Effect of convection on magnetohydrodynamic kink stability

A magnetohydrodynamic boundary layer analysis is performed treating the effect of the convective term of the equation of motion near the singular surface. The nonlinear equations in this region are separable; the time evolution of the solution is determined by the Riccati equation and nonlinear harmonics are generated at wavenumbers which are multiples of the fundamental. This solution is matched to the linear solution in the outer region yielding modes reminiscent of resistive instabilities which nevertheless are not normal modes of the system