitudinal exponents as well as their derivatives with respect to the moment order n, and estimate the most probable value of the Hölder exponent. We demonstrate that the transverse scaling exponents saturate for large n, and trace this trend to the presence of large localized jumps in the signal. The saturation value of about 2 at the highest Reynolds number suggests, when interpreted in the spirit of fractals, the presence of vortex sheets rather than more complex singularities. In general, the scaling concept in hydrodynamic turbulence appears to be more complex than even the multifractal description.

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  • Received 17 January 2020
  • Accepted 23 April 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.054605

©2020 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & ThermodynamicsFluid Dynamics

Authors & Affiliations

Kartik P. Iyer1, Katepalli R. Sreenivasan1,2,*, and P. K. Yeung3

  • 1Department of Mechanical and Aerospace Engineering, New York University, New York, New York 11201, USA
  • 2Department of Physics and the Courant Institute of Mathematical Sciences, New York University, New York, New York 11201, USA
  • 3Schools of Aerospace and Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

  • *krs3@nyu.edu

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Vol. 5, Iss. 5 — May 2020

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