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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2014

Two-scale correlation and energy cascade in three-dimensional turbulent flows

Yongxiang Huang
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Yves Gagne
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Résumé

In this paper, we propose a high-order harmonic-free methodology, namely arbitrary-order Hilbert spectral analysis, to estimate the two-scale correlation (TSC). When applied to fully developed turbulent velocity, we nd that the scale-dependent Hilbert energy satis es a lognormal distribution on both the inertial and dissipation ranges. The maximum probability density function of the logarithm of the Hilbert energy obeys a power law with a scaling exponent ' 0:33 in the inertial range. For the measured TSC, we observe a logarithmic correlation law with an experimental exponent ' 0:37 on both the inertial and dissipation ranges. The correlation itself is found to be self-similar with respect to the distance between the two considered scales and a central frequency !c in the logarithm space. An empirical nonlinear and nonlocal triad- scale interaction formula is proposed to describe the observed TSC. This triadic interaction can be interpreted as experimental evidence of a small-scale nonlinear and nonlocal coupling inside the self-similarity of the Richardson{Kolmogorov phenomenological cascade picture.

Domaines

Océanographie
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Dates et versions

hal-01009898 , version 1 (18-06-2014)

Identifiants

  • HAL Id : hal-01009898 , version 1

Citer

Yongxiang Huang, François G Schmitt, Yves Gagne. Two-scale correlation and energy cascade in three-dimensional turbulent flows. Journal of Statistical Mechanics: Theory and Experiment, 2014, pp.P05002. ⟨hal-01009898⟩
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