On the log-Poisson statistics of the energy dissipation field and related problems of developed turbulence

Abstract

An energy cascading model of intermittency involving rare localized regions of both large and/or weak energy dissipation (dynamical intermittency) is considered and compared to the case of intermittency arising from a large number of regions with nearly equal dissipation rates (space intermittency). The latter leads to the log-normal statistics of the dissipation rate while the first scenario leads to shifted log-Poisson distributions either for a large or for weak energy dissipation. The only difference between these two cases is that small values of dissipation (with respect to the maximum of PDF) are more probable for intermittency of the regions with weak dissipation than for intermittency of the regions with large values of dissipation. Some consequences are derived which show that Novikov’s inequalities are valid for intermittency with rare regions of a weak dissipation only. Different experimental data of probability distributions of dissipation are presented and compared to theoretical predictions. Some experimental evidences of quasi-two-dimensional vortical structures with weak dissipation are discussed. They suggest that the scenario involving dynamical intermittency with holes of dissipation could apply to a real world turbulence.