- Title
- Self-preservation relation to the Kolmogorov similarity hypotheses
- Creator
- Djenidi, Lyazid; Antonia, Robert A.; Danaila, Luminita
- Relation
- Physical Review Fluids Vol. 2, Issue 5, no. 054606
- Publisher Link
- http://dx.doi.org/10.1103/PhysRevFluids.2.054606
- Publisher
- American Physical Society
- Resource Type
- journal article
- Date
- 2017
- Description
- The relation between self-preservation (SP) and the Kolmogorov similarity hypotheses (Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 301 (1941) [Proc. R. Soc. London A 434, 9 (1991)]) is investigated through the transport equations for the second- and third-order moments of the longitudinal velocity increments [δu(r,t)=u(x,t)−u(x+r,t), where x,t, and r are the spatial point and the time and longitudinal separation between two points, respectively]. It is shown that the fluid viscosity ν and the mean turbulent kinetic energy dissipation rate ⋶ (the overbar represents an ensemble average) emerge naturally from the equations of motion as controlling parameters for the velocity increment moments when SP is assumed. Consequently, the Kolmogorov length scale η [≡(ν³/⋶)1/4] and velocity scale vK [≡(ν⋶)1/4] also emerge as natural scaling parameters in conformity with SP, indicating that Kolmogorov's first hypothesis is subsumed under the more general hypothesis of SP. Further, the requirement for a very large Reynolds number is also relaxed, at least for the first similarity hypothesis. This requirement however is still necessary to derive the two-thirds law (or the four-fifths law) from the analysis. These analytical results are supported by experimental data in wake, jet, and grid turbulence. An expression for the fourth-order moment of the longitudinal velocity increments (δu)⁴ is derived from the analysis carried out in the inertial range. The expression, which involves the product of (δu)² and ∂δp/∂x, does not require the use the volume-averaged dissipation ⋶r, introduced by Oboukhov [Oboukhov, Some specific features of atmospheric turbulence, J. Fluid Mech. 13, 77 (1962)] on a phenomenological basis and used by Kolmogorov to derive his refined similarity hypotheses [Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech. 13, 82 (1962)], suggesting that ⋶r is not, like ⋶, a quantity issuing from the Navier-Stokes equations.
- Subject
- Kolmogorov theory; kinetic energy; Reynolds numbers; self preservation analyses
- Identifier
- http://hdl.handle.net/1959.13/1398097
- Identifier
- uon:34388
- Identifier
- ISSN:2469-990X
- Rights
- Copyright © 2011 by American Physical Society. All rights reserved. Individual articles may be downloaded for personal use; users are forbidden to reproduce, republish, redistribute, or resell any materials from this journal in either machine-readable form or any other form without permission of the APS or payment of the appropriate royalty for reuse.
- Language
- eng
- Full Text
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