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