Interpretation of turbulent mixing using fractals and multifractals

Abstract

Many phenomena depend in principle on the fine-scale properties of turbulence, including its intermittency. Traditionally, the impact of intermittency has not been taken into account, but rather theories were based on average values of the rate of kinetic energy dissipation, velocity fluctuations, rates of strain, turbulent stresses, etc. A multifractal formalism describes intermittency and was used to deduce the distributions of the already mentioned quantities. It was applied to derive corrections to the traditional equations describing micromixing, concentration spectra, rates of particle encounter, turbulent rupture of flocs and drop breakup in both the inertial and viscous subranges of the turbulence spectrum. Exponents on 〈ε〉 and ν are modified and, when scaling-up, intermittency changes the fine-scale turbulence and its interactions with the process even when the power per unit volume is held constant. Those processes whose time constants are smaller than the duration of the related turbulent events are strongly modified by intermittency. In particular, in the case of drop breakup in the inertial subrange, a drift of the exponent on the Weber number from −0.60 to −0.93 is predicted as rare, but strong bursts of energy dissipation have time to become influential. Some new experimental results are consistent with the predictions. It is concluded that in some chemical engineering operations the traditional approach to turbulence, based on the Kolmogorov theory, should be extended to include the influence of intermittency.