Numerical Simulations of Torsional Alfv\'en Waves in Axisymmetric Solar Magnetic Flux Tubes

We investigate numerically Alfv\'en waves propagating along an axisymmetric and non-isothermal solar flux tube embedded in the solar atmosphere. The tube magnetic field is current-free and diverges with height, and the waves are excited by a periodic driver along the tube magnetic field lines. The main results are that the two wave variables, the velocity and magnetic field perturbations in the azimuthal direction, behave differently as a result of gradients of physical parameters along the tube. To explain these differences in the wave behavior, the time evolution of the wave variables and the resulting cutoff period for each wave variable are calculated, and used to determine regions in the solar chromosphere where strong wave reflection may occur.