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The solar-wind magnetohydrodynamic turbulence is observed to be mainly made of Alfv\'enic fluctuations propagating away from the sun. It is shown that such an asymmetric state is a general consequence of the evolution of developed magnetohydrodynamic turbulence, which, starting from an initial asymmetry between modes with cross helicity + 1 and - 1, tends, as a consequence of nonlinear interactions, towards a state where the only modes left are those initially prevailing (with either cross helicity + 1 or - 1).
Dobrowolny et al. (Mon,) studied this question.