Multifractality in a nested velocity gradient model for intermittent turbulence

Abstract

Small scale intermittency is ubiquitous in turbulent flows. Many features of small-scale motions can be described by the velocity gradient tensor (VGT) for which the nonlinear term in the Navier-Stokes equations (NSE) is a source of strong fluctuations. The figure shows intermittent time signals of longitudinal VGT elements along Lagrangian trajectories from five levels of a recently proposed nested multiple time-scale model (MTSM), partly derived from NSE. We show that a single level of MTSM valid at moderate Reynolds numbers (Re) can generate valid statistics and scaling exponents for arbitrarily high Re. Excellent agreement with direct numerical simulation and experimental data is found.