- Cross helicity (velocity–magnetic-field correlation) is one of the basic quantities in magnetohydrodynamics. In the presence of large-scale vortical motion, if there is posi-tive (or negative) cross helicity in turbulence, a contribution to the electromotive force parallel (or anti-parallel) to the large-scale vorticity arises. By considering the evolution equation of turbulent cross helicity, the mechanisms that create turbulence with cross helicity are investigated. In order to analyze cross helicity-related transport and cross-helicity generation mechanisms, three kinds of numerical simulations are performed: (i) direct numerical simulations of the local Kolmogorov flow with an imposed magnetic field, (ii) global direct simulation of a rotating spherical fluid shell, and (iii) large-eddy simulation of the local compressible flow near the sunspot region. Through these simula-tions, the importance of the cross-helicity effect is validated. The cross-helicity generation mechanisms relevant to the incompressible and compressible cases are also discussed.