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

Abstract

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.

Shock identification and classification in 2D MHD compressible turbulence -- Orszag-Tang vortex

“…However, here there are comparable numbers of fast and slow shocks in the system after 𝑡 = 0.8, and large un-corrugated coherent slow-mode shock structures exist in the simulation, see Figure 1b-d. A recent study has shown that the the corrugation instability can actually increase the number of detected shock pixels due to an increased shock length (Snow and Hillier, 2021).…”

“…The Orszag-Tang vortex has been well studied in the literature (Dahlburg and Picone, 1989;Picone and Dahlburg, 1991;Jiang and Wu, 1999;Parashar et al, 2009;Uritsky et al, 2010). The initial conditions are evolved in 2D for ideal MHD equations using the 4th order central-difference solver in the (PIP) code (Hillier et al, 2016), which has been used previously to study shocks (e.g., Snow and Hillier, 2021). The simulations are performed using 1024 × 1024 cells with periodic boundary conditions.…”

Two-fluid implementation in MPI-AMRVAC with applications to the solar chromosphere

“…Differently to the Orszag-Tang test presented earlier, the charged fluid might evolve similarly to the plasma in the MHD assumption, even if the collisional coupling is weak. A very demanding numerical experiment is the simulation of a perturbed 2D MHD slow shock front, leading in most of the cases to the corrugation instability (Stone & Edelman 1995;Snow & Hillier 2021). We use a background medium similar to that used by Snow & Hillier (2021) for parallel shocks.…”

“…A very demanding numerical experiment is the simulation of a perturbed 2D MHD slow shock front, leading in most of the cases to the corrugation instability (Stone & Edelman 1995;Snow & Hillier 2021). We use a background medium similar to that used by Snow & Hillier (2021) for parallel shocks. We use subscript 1 for downstream variables (x < 0) and subscript for 2 upstream variables (x > 0), where we exploit the frame of reference of the shock front, fixed at the location x = 0.…”

“…Given upstream quantities, we can get downstream quantities from the flux conservation laws, assuming a stationary solution. We use the same values given in Table A1 in Snow & Hillier (2021) for the left and right states with respect to interface of discontinuity. The 2D x − y domain [−1.5, 1] × [0, 0.1] is covered by 1024 × 256 points as base resolution and we used 4 levels of refinement.…”