Distributed chaos and turbulence in Bénard-Marangoni and Rayleigh-Bénard convection

Abstract

Temporal and spatio-temporal (turbulence) distributed chaos in Bénard-Marangoni and Rayleigh-Bénard convection have been studied using results of laboratory experiments and direct numerical simulations in the terms of effective chaotic diffusivity (viscosity) and action. It is shown that for the both cases decaying part of the power spectra has stretched exponential form - for temporal spectrum $E(f)\propto \exp -(f/f_{\beta }{)}^{1/2}$ and for spatial spectrum $E(k)\propto \exp -(k/k_{\beta }{)}^{2/3}$, where the $f_{\beta }$ and $k_{\beta }$ represent low-frequency (large-scale) coherent oscillations.

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