Single-point velocity distribution in turbulence

Abstract

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 $\tau$ produces velocity PDF tails $\ln \mathcal{P}(v)\propto -v^4$ at $v\gg v_{rms},L/\tau$. For a short-correlated forcing when $\tau \ll L/v_{rms}$ there is an intermediate asymptotics $\ln \mathcal{P}(v)\propto -v^3$ at $L/\tau \gg v\gg v_{rms}$.

9 pages, revtex, no figures

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