Distributed chaos and turbulence in B\'{e}nard-Marangoni and Rayleigh-B\'{e}nard convection

Temporal and spatio-temporal (turbulence) distributed chaos in B\'{e}nard-Marangoni and Rayleigh-B\'{e}nard 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.