  Conditional statistics of homogeneous isotropic turbulent flow is
investigated by means of high-Reynolds number direct numerical simulations
performed with $2048^3$ collocation points. Eulerian as well as Lagrangian
velocity increment statistics under several conditions are analyzed and
compared. In agreement with experimental data longitudinal probability density
functions $P(\delta^{||}_l u|\epsilon_l)$ conditioned on a scale-averaged
energy dissipation rate are close to Gaussian distributions over all scales
within the inertial range of scales. Also transverse increments conditioned on
either the dissipation rate or the square of the vorticity have quasi-Gaussian
probability distribution functions (PDFs). Concerning Lagrangian statistics we
found that conditioning on a trajectory averaged energy-dissipation rate
$\epsilon_\tau$ significantly reduces the scale dependence of the increment
PDFs $P(\delta_\tau u_i|\epsilon_\tau)$. By means of dimensional arguments we
propose a novel condition for Lagrangian increments which is shown to reduce
even more the flatness of the corresponding PDFs and thus intermittency in the
inertial range of scales. The conditioned Lagrangian PDF corresponding to the
smallest increment considered is reasonably well described by the
K41-prediction of the PDF of acceleration. Conditioned structure functions show
approximately K41-scaling with a larger scaling range than the unconditioned
ones.
