Single-point velocity distribution in turbulence

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 tau produces velocity PDF tails In P(v) proportional to - v(4) at v much greater than v(rms), L/tau. For a short-correlated forcing when tau much less than L/v(rms) there is an intermediate asymptotics In P(v) proportional to - v(3) at L/tau much greater than v much greater than v(rms).