Power and complexity in stochastic reconnection

Previous work has invoked kinetic and magnetic spatial complexities, associated with velocity and magnetic fields u(x,t) and B(x,t), respectively, in order to study magnetic reconnection and diffusion in turbulent and magnetized fluids. In this paper, using the coarse-grained momentum equation, we argue that the fluid jets associated with magnetic reconnection events at an arbitrary scale l in the turbulence inertial range are predominantly driven by the Lorentz force Nl=(j×B)l−jl×Bl. This force is induced by the subscale currents and is analogous to the turbulent electromotive force El=(u×B)l−ul×Bl in dynamo theories. Typically, high (low) magnetic complexities during reconnection imply large (small) spatial gradients for the magnetic field, i.e., strong (weak) Lorentz forces Nl. Reconnection launches jets of fluid, hence the rate of change of kinetic complexity is expected to strongly correlate with the power injected by the Lorentz force Nl. We test this prediction using an incompressible, homogeneous magnetohydrodynamic (MHD) simulation and associate it with previous results. It follows that the stronger (weaker) the turbulence, the more (less) complex the magnetic field and the stronger (weaker) the driving Lorentz forces and thus the ensuing reconnection.