Abstract
Planar acoustically dominated magnetohydrodynamic waves are initiated at the high-\(\beta\) base of a simulated 2D isothermal stratified atmosphere with potential magnetic field exhibiting both open and closed field regions as well as neutral points. They shock on their way upward toward the Alfvén–acoustic equipartition surface \(a=c\), where \(a\) and \(c\) are the Alfvén and sound speeds, respectively. Expanding on recent 1.5D findings that such shocks mode-convert to fast shocks and slow smoothed waves on passing through \(a=c\), we explore the implications for these more complex magnetic geometries. It is found that the 1.5D behaviour carries over to the more complex case, with the fast shocks strongly attracted to neutral points, which are disrupted producing extensive fine structure. It is also observed that shocks moving in the opposite direction, from \(a>c\) to \(a< c\), split into fast and slow components too, and that again it is the slow component that is smoothed.
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Notes
However, as pointed out by Whitham (1974), Section 8.8, this is an artefact of linearization. With shocks already present, the wave fronts speed up and typically push the rays apart, thereby inhibiting caustic formation. Nevertheless, their appearance in linearized ray-tracing certainly suggests the development of nonlinearity in reality.
Similar ray calculations were carried out by Tarr and Linton (2019) in 3D, including the Alfvén wave which we have neglected.
A stiffness-switching scheme with projection is used to maintain \(\mathcal{D}=0\) to high order.
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Pennicott, J.D., Cally, P.S. Conversion and Smoothing of MHD Shocks in Atmospheres with Open and Closed Magnetic Field and Neutral Points. Sol Phys 296, 97 (2021). https://doi.org/10.1007/s11207-021-01829-x
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DOI: https://doi.org/10.1007/s11207-021-01829-x