The interaction between Alfven-wave turbulence and the background solar wind
affects the cross helicity in two ways. Non-WKB reflection converts
outward-propagating Alfven waves into inward-propagating Alfven waves and vice
versa, and the turbulence transfers momentum to the background flow. When both
effects are accounted for, the total cross helicity is conserved. In the
special case that the background density and flow speed are independent of
time, the equations of cross-helicity conservation and total-energy
conservation can be combined to recover a well-known equation derived by
Heinemann and Olbert that has been interpreted as a non-WKB generalization of
wave-action conservation. This latter equation (in contrast to cross-helicity
and energy conservation) does not hold when the background varies in time.
