TY - JOUR

T1 - High-resolution direct numerical simulation of turbulence

AU - Kaneda, Y.

AU - Ishihara, T.

N1 - Funding Information:
The DNS studies using the ES and the VPP5000 system were carried out under collaboration with Drs K. Yoshida, M. Yokokawa, K. Itakura and A. Uno. The authors would like to express their thanks to them. They are also grateful to Mr M. Yagyu for his assistance in making the animations. This work was partially supported by Grant-in-Aids for the 21st COE ‘Frontiers of Computational Science’, (B)(2)14340033, (B)17340117, (C)(2)15607011, and (C)17560051 from the Japan Society for the Promotion of Science.

PY - 2006

Y1 - 2006

N2 - We performed high-resolution direct numerical simulations (DNS) of incompressible turbulence in a periodic box by using a Fourier spectral method with the number of grid points up to 40963. The simulations consist of two series: one with kmaxη ∼ 1 (series 1), and the other with kmaxη ∼ 2 (series 2), where kmax is the highest wavenumber in each simulation, and η is the Kolmogorov length scale. In the 40963 DNS, the Taylor scale Reynolds number Rλ ∼ 1200 and the ratio of L/η of the integral length scale L to η is approximately 2200, in series 1. The DNS data analysis reveals simple scaling of various spectra, and also sheds some light on (i) the energy spectrum at high Rλ, (ii) the asymptotic Rλ-dependence of the normalized energy dissipation rate, (iii) the anomalous scaling of the spectra of energy dissipation and enstrophy, and so on. After some preliminary remarks on the methods and limitations of the DNS, this paper presents a review of the DNS data analysis. Discussions are also made on some questions invoked by the DNS.

AB - We performed high-resolution direct numerical simulations (DNS) of incompressible turbulence in a periodic box by using a Fourier spectral method with the number of grid points up to 40963. The simulations consist of two series: one with kmaxη ∼ 1 (series 1), and the other with kmaxη ∼ 2 (series 2), where kmax is the highest wavenumber in each simulation, and η is the Kolmogorov length scale. In the 40963 DNS, the Taylor scale Reynolds number Rλ ∼ 1200 and the ratio of L/η of the integral length scale L to η is approximately 2200, in series 1. The DNS data analysis reveals simple scaling of various spectra, and also sheds some light on (i) the energy spectrum at high Rλ, (ii) the asymptotic Rλ-dependence of the normalized energy dissipation rate, (iii) the anomalous scaling of the spectra of energy dissipation and enstrophy, and so on. After some preliminary remarks on the methods and limitations of the DNS, this paper presents a review of the DNS data analysis. Discussions are also made on some questions invoked by the DNS.

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U2 - 10.1080/14685240500256099

DO - 10.1080/14685240500256099

M3 - Review article

AN - SCOPUS:33645554689

VL - 7

SP - 1

EP - 17

JO - Journal of Turbulence

JF - Journal of Turbulence

SN - 1468-5248

ER -