Convective instability in a solar flux tube. I. Nonlinear calculations for an adiabatic inviscid fluid

The temporal evolution of a slender flux tube extending vertically in the convection zone of the Sun is modeled by numerical solution of the MHD equaitons. Initial states in hydrostatic equilibrium and for which β (the ratio of the thermal to magnetic pressure at the initial epoch) is constant with depth are considered. The time-dependent response of these states to a velocity perturbation is examined. When the perturbation is a downflow, convective collapse of the flux tube occurs when β> or approx. =2. The numerical solutions are followed for long enough times for the instability to be quenched. An important finding to emerge is that the final state is not a steady one, but rather a stationary oscillating one. The surface magnetic field in the final state has an average value of about 1400 G, with an oscillating amplitude of approx.200 G. There is an oscillating flow with an amplitude of approx.600 m s-1 with an average value that is approximately zero. The observational implications of these results are discussed