Vorticity statistics in the direct cascade of twodimensional turbulence
Abstract
For the direct cascade of steady twodimensional (2D) NavierStokes turbulence, we derive analytically the probability of strong vorticity fluctuations. When ϖ is the vorticity coarsegrained over a scale R, the probability density function (PDF), P(ϖ), has a universal asymptotic behavior lnP~ϖ/ϖ_{rms} at ϖ≫ϖ_{rms}=[Hln(L/R)]^{1/3}, where H is the enstrophy flux and L is the pumping length. Therefore, the PDF has exponential tails and is selfsimilar, that is, it can be presented as a function of a single argument, ϖ/ϖ_{rms}, in distinction from other known direct cascades.
 Publication:

Physical Review E
 Pub Date:
 April 2011
 DOI:
 10.1103/PhysRevE.83.045301
 arXiv:
 arXiv:1011.3647
 Bibcode:
 2011PhRvE..83d5301F
 Keywords:

 47.27.Gs;
 Isotropic turbulence;
 homogeneous turbulence;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 doi:10.1103/PhysRevE.83.045301