Vorticity statistics in the direct cascade of two-dimensional turbulence

TL;DR

This paper analytically derives the probability distribution of strong vorticity fluctuations in the steady-state direct cascade of 2D turbulence, revealing a universal self-similar form with exponential tails.

Contribution

It provides the first analytical derivation of the vorticity fluctuation distribution in 2D turbulence's direct cascade, highlighting its universal self-similar nature.

Findings

Vorticity pdf has a universal self-similar form.

The tails of the vorticity pdf are exponential.

The derived distribution applies to the inertial interval in 2D 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.