Multiscale self-organized criticality and powerful X-ray flares

A combination of spectral and moments analysis of the continuous X-ray flux data is used to show consistency of statistical properties of the powerful solar flares with 2D BTW prototype model of self-organized criticality

Logarithmic scaling in the near-dissipation range of turbulence

A logarithmic scaling for structure functions, in the form $S_p \sim [\ln (r/\eta)]^{\zeta_p}$, where $\eta$ is the Kolmogorov dissipation scale and $\zeta_p$ are the scaling exponents, is suggested for the statistical description of the near-dissipation range for which classical power-law scaling does not apply. From experimental data at moderate Reynolds numbers, it is shown that the logarithmic scaling, deduced from general considerations for the near-dissipation range, covers almost the entire range of scales (about two decades) of structure functions, for both velocity and passive scalar fields. This new scaling requires two empirical constants, just as the classical scaling does, and can be considered the basis for extended self-similarity

Logarithmically modified scaling of temperature structure functions in thermal convection

Using experimental data on thermal convection, obtained at a Rayleigh number of 1.5 $\times 10^{11}$, it is shown that the temperature structure functions $$, where $\Delta T_r$ is the absolute value of the temperature increment over a distance $r$, can be well represented in an intermediate range of scales by $r^{\zeta_p} \phi (r)^{p}$, where the $\zeta_p$ are the scaling exponents appropriate to the passive scalar problem in hydrodynamic turbulence and the function $\phi (r) = 1-a(\ln r/r_h)^2$. Measurements are made in the midplane of the apparatus near the sidewall, but outside the boundary layer

Multiscale SOC in turbulent convection

Using data obtained in a laboratory thermal convection experiment at high Rayleigh numbers, it is shown that the multiscaling properties of the observed mean wind reversals are quantitatively consistent with analogous multiscaling properties of the Bak-Tang-Wiesenfeld prototype model of self-organized criticality in two dimensions

Beyond scaling and locality in turbulence

An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form $S(r) \cong cr^{\alpha_0}[\ln(r/\eta)]^{\alpha_1}$, where $\eta$ is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with $\alpha_0 =0$ can describe turbulence statistics in the near-dissipation range $r > \eta$, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed.Comment: extended versio