  We study the dynamical and statistical properties of turbulent cross-helicity
(correlation of the aligned fluctuating velocity and magnetic field
components). We derive an equation governing generation and evolution of the
turbulent cross-helicity and discuss its meaning for the dynamo. Using symmetry
properties of the problem we suggest a general expression for the turbulent
cross-helicity pseudo-scalar and compute the turbulent coefficients in this
expression. Effects of the density stratification, large-scale magnetic fields,
differential rotation and turbulent convection are taken into account. We
investigate the relative contribution of these effects to the cross-helicity
evolution for two kinds of dynamo models of the solar cycle including a
distributed mean-field model and a flux-transport dynamo model. We show that
the contribution from the density stratification follows the evolution of the
radial magnetic field, while large-scale electric currents produce a more
complicated pattern of the cross-helicity of the comparable magnitude. We
suggest that the results of observational analysis of the cross-helicity will
depend on the averaging scales. Our results show that the pattern of the
cross-helicity evolution strongly depends on details of the dynamo mechanism.
Thus, we anticipate that direct observations of the cross-helicity on the Sun
may serve for the diagnostic purpose of the solar dynamo process.
