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The cross helicity (velocity--magnetic-field correlation) effects in themagnetic-field induction and momentum transport in the magnetohydrodynamic(MHD) turbulence are investigated with the aid of the multiple-scalerenormalized perturbation expansion analysis. The outline of the theory ispresented with reference to the role of the cross-interaction responsefunctions between the velocity and magnetic field. In this formulation, theexpressions of the turbulent fluxes: the turbulent electromotive force (EMF) inthe mean induction equation and the Reynolds and turbulent Maxwell stresses inthe momentum equation are obtained. Related to the expression of EMF, thephysical origin of the cross-helicity effect in dynamos, as well as otherdynamo effects, is discussed. In order to understand the actual role of theturbulent cross helicity, its transport equations is considered. Severalgeneration mechanisms of cross helicity are discussed with illustrativeexamples. On the basis of the cross-helicity production mechanisms, its effectin stellar dynamos is discussed. The role of cross helicity in the momentumtransport and global flow generation is also argued. Characteristic features ofturbulence effects in fast reconnection are reviewed with special emphasis onthe role of cross helicity in localizing the effective resistivity. Finally, aremark is addressed on an approach that elucidates the structure generation andsustainment in extremely strong turbulence. An appropriate formulation for theanti-diffusion effect, which acts against the usual diffusion effect, isneeded. Turbulence modeling approach based on such an analytical formulation isalso argued in comparison with the conventional heuristic modeling. Theimportance of the self-consistent framework treating the non-linear interactionbetween the mean field and turbulence is stressed as well.

Unappreciated cross-helicity effects in plasma physics: Anti-diffusion effects in dynamo and momentum transport