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Can small-scale turbulence approach a quasi-universal state?

Shunlin Tang*

Robert A. Antonia and Lyazid Djenidi

Yu Zhou

  • Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China

  • Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 New South Wales, Australia

  • Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China and Digital Engineering Laboratory of Offshore Equipment, Shenzhen, 518055, China

  • *shunlin.tang88@gmail.com
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Phys. Rev. Fluids 4, 024607 – Published 19 February, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.024607

Abstract

For the past 50 years or so, Kolmogorov's (1962) correction (K62) to his 1941 hypotheses (K41) has been embraced by an overwhelming majority of turbulence researchers. However, we show in this paper that there are no valid reasons for abandoning K41, a similarity framework known for its simplicity and elegance. In particular, analytical considerations, based on the Navier-Stokes equations, which take into account the finite Reynolds number (FRN) effect, together with all available experimental laboratory data, confirm a tendency towards the universal predictions of K41 as the Reynolds number continues to increase. This is especially true when the focus is on the energy spectrum and velocity structure function in the dissipative range. Incorrectly accounting for the FRN effect, which has been almost invariably mistaken for the intermittency effect, and the inclusion of the atmospheric surface layer data are the major factors which have contributed to the heretofore almost unrivalled acceptance of K62.

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Phys. Rev. Fluids 4, 024607– Published 19 February, 2019
  • Received 25 March 2018
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