Single-point velocity distribution in turbulence

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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 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 P(v)∝-v⁴ at v≫ vrms, L/τ. For a short-correlated forcing when τ≪ L/vrms there is an intermediate asymptotics P(v)∝-v³ at L/τ≫ v≫ vrms.