- Title
- A general self-preservation analysis for decaying homogeneous isotropic turbulence
- Creator
- Djenidi, L; Antonia, RA
- Relation
- Journal of Fluid Mechanics Vol. 773, p. 345-365
- Publisher Link
- http://dx.doi.org/10.1017/jfm.2015.250
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2015
- Description
- A general framework of self-preservation (SP) is established, based on the transport equation of the second-order longitudinal velocity structure function in decaying homogeneous isotropic turbulence (HIT). The analysis introduces the skewness of the longitudinal velocity increment, S(r, t) (r and t are space increment and time), as an SP controlling parameter. The present SP framework allows a critical appraisal of the specific assumptions that have been made in previous SP analyses. It is shown that SP is achieved when S(r, t) varies in a self-similar manner, i.e. S=c(t)φ(r/l) where l is a scaling length, and c(t) and f(r/l) are dimensionless functions of time and (r/l), respectively. When c(t) is constant, l can be identified with the Kolmogorov length scale η, even when the Reynolds number is relatively small. On the other hand, the Taylor microscale λ is a relevant SP length scale only when certain conditions are met. The decay law for the turbulent kinetic energy (k) ensuing from the present SP is a generalization of the existing laws and can be expressed as k ~ (t-t₀)n+B, where B is a constant representing the energy of the motions whose scales are excluded from the SP range of scales. When B = 0, SP is achieved at all scales of motion and λ becomes a relevant scaling length together with η. The analysis underlines the relation between the initial conditions and the power-law exponent n and also provides a link between them. In particular, an expression relating n to the initial values of the scaling length and velocity is developed. Finally, the present SP analysis is consistent with both experimental grid turbulence data and the eddy-damped quasi-normal Markovian numerical simulation of decaying HIT by Meldi & Sagaut (J. Turbul., vol. 14, 2013, pp. 24-53).
- Identifier
- http://hdl.handle.net/1959.13/1321199
- Identifier
- uon:24285
- Identifier
- ISSN:0022-1120
- Language
- eng
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