Self‐organization in the two‐dimensional magnetohydrodynamic transverse Kelvin‐Helmholtz instability

Abstract

For a two‐dimensional transverse configuration in a compressible plasma a magnetohydrodynamic simulation of the Kelvin‐Helmholtz (K‐H) instability has been performed for a subfast shear flow. The simulation shows that after the linear growth and the subsequent nonlinear saturation of the fastest growing vortices these vortices are susceptible to vortex pairings, which occur because of the growth of subharmonics. The total kinetic energy remains almost constant in the evolution of the instability, but the enstrophy decreases rapidly owing to the selective dissipation by an artificial viscosity, which is added to prevent mesh oscillations. Therefore the nonlinear evolution of the two‐dimensional transverse K‐H instability, in particular, the successive pairings of vortices, are well described as a self‐organization process resulting from the interplay of the nonlinearity and the dissipation. After the early stage of the instability development the kinetic energy and the squared vorticity cascade toward the long wavelength (inverse cascade) to form power law spectra in the wavenumber space. The inverse cascade in the wavenumber space corresponds, in the configuration space, to an emergence of a large isolated flow vortex and an associated eddy of inertia current out of trains of small‐scale vortices and current eddies in the early stage. At the end of the simulation run the power law exponents in the wavenumber space of the kinetic energy, the squared vorticity, and the magnetic energy, which are all integrated across the initial flow direction, become −3.89, −2.08, and −4.58, respectively, in the intermediate wavenumber subrange.