Abstract
For the direct cascade of steady two-dimensional (2D) Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. When is the vorticity coarse-grained over a scale , the probability density function (PDF), , has a universal asymptotic behavior at , where is the enstrophy flux and is the pumping length. Therefore, the PDF has exponential tails and is self-similar, that is, it can be presented as a function of a single argument, , in distinction from other known direct cascades.
- Received 17 November 2010
DOI:https://doi.org/10.1103/PhysRevE.83.045301
©2011 American Physical Society