Turbulent Erosion of Magnetic Flux Tubes

Results from a numerical and analytical investigation of the solution of a nonlinear axisymmetric diffusion equation for the magnetic field are presented for the case when the nonlinear dependence of the diffusivity ν( B ) on the magnetic field satisfies basic physical requirements. We find that for sufficiently strong nonlinearity (i.e., for sufficiently strong reduction of ν inside the tube) a current sheet is spontaneously formed around the tube within one diffusion timescale. This sheet propagates inward with a velocity inversely proportional to the ratio of the field strength just inside the current sheet to the equipartition field strength B 0 / B e , so the lifetime of a tube with constant internal flux density is increased approximately by a factor not exceeding B 0 / B e , even for infinitely effective inhibition of turbulence inside the tube . Among the applications of these results, we point out that toroidal flux tubes in the solar convective zone are subject to significant flux loss owing to turbulent erosion on a timescale of ~1 month and that turbulent erosion may be responsible for the formation of a current sheet around a sunspot. It is further proposed that, despite the simplifying assumptions involved, our solutions correctly reflect the essential features of the sunspot decay process.