Simple multifractal cascade model for fully developed turbulence

Abstract

A simple model is presented for the energy-cascading process in the inertial range that fits remarkably well the entire spectrum of scaling exponents for the dissipation field in fully developed turbulence. The scheme is a special case of weighted curdling and its one-dimensional version is a simple generalized two-scale Cantor set with equal scales but unequal weights (with ratio\ensuremath{\sim}(7/3). This set displays all the measured multifractal properties of one-dimensional sections of the dissipation field.