SinglePoint Velocity Distribution in Turbulence
Abstract
We show that the tails of the singlepoint velocity probability distribution function (PDF) are generally nonGaussian in developed turbulence. By using instanton formalism for the randomly forced NavierStokes equation, we establish the relation between the PDF tails of the velocity and those of the external forcing. In particular, we show that a Gaussian random force having correlation scale L and correlation time τ produces velocity PDF tails lnP\(v\)~v^{4} at v>>v_{rms},L/τ. For a shortcorrelated forcing when τ<<L/v_{rms} there is an intermediate asymptotics lnP\(v\)~v^{3} at L/τ>>v>>v_{rms}.
 Publication:

Physical Review Letters
 Pub Date:
 November 1997
 DOI:
 10.1103/PhysRevLett.79.4159
 arXiv:
 arXiv:chaodyn/9708002
 Bibcode:
 1997PhRvL..79.4159F
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 9 pages, revtex, no figures