  Strong incompressible three-dimensional magnetohydrodynamic turbulence is
investigated by means of high resolution direct numerical simulations. The
simulations show that the configuration space is characterized by regions of
positive and negative cross-helicity, corresponding to highly aligned or
anti-aligned velocity and magnetic field fluctuations, even when the average
cross-helicity is zero. To elucidate the role of cross-helicity, the spectra
and structure of turbulence are obtained in imbalanced regions where
cross-helicity is non-zero. When averaged over regions of positive and negative
cross-helicity, the result is consistent with the simulations of balanced
turbulence. An analytical explanation for the obtained results is proposed.
