Vorticity statistics in the direct cascade of two-dimensional turbulence

Abstract

For the steady-state direct cascade of two-dimensional Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. The probability density function (pdf) of the vorticity coarse-grained over a scale in the inertial interval is shown to have a universal self-similar form, in distinction from other known direct cascades. The tails of the pdf are found to be exponential.