Intermittency of small-scale motions is an ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem. Here, a multiple-time-scale stochastic model is introduced for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. Unlike previous phenomenological models of intermittency, in the proposed model the dynamics driving the growth of intermittency due to gradient self-stretching and rotation are derived directly from the Navier-Stokes equations. Numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen directions of the strain rate.

• Received 29 March 2017
• Corrected 29 January 2018

DOI:https://doi.org/10.1103/PhysRevFluids.2.072601