TY - JOUR
T1 - The bottleneck effect and the Kolmogorov constant in isotropic turbulence
AU - Donzis, D. A.
AU - Sreenivasan, K. R.
N1 - Funding Information:
The DNS database used in this work, including the data from the largest 40963 simulations, has been generated in collaboration with P. K. Yeung at the Georgia Institute of Technology. The authors would like to thank U. Frisch for useful comments on the ideas presented here. They also acknowledge the computational time at the Texas Advanced Computing Center, Austin, TX, and the National Institute for Computational Sciences, Oak Ridge, TN. This work was supported by the National Science Foundation Grants CBET-553867 and CTS-0553602.
PY - 2010/8
Y1 - 2010/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77957168529&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77957168529&partnerID=8YFLogxK
U2 - 10.1017/S0022112010001400
DO - 10.1017/S0022112010001400
M3 - Article
AN - SCOPUS:77957168529
SN - 0022-1120
VL - 657
SP - 171
EP - 188
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -