The magnetohydrodynamic equations in terms of waveframe variables

Abstract

Generalising the Elsässer variables, we introduce the $Q$ -variables. These are more flexible than the Elsässer variables, because they also allow us to track waves with phase speeds different than the Alfvén speed. We rewrite the magnetohydrodynamics (MHD) equations with these $Q$ -variables. We consider also the linearised version of the resulting MHD equations in a uniform plasma, and recover the classical Alfvén waves, but also separate the fast and slow magnetosonic waves into upward- and downward-propagating waves. Moreover, we show that the $Q$ -variables may also track the upward- and downward-propagating surface Alfvén waves in a non-uniform plasma, displaying the power of our generalisation. In the end, we lay the mathematical framework for driving solar wind models with a multitude of wave drivers.