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Turbulent cross-helicity in the mean-field solar dynamo problem

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.