Resistive and viscous dynamics of finite-amplitude shear waves at a magnetic X-point

The dynamics and dissipation of axial shear waves, superposed on a planar magnetic X-point in a resistive viscous incompressible plasma, are analyzed numerically and analytically. The interplay of viscous and resistive effects is demonstrated by deriving solutions for various values of the scalar coefficients of viscosity and resistivity. These solutions show that viscous-resistive coupling can dramatically affect the global energy dissipation. When either viscosity or resistivity vanishes, the solutions are characterized by oscillatory decaying eigenmodes that maintain equipartition between the magnetic and kinetic energies. This behavior persists when resistivity is the dominant dissipation mechanism. When viscosity is the dominant dissipation mechanism, initial oscillations are followed by exponential decay at sufficiently long times. The applicability of the results to flares in solar active regions, where the viscous Reynolds number can be much smaller than the resistive one, is discussed