On the dynamics of a plasma vortex street and its topological signatures

Abstract

A plasma vortex street configuration can evolve when two velocity and one magnetic shear layer interact strongly. A study of the interaction between two- and three-dimensional plasma modes and a mean sheared magnetic field is undertaken using a three-dimensional magnetohydrodynamic spectral Galerkin computation. The initial state is a simple magnetic shear in a plane perpendicular to the plasma velocity shear plane. In a very weak magnetic field, secondary instabilities (three-dimensional modes), expressed by the kinking of vortex tubes, lead to plasma flow along and around the axes of the vortex cores, creating characteristic patterns of kinetic helicity and linkages between vortex filaments. Three-dimensionality leads to the vortex breakdown process. A strong sheared magnetic field inhibits the kinking of vortex tubes, maintaining two-dimensionality. This inhibits vortex breakdown over long dynamical times. There is an anticorrelation in time between linkage indices of the vortex filament (related to kinetic helicity), suggesting that the ellipticity axes of the vortex cores along the street undergo a global inphase evolution. This anticorrelation has a dynamical interpretation. It extends to a relaxing plasma in the Navier–Stokes flow notion that helical regions of opposite helicities interact and screen each other off so that the global helicity remains bounded.