  The quasilinear mean-field theory for driven MHD turbulence leads to the
result that the observed cross helicity <u \cdot b> may directly yield the
magnetic eddy diffusivity \eta_{T} of the quiet Sun. In order to model the
cross helicity at the solar surface, magnetoconvection under the presence of a
vertical large-scale magnetic field is simulated with the nonlinear MHD code
NIRVANA. The very robust result of the calculations is that < u_z b_z >\simeq 2
< u\cdot b> independent of the applied magnetic field amplitude. The
correlation coefficient for the cross helicity is about 10%. Of similar
robustness is the finding that the rms value of the magnetic perturbations
exceeds the mean-field amplitude (only) by a factor of five. The characteristic
helicity speed u_{\eta} as the ratio of the eddy diffusivity and the density
scale height for an isothermal sound velocity of 6.6 km/s proves to be 1 km/s
for weak fields. This value well coincides with empirical results obtained from
the data of the HINODE satellite and the Swedish 1-m Solar Telescope (SST)
providing the cross helicity component < u_z b_z >. Both simulations and
observations thus lead to a numerical value of \eta_{T} \simeq 10^12 cm^2 /s as
characteristic for the surface of the quiet Sun.
