On the infra-red asymptotic behavior of the pair correlator of the energy dissipation rate for well-developed turbulence

1998 ◽  
Vol 88 (2) ◽  
pp. 159-161
Author(s):  
N. V. Antonov
Keyword(s):  
Asymptotic Behavior ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Developed Turbulence ◽  
Infra Red ◽  
Pair Correlator

The evolution of turbulent bursts: the b—ε model

1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner
Keyword(s):  
Partial Differential Equations ◽  
Energy Dissipation ◽  
Energy Density ◽  
Differential Equations ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Semi Empirical

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.

scholarly journals NEW EVIDENCE OF DISCRETE SCALE INVARIANCE IN THE ENERGY DISSIPATION OF THREE-DIMENSIONAL TURBULENCE: CORRELATION APPROACH AND DIRECT SPECTRAL DETECTION

2003 ◽  
Vol 14 (04) ◽  
pp. 459-470 ◽  
Author(s):  
WEI-XING ZHOU ◽  
DIDIER SORNETTE ◽  
VLADILEN PISARENKO
Keyword(s):  
Energy Dissipation ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Corrections To Scaling ◽  
Developed Turbulence ◽  
Pairwise Correlations ◽  
Spectral Detection ◽  
Simple Variant ◽  
High Reynolds ◽  
New Evidence

We extend the analysis of Ref. 16 showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (≈ 2500) of three-dimensional fully developed turbulence. First, we develop a simple variant of the canonical averaging method using a rephasing scheme between different samples based on pairwise correlations that confirms Zhou and Sornette's previous results. The second analysis uses a simpler local spectral approach and then performs averages over many local spectra. This yields stronger evidence of the existence of underlying log-periodic undulations, with the detection of more than 20 harmonics of a fundamental logarithmic frequency f = 1.434 ± 0.007 corresponding to the preferred scaling ratio γ = 2.008 ± 0.006.

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