Vorticity statistics in the direct cascade of two-dimensional turbulence

Gregory Falkovich, Vladimir Lebedev
2011 Physical Review E  
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.
doi:10.1103/physreve.83.045301 pmid:21599229 fatcat:zefiwakg3ncthi3dbonfw2gu2m