## Abstract

We examine the behavior of the Kolmogorov constants C_{2}, C _{k}, and C_{k1}, which are, respectively, the prefactors of the second-order longitudinal structure function and the three-dimensional and one-dimensional longitudinal energy spectrum in the inertial range. We show that their ratios, C_{2}/C_{k1} and C_{k}/C_{k1}, exhibit clear dependence on the microscale Reynolds number R_{λ}, implying that they cannot all be independent of R_{λ}. In particular, it is found that (C_{k1}/C_{2}-0.25)=1.95Rλ- 0.68. The study further reveals that the widely used relation C _{2}=4.02C_{k1} holds only asymptotically when R _{λ}â‰3105. It is also found that C_{2} has much stronger R_{λ} dependence than either C_{k} or C_{k1} if the latter indeed has a systematic dependence on R _{λ}. We further show that the varying dependence on R _{λ} of these three numbers can be attributed to the difference of the inertial range in real- and wave-number space, with the inertial range in real-space known to be much shorter than that in wave-number space.

Original language | English (US) |
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Article number | 023002 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 87 |

Issue number | 2 |

DOIs | |

State | Published - Feb 5 2013 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics