Energy Transfer in Isotropic Turbulence

Uberoi, Mahinder S.

doi:10.1063/1.1706861

Cited by 88 publications

(38 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is widely believed that a K -t -' asymptotic decay law is in violation of experimental data for isotropic turbulence. This experimental data (see Uberoi 1963, Kistler and Vrebalovich 1966, Comte-Bellot and Corrsin 1966, 1971, and Warhaft and Lumley 1978 has yielded power law decays with exponents varying froi 1 to 1.4 with a mean of approximately 1.25. However, great caution must be taken in using this data to dismiss the possibility of a K -tl asymptotic power law decay at high Reynolds numbers since most of this data is for a limited number of eddy turnover times (typically for t/IKo' < 4).…”

Section: Such Small Departures Can Be Characterized By the Perturbationsmentioning

confidence: 89%

The energy decay in self-preserving isotropic turbulence revisited

1992

View full text Add to dashboard Cite

The assumption of self-preservation permits an analytical determination of the energy decay in isotropic turbulence. Batchelor (1948), who was the first to carry out a detailed study of this problem, based his analysis on the assumption that the Loitsianskii integral is a dynamic invariant – a widely accepted hypothesis that was later discovered to be invalid. Nonetheless, it appears that the self-preserving isotropic decay problem has never been reinvestigated in depth subsequent to this earlier work. In the present paper such an analysis is carried out, yielding a much more complete picture of self-preserving isotropic turbulence. It is proven rigorously that complete self-preserving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K ∼ t−1 and one where K ∼ t−α with an exponent α > 1 that is determined explicitly by the initial conditions. By a fixed-point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K ∼ t−1 power law decay is the asymptotically consistent high-Reynolds-number solution; the K ∼ t−α decay law is only achieved in the limit as t → ∞ and the turbulence Reynolds number Rt vanishes. Arguments are provided which indicate that a t−1 power law decay is the asymptotic state toward which a complete self-preserving isotropic turbulence is driven at high Reynolds numbers in order to resolve an O(R1½) imbalance between vortex stretching and viscous diffusion. Unlike in previous studies, the asymptotic approach to a complete self-preserving state is investigated which uncovers some surprising results.

show abstract

Section: Such Small Departures Can Be Characterized By the Perturbationsmentioning

confidence: 89%

The energy decay in self-preserving isotropic turbulence revisited

1992

View full text Add to dashboard Cite

show abstract

“…Its determination from experi ment is therefore of the utmost importance. It may be calculated from measurements of E9(K, t) using Equation (6), as was first done by Uberoi (1963). Unfortunately, the reliability of his results is questionable, since the isotropy assumption is not satisfied in his experiment, due to the rather large value (1.2) of the ratio «uf>/<U�»1/2.…”

Section: 1 Homogeneous and Isotropic Turbulencementioning

confidence: 94%

Homogeneous Turbulence

Gence¹

1983

Annu. Rev. Fluid Mech.

View full text Add to dashboard Cite

“…Influential works of [Kolmogorov(1941)], [Batchelor & Proudman(1956)] and [Saffman(1967a)] have shown that the value of the decay exponent value n ( or equivalent power law exponent for other global physical quantities) is not unique but mainly governed by initial conditions (see also [Lavoie et al(2007)], [Uberoi(1963)]). Theory of self-similar decay has been addressed by many authors, among them [George (1992)] and [Speziale & Bernard (1992)], in which an explicit dependency with respect to initial conditions is taken into account.…”

Section: Introductionmentioning

confidence: 99%

A stochastic view of isotropic turbulence decay

2011

View full text Add to dashboard Cite

A stochastic EDQNM approach is used to investigate self-similar decaying isotropic turbulence at high Reynolds number ($400 \leq Re_\lambda \leq 10^4$). The realistic energy spectrum functional form recently proposed by Meyers & Meneveau is generalised by considering some of the model constants as random parameters, since they escape measure in most experimental set-ups. The induced uncertainty on the solution is investigated building response surfaces for decay power-law exponents of usual physical quantities. Large-scale uncertainties are considered, the emphasis being put on Saffman and Batchelor turbulence. The sensitivity of the solution to initial spectrum uncertainties is quantified through probability density functions of the decay exponents. It is observed that initial spectrum shape at very large scales governs the long-time evolution, even at high Reynolds number, a parameter which is not explicitly taken into account in many theoretical works. Therefore, a universal asymptotic behavior in which kinetic energy decays as $t^{-1}$ is not detected. But this decay law is observed at finite Reynolds number with low probability for some initial conditions

show abstract

Energy Transfer in Isotropic Turbulence

Cited by 88 publications

References 6 publications

The energy decay in self-preserving isotropic turbulence revisited

The energy decay in self-preserving isotropic turbulence revisited

Homogeneous Turbulence

A stochastic view of isotropic turbulence decay

Contact Info

Product

Resources

About