On the Conservation of Cross Helicity and Wave Action in Solar-Wind Models with Non-WKB Alfven Wave Reflection

TL;DR

This paper demonstrates that in solar wind models with non-WKB Alfven wave reflection, the total cross helicity remains conserved when considering wave-turbulence interactions, extending previous wave-action concepts to dynamic backgrounds.

Contribution

It shows that total cross helicity is conserved in non-WKB Alfven wave reflection models, generalizing wave-action conservation to time-varying solar wind conditions.

Findings

Total cross helicity is conserved with wave-turbulence interactions.

The wave-action conservation equation is recovered for steady backgrounds.

Wave-action conservation does not hold in time-varying backgrounds.

Abstract

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.