- Title
- Finite Reynolds number effect and the 4/5 law
- Creator
- Antonia, R. A.; Tang, S. L.; Djenidi, L.; Zhou, Y.
- Relation
- Physical Review Fluids Vol. 4, Issue 8, no. 084602
- Publisher Link
- http://dx.doi.org/10.1103/PhysRevFluids.4.084602
- Publisher
- American Physical Society
- Resource Type
- journal article
- Date
- 2019
- Description
- Kolmogorov [A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941)] formulated a theory of small-scale turbulence (K41), valid at extremely large Reynolds numbers, based on two similarity hypotheses and on an exact result derived from the transport equation for the second-order structure function, known as the 4/5 law. Although K41 was praised for its simplicity and elegance, Kolmogorov [A. N. Kolmogorov, J. Fluid Mech. 13, 82 (1962).] proposed a new refined similarity hypothesis (K62) mainly to account for the effect of the large scales on the small scales. It has been widely interpreted in the literature as a correction to K41 arising from the intermittency of the instantaneous energy dissipation rate ε. In this paper we argue that since K62 retains the 4/5 law, it must satisfy the same constraints as K41, viz., extremely large Reynolds number and flow stationarity. The retention of the 4/5 law is not however consistent with the presence of nonstationarity due to the effect of the large scales, as postulated by K62. A relatively extensive survey of published data shows that, indeed, the 4/5 law has not yet been observed in either experiments or simulations due to the Reynolds number not being sufficiently large. The use of the transport equation for the second-order structure function, together with an empirical model for the Kolmogorov-normalized second-order velocity structure function, confirms that the 4/5 law is established only after this structure function becomes independent of the Reynolds number.
- Subject
- 4/5 law; energy dissipation rate; Reynolds number; Kolmogorov
- Identifier
- http://hdl.handle.net/1959.13/1459161
- Identifier
- uon:45594
- Identifier
- ISSN:2469-990X
- Language
- eng
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