Multiplier phenomenology in random multiplicative cascade processes

Abstract

We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artifact of the observation procedure. Taking the latter into account, all reported properties of both unconditioned and conditioned multiplier distributions can be reproduced by cascade models with uncorrelated random weights if their bivariate splitting function is nonenergy conserving. For the $\ensuremath{\alpha}$ model we show that the simulated multiplier distributions converge to a limiting form, which is very close to the experimentally observed one. If random translations of the observation window are accounted for, also the subtle effects found in conditioned multiplier distributions are precisely reproduced.