title: Origin of non-Gaussian statistics in hydrodynamic turbulence.
abstract: Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain rate with highly non-Gaussian statistics. Quantitatively, intermittency is manifested in highly elongated tails in the probability density functions of the velocity increments between pairs of points. A long-standing open issue has been to predict the origins of intermittency and non-Gaussian statistics from the Navier-Stokes equations. Here we derive, from the Navier-Stokes equations, a simple nonlinear dynamical system for the Lagrangian evolution of longitudinal and transverse velocity increments. From this system we are able to show that the ubiquitous non-Gaussian tails in turbulence have their origin in the inherent self-amplification of longitudinal velocity increments, and cross amplification of the transverse velocity increments.
authors.affiliation: Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
authors.forename: Yi
authors.initials: Y
authors.lastname: Li
authors.forename: Charles
authors.initials: C
authors.lastname: Meneveau