 
Summary: J. Fluid Mech. (2011), vol. 676, pp. 191217. c Cambridge University Press 2011
doi:10.1017/jfm.2011.39
191
On the velocity distribution in homogeneous
isotropic turbulence: correlations and
deviations from Gaussianity
MICHAEL WILCZEK, ANTON DAITCHE
AND RUDOLF FRIEDRICH
Institute for Theoretical Physics, Westf¨alische WilhelmsUniversit¨at, WilhelmKlemmStraße 9,
48149 M¨unster, Germany
(Received 15 November 2010; revised 6 January 2011; accepted 19 January 2011;
first published online 12 April 2011)
We investigate the singlepoint probability density function of the velocity in three
dimensional stationary and decaying homogeneous isotropic turbulence. To this
end, we apply the statistical framework of the LundgrenMoninNovikov hierarchy
combined with conditional averaging, identifying the quantities that determine the
shape of the probability density function. In this framework, the conditional averages
of the rate of energy dissipation, the velocity diffusion and the pressure gradient with
respect to velocity play a key role. Direct numerical simulations of the NavierStokes
equation are used to complement the theoretical results and assess deviations from
