Excitation and dissipation of torsional modes in solar photospheric magnetic flux tubes

The turbulent excitation of torsional Alfvén waves is presented on the basis of Lighthill-Stein theory. Due to the special properties of torsional modes, we can apply the theory to the inhomogeneous magnetic flux tube embedded in the solar photosphere, to evaluate the wave energy generated from the turbulent source in the convection zone. Torsional wave spectrum distribution along the r coordinate is achieved. In order to estimate the net wave energy transported to the chromosphere, we investigate the wave propagation and dissipation in the photospheric flux tube by simple phase mixing due to the inhomogeneity. Results for several cases with different model parameters are compared. Conclusions are drawn on the significant role of the energy carried by torsional Alfvén waves in the chromospheric and coronal heating, and the wave spectrum may be helpful in understanding the problem of footpoint azimuthal motion of coronal loops.