Abstract. In a collisionless plasma, when reconnection instability takes place, strong shear flows may develop. Under appropriate conditions these shear flows become unstable to the Kelvin-Helmholtz instability. Here, we investigate the coupling between these instabilities in the framework of a four-field model. Firstly, we recover the known results in the low β limit, β being the ratio between the plasma and the magnetic pressure. We concentrate our attention on the dynamical evolution of the current density and vorticity sheets which evolve coupled together according to a laminar or a turbulent regime. A three-dimensional extension in this limit is also discussed. Secondly, we consider finite values of the β parameter, allowing for compression of the magnetic and velocity fields along the ignorable direction. We find that the current density and vorticity sheets now evolve separately. The Kelvin-Helmholtz instability involves only the vorticity field, which ends up in a turbulent regime, while the current density maintains a laminar structure.
Hamiltonian four-field model for magnetic reconnection: nonlinear dynamics and extension to three dimensions with externally applied fields