  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.
