Magnetohydrodynamic Waves in an Asymmetric Magnetic Slab with Different External Flows

Building on recent studies of the Kelvin-Helmholtz instability (KHI) in the solar atmosphere, we investigate a simple analytical model that can further our understanding of how the presence of bulk flows influences the propagation of magnetohydrodynamic (MHD) waves. Our model builds on a series of recent works on stationary MHD waveguides and looks at a magnetic slab with a density asymmetry, as well as asymmetric background steady flows present in its environment. We obtained approximate solutions to the dispersion relation for the important and applicable limiting cases of a thin or a wide slab, as well as low- and high-β plasmas. We also explored the relation between the angular frequency of trapped MHD waves, the limit for the onset of the KHI, and small parameters describing the flow and density asymmetries. Our analytical investigation is complemented by a numerical analysis for various bulk flow speeds and slab widths. Both these avenues of study reveal that the flow field asymmetry has an important effect on both the cutoff frequencies and the stability of trapped MHD waves in the slab configuration.