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The bottleneck effect and the Kolmogorov constant in isotropic turbulence

Published online by Cambridge University Press:  10 June 2010

D. A. DONZIS  and
K. R. SREENIVASAN
D. A. DONZIS*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
K. R. SREENIVASAN
Affiliation:
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA Department of Physics and the Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: donzis@tamu.edu
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Abstract

A large database from direct numerical simulations of isotropic turbulence, including recent simulations for box sizes up to 40963 and the Taylor–Reynolds number Rλ ≈ 1000, is used to investigate the bottleneck effect in the three-dimensional energy spectrum and second-order structure functions, and to determine the Kolmogorov constant, CK. The difficulties in estimating CK at any finite Reynolds number, introduced by intermittency and the bottleneck, are assessed. The data conclusively show that the bottleneck effect decreases with the Reynolds number. On this basis, an alternative to the usual procedure for determining CK is suggested; this proposal does not depend on the particular choices of fitting ranges or power-law behaviour in the inertial range. Within the resolution of the numerical data, CK thus determined is a Reynolds-number-independent constant of ≈1.58 in the three-dimensional spectrum. A simple model including non-local transfer is proposed to reproduce the observed scaling features of the bottleneck.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010 , pp. 171 - 188
Copyright
Copyright © Cambridge University Press 2010

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