  The measure of the third-order structure function, Y, is employed in the
solar wind to compute the cascade rate of turbulence. In the absence of a mean
field B0=0, Y is expected to be isotropic (radial) and independent of the
direction of increments, so its measure yields directly the cascade rate. For
turbulence with mean field, as in the solar wind, Y is expected to become more
two dimensional (2D), that is, to have larger perpendicular components, loosing
the above simple symmetry. To get the cascade rate one should compute the flux
of Y, which is not feasible with single-spacecraft data, thus measurements rely
upon assumptions about the unknown symmetry. We use direct numerical
simulations (DNS) of magneto-hydrodynamic (MHD) turbulence to characterize the
anisotropy of Y. We find that for strong guide field B0=5 the degree of
two-dimensionalization depends on the relative importance of shear and pseudo
polarizations (the two components of an Alfv\'en mode in incompressible MHD).
The anisotropy also shows up in the inertial range. The more Y is 2D, the more
the inertial range extent differs along parallel and perpendicular directions.
We finally test the two methods employed in observations and find that the
so-obtained cascade rate may depend on the angle between B0 and the direction
of increments. Both methods yield a vanishing cascade rate along the parallel
direction, contrary to observations, suggesting a weaker anisotropy of solar
wind turbulence compared to our DNS. This could be due to a weaker mean field
and/or to solar wind expansion.
