General three-dimensional equilibria for gravitating ideal magnetohydrodynamics of field-aligned steady incompressible flows with an application to solar prominences

Abstract

This paper investigates the motion of three-dimensional ideal magnetohydrodynamics with incompressible flows. The governing equation is performed at steady state, with the magnetic field parallel to the plasma flow. The equations of stationary equilibrium are derived and described mathematically in Cartesian space. Two approaches for derivation of general three-dimensional solutions for Alfvénic and non-Alfvénic flows at constant and variable fluid densities are constructed. The general vector and scalar potentials of the velocity field are used to derive general formulas of general three-dimensional solutions for Alfvénic and non-Alfvénic flows. To verify the general results we have obtained, some examples are presented. An application that may be of interest for coronal loops and solar prominences is presented.