Non-linear dynamics of Kelvin-Helmholtz unstable magnetized jets: three-dimensional effects

The Kelvin-Helmholtz (KH) instability is a basic hydrodynamic phenomenon in sheared flows. Magnetic fields can strongly influence the linear and non-linear behavior of this instability. A recent full parameter study (Paper I) of the growth and saturation of the KH instability in two-dimensional (2D) compressible magnetohydrodynamics (MHD) augmented the vast body of knowledge on magnetically induced effects4–11. It illustrated how a weak, uniform B field gets amplified by the developing vortical flow and how this in turn changes the redistribution of mass as compared to pure hydrodynamic cases. Figure 1, taken from Paper I, shows a close-up of the density pattern after four transverse sound travel times in a magnetically modified KH evolution. Parameter values are listed below in section II B. The magnetic field becomes dynamically dominant at the time shown, halting the further growth in the transverse y-direction. The x-direction is periodic, so Fig. 1 shows alternating regions of density enhancements (bright) and depletions (dark). The narrow lanes of low density intersecting the high density regions signal sites of strong magnetic fields. The KH instability is important for numerous astrophysical applications. Shear flows occur in jets ejected from star forming regions, in stellar winds, in winds emanating from accretion disks, . . . Many of the jet-type astrophysical flows are at such high speeds that the dominant dynamics is through shock interaction both internal to the jet and at its leading working surface where the jet penetrates the ambient plasma. The fundamental shear-induced instabilities that can develop at the jet surface are ultimately responsible for entrainment and mixing with the ambient material. Recently, Bodo et al. performed comparative 2D and 3D hydrodynamic simulations of supersonic (Mach 10) jets. In their 3D simulations of a jet, 10 times less dense than its environment, faster decay into small-scale structure was demonstrated, as well as strong mixing with the external medium. The evolution was governed by the formation of internal shocks, induced external shocks, and consequent momentum and material mixing processes. Usually, the initial perturbation in 2D and 3D studies of this kind consists of a superposition of all linear wave modes, mimicking the dynamics resulting from random excitations. It is then very difficult to disentangle what causes the separate modes to couple. Therefore, we take a different approach and perturb at selected mode pairs. Our aim is to clearly identify cause and effect in the non-linear dynamics.