Phys. Rev. Lett. 79, 4159–4161 (1997)Single-Point Velocity Distribution in TurbulenceReceived 13 March 1997; revised 20 May 1997; published in the issue dated 24 November 1997 We show that the tails of the single-point velocity probability distribution function (PDF) are generally non-Gaussian in developed turbulence. By using instanton formalism for the randomly forced Navier-Stokes 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)∝-v4 at v≫vrms,L/τ. For a short-correlated forcing when τ≪L/vrms there is an intermediate asymptotics lnP(v)∝-v3 at L/τ≫v≫vrms. © 1997 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.79.4159
DOI:
10.1103/PhysRevLett.79.4159
PACS:
47.27.Ak, 05.40.+j, 47.10.+g
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