- Title
- Dual scaling and the n-thirds law in grid turbulence
- Creator
- Tang, S. L.; Antonia, R. A.; Djenidi, L.
- Relation
- Journal of Fluid Mechanics Vol. 975, no. A32
- Publisher Link
- http://dx.doi.org/10.1017/jfm.2023.888
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2023
- Description
- A dual scaling of the turbulent longitudinal velocity structure function (δu)n, i.e. a scaling based on the Kolmogorov scales (uK , η) and another based on (u′, L) representative of the large scale motion, is examined in the context of both the Kármán–Howarth equation and experimental grid turbulence data over a significant range of the Taylor microscale Reynolds number Reλ. As Reλ increases, the scaling based on (u′, L) extends to increasingly smaller values of r/L while the scaling based on (uK , η) extends to increasingly larger values of r/η. The implication is that both scalings should eventually overlap in the so-called inertial range as Reλ continues to increase, thus leading to a power-law relation (δu)n ∼ r n/3 when the inertial range is rigorously established. The latter is likely to occur only when Reλ → ∞. The use of an empirical model for (δu)n, which complies with (δu)n ∼ r n/3 as Reλ → ∞, shows that the finite Reynolds number effect may differ between even- and odd-orders of (δu)n. This suggests that different values of Reλ may be required between even and odd values of n for compliance with (δu)n ∼ r n/3 . The model describes adequately the dependence on Reλ of the available experimental data for (δu)n and supports indirectly the extrapolation of these data to infinitely large Reλ.
- Subject
- turbulence theory; dual scaling; Kolmogorov scales; grid turbulence
- Identifier
- http://hdl.handle.net/1959.13/1500326
- Identifier
- uon:54903
- Identifier
- ISSN:0022-1120
- Language
- eng
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