Stability of two-fluid partially-ionised slow-mode shock fronts

• Main Authors: Snow, Ben, Hillier, Andrew
• Format: Journal Article
• Language: English
• Published: 08-06-2021
• Subjects: Physics - Fluid Dynamics; Physics - Solar and Stellar Astrophysics
• DOI: 10.48550/arxiv.2106.04199

A magnetohydrodynamic (MHD) shock front can be unstable to the corrugation
instability, which causes a perturbed shock front to become increasingly
corrugated with time. An ideal MHD parallel shock (where the velocity and
magnetic fields are aligned) is unconditionally unstable to the corrugation
instability, whereas the ideal hydrodynamic (HD) counterpart is unconditionally
stable. For a partially ionised medium (for example the solar chromosphere),
both hydrodynamic and magnetohydrodynamic species coexist and the stability of
the system has not been studied. In this paper, we perform numerical
simulations of the corrugation instability in two-fluid partially-ionised shock
fronts to investigate the stability conditions, and compare the results to HD
and MHD simulations. Our simulations consist of an initially steady 2D parallel
shock encountering a localised upstream density perturbation. In MHD, this
perturbation results in an unstable shock front and the corrugation grows with
time. We find that for the two-fluid simulation, the neutral species can act to
stabilise the shock front. A parameter study is performed to analyse the
conditions under which the shock front is stable and unstable. We find that for
very weakly coupled or very strongly coupled partially-ionised system the shock
front is unstable, as the system tends towards MHD. However, for a finite
coupling, we find that the neutrals can stabilise the shock front, and produce
new features including shock channels in the neutral species. We derive an
equation that relates the stable wavelength range to the ion-neutral and
neutral-ion coupling frequencies and the Mach number. Applying this relation to
umbral flashes give an estimated range of stable wavelengths between 0.6 and 56
km.