Non-Gaussian self-similarity in the inertial range of turbulence

Abstract

Besides Gaussian self-similarity, there is non-Gaussian self-similarity, i.e. a self-similar probability density function (PDF) is far away from Gaussian. By using a non-Gaussian PDF model of intermittent velocity increment, we study the non-Gaussian self-similarity in Kolmogorov's inertial range of hydrodynamic turbulence. In the limit of infinite Reynolds number, a central part of scaling range becomes the inertial range, and we have a non-Gaussian self-similarity in the inertial range. In scaling ranges at experimental Reynolds numbers, the self-similarity is broken due to viscosity and large-scale effects. Experimental facts of structure function exponents being anomalous, are not against the non-Gaussian self-similarity in the inertial range.