The hydrodynamics of magnetic nonequilibrium

The strongest fluid motions produced by the general dynamical nonequilibrium of close-packed twisted flux tubes are associated with the neutral point reconnection of the magnetic field, expelling jets of fluid along the neutral sheet away from each reconnection point at velocities comparable to the Alfven speed. Most of the energy of the reconnecting field goes into the kinetric energy of the jets. It is pointed out that the dynamical nonequilibrium of close packed twisted flux tubes is essentially the problem of two dimensional MHD turbulence. Hence the extensive literature on two dimensional turbulence represents the hydrodynamics of magnetic nonequilibrium. Conversely, many features of the turbulence can be understood as a consequence of the dynamical nonequilibrium. Numerical simulations of two dimensional turbulence show the strong jets of fluid from the points of reconnection. The present paper is concerned primarily with the dynamics of those jets. The simulations show the jets often to be of remarkably uniform widths. We provide some simple examples to show that this can be understood as a direct consequence of the form of the pressure of the magnetic fields between which the jets are confined. It is shown that the general hydrodynamics of a layer of fluid confined by steady pressures is reducible to a quadrature so that a variety of effects may be considered, including gravitation. The equations show the nonlinear bunching of fluid, leading to deceleration of the initial jet. The ultimate degradation of the kinetic energy of the jets is turbulence, so that no matter how small the electrical resistivity and the molecular viscosity, the energy in the original transverse magnetic field passes rapidly through the nonequilibrium fluid motions into heat in the fluid. A brief discussion of the dissipation in the corona of the sun is contained in the concluding section.