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Different results for the cascade power in strong, incompressible MHDturbulence with nonzero cross helicity appear in the literature. In this paper,we discuss the conditions under which these different results are valid. Wedefine z+ to be the rms amplitude of Alfven waves propagating parallel to thebackground magnetic field, and z- to be the rms amplitude of Alfven wavespropagating anti-parallel to the background magnetic field. Nonzero crosshelicity implies that z+ and z- differ, and we take z- to be less than z+. Wefind that the mechanism that generates the z- fluctuations strongly affects thecascade power, because it controls the coherence time for interactions betweenoppositely directed wave packets at the outer scale. In particular, for fixedvalues of z+ and z-, the cascade power is in many cases larger when the z-fluctuations are generated by the reflection of z+ fluctuations than when thez- fluctuations are generated by forcing that is only weakly correlated withthe z+ fluctuations.

The Turbulent Heating Rate in Strong MHD Turbulence with Nonzero Cross Helicity