Evolution of the Orszag–Tang vortex system in a compressible medium. II. Supersonic flow

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Abstract
The numerical investigation of Orszag–Tang vortex system in compressible magnetofluids continues, this time using initial conditions with embedded supersonic regions. The simulations have initial average Mach numbers M=1.0 and 1.5 and β=10/3 with Lundquist numbers S=50, 100, or 200. Depending on the particular set of parameters, the numerical grid contains 2562 or 5122 collocation points. The behavior of the system differs significantly from that found previously for the incompressible and subsonic analogs. Shocks form at the downstream boundaries of the embedded supersonic regions outside the central magnetic X point and produce strong local current sheets that dissipate appreciable magnetic energy. Reconnection at the central X point, which dominates the incompressible and subsonic systems, peaks later and has a smaller impact as M increases from 0.6 to 1.5. Reconnection becomes significant only after shocks reach the central region, compressing the weak current sheet there. Similarly, the correlation between the momentum and magnetic field begins significant growth later than in subsonic and incompressible flows. The shocks bound large compression regions, which dominate the wave‐number spectra of autocorrelations in mass density, velocity, and magnetic field. The normalized spectral amplitude of the cross helicity is almost zero over the middle and upper portions of the wave‐number domain, unlike the incompressible and subsonic flows. The thermal and magnetic pressures are anticorrelated over a wide wave‐number range during the earlier portion of the calculations, consistent with the presence of quasistationary structures bounded by shocks.