  The so-called 2/15-law for two-point, third-order velocity statistics in
isotropic turbulence with helicity is computed for the first time from a direct
numerical simulation of the Navier-Stokes equations in a 512^3 periodic domain.
This law is a statement of helicity conservation in the inertial range,
analogous to the benchmark Kolmogorov 4/5-law for energy conservation in
high-Reynolds number turbulence. The appropriately normalized parity-breaking
statistics, when measured in an arbitrary direction in the flow, disagree with
the theoretical value of 2/15 predicted for isotropic turbulence. They are
highly anisotropic and variable and remain so over a long times. We employ a
recently developed technique to average over many directions and so recover the
statistically isotropic component of the flow. The angle-averaged statistics
achieve the 2/15 factor to within about 7% instantaneously and about 5% on
average over time. The inertial- and viscous-range behavior of the
helicity-dependent statistics and consequently the helicity flux, which appear
in the 2/15-law, are shown to be more anisotropic and intermittent than the
cor- responding energy-dependent reflection-symmetric structure functions, and
the energy flux, which appear in the 4/5-law. This suggests that the Kolmogorov
assumption of local isotropy at high Reynolds numbers needs to be modified for
the helicity-dependent statistics investigated here.
