Conservation of total wave action and the one dimensional evolution of
simple waves in the solar wind
We investigate the evolution of outwardly propagating simple MHD waves
in a model of the expanding solar wind using MHD simulations. In order
to understand the different evolution of slow, Alfvén and fast modes,
the question of wave-action conservation is re-examined theoretically.
Using the fluctuation averaged Lagrangian, we discuss the conservation
of total wave action and Equi-partition of wave energy for MHD waves.
Results show that, even though the wave action for a simple
monochromatic wave is subject to loss under resonance/degeneracy
condition - conditions that can occur in the expanding solar wind in the
regions where plasma ß crosses one, the total wave action possessed by
all modes remains conserved, representing a wave action exchange between
different degrees of freedom. The Expanding Box simulations demonstrate
the results of the theoretical modeling, and reveal further details
about mode-mixing, Alfvén resonance and wave steepening. All of these
may help to understand the evolution of fluctuations from the inner
heliosphere out to Earth orbit and beyond.