Generalized Expanding-Box Formulations of Reduced Magnetohydrodynamics in the Solar Wind

Abstract

We derive a set of simplified equations that can be used for numerical studies of reduced magnetohydrodynamic turbulence within a small patch of the radially expanding solar wind. We allow the box to be either stationary in the Sun's frame or to be moving at an arbitrary velocity along the background magnetic field lines, which we take to be approximately radial. We focus in particular on the case in which the box moves at the same speed as outward-propagating Alfv\'en waves. To aid in the design and optimization of future numerical simulations, we express the equations in terms of scalar potentials and Clebsch coordinates. The equations we derive will be particularly useful for conducting high-resolution numerical simulations of reflection-driven magnetohydrodynamic turbulence in the solar wind, and may also be useful for studying turbulence within other astrophysical outflows.