Nonlinear development of convective instability within slender flux tubes. I. Adiabatic flow

The nonlinear development of convective instability within slender flux tubes is studied using the method of characteristics. It is seen that the initial magnetic field influences the development of the instability. The asymptotic state of the unstable tube depends on the boundary conditions. Flux tubes subjected to ’open’ boundary conditions show a better evidence for field amplification than those subjected to ’closed’ boundary conditions. In either case, convective instability results in the generation of significant gas flow within slender flux tubes.