Non-Gaussianity and intermittency in an ensemble of Gaussian fields

Abstract

Motivated by the need to capture statistical properties of turbulent systems in simple, analytically tractable models, an ensemble of Gaussian sub-ensembles with varying properties of the correlation function such as variance and length scale is investigated. The ensemble statistics naturally exhibit non-Gaussianity and intermittency. Due to the simplicity of Gaussian random fields, many explicit results can be obtained analytically, revealing the origin of non-Gaussianity in this framework. Potential applications of the proposed model ensemble for the description of non-equilibrium statistical mechanics of complex turbulent systems are briefly discussed.