- Title
- Scaling of turbulent velocity structure functions: plausibility constraints
- Creator
- Djenidi, L.; Antonia, R. A.; Tang, S. L.
- Relation
- Journal of Fluid Mechanics Vol. 965, no. A14
- Publisher Link
- http://dx.doi.org/10.1017/jfm.2023.416
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2023
- Description
- The nh-order velocity structure function Sn homogeneous isotropic turbulence is usually represented by Sn ∼ rζn, where the spatial separation r lies within the inertial range. The first prediction for ζn (i.e. ζ3 = n/3) was proposed by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941) using a dimensional argument. Subsequently, starting with Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85), models for the intermittency of the turbulent energy dissipation have predicted values of ζn that, except for n = 3, differ from n/3. In order to assess differences between predictions of ζn, we use the Hölder inequality to derive exact relations, denoted plausibility constraints. We first derive the constraint (p3 − p1)ζ2p2 = (p3 − p2)ζ2p1 + (p2 − p1)ζ2p3 between the exponents ζ2p, where p1 ≤ p2 ≤ p3 are any three positive numbers. It is further shown that this relation leads to ζ2p = pζ2. It is also shown that the relation ζn = n/3, which complies with ζ2p = pζ2, can be derived from constraints imposed on ζn using the Cauchy-Schwarz inequality, a special case of the Hölder inequality. These results show that while the intermittency of ϵ, which is not ignored in the present analysis, is not incompatible with the plausible relation ζn = n/3, the prediction ζn = n/3 + αn is not plausible, unless αn = 0.
- Subject
- turbulent flows; turbulence theory; isotropic turbulence; computational complexity; energy dissipation
- Identifier
- http://hdl.handle.net/1959.13/1489727
- Identifier
- uon:52755
- Identifier
- ISSN:0022-1120
- Language
- eng
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