Non-linear damping of visco-resistive Alfv,n waves in solar spicules

Interaction of Alfv,n waves with plasma inhomogeneities generates phase mixing which can lead to dissipate Alfv,n waves and to heat the solar plasma. Here we study the dissipation of Alfv,n waves by phase mixing due to viscosity and resistivity variations with height. We also consider nonlinear magnetohydrodynamic (MHD) equations in our theoretical model. Non-linear terms of MHD equations include perturbed velocity, magnetic field, and density. To investigate the damping of Alfv,n waves in a stratified atmosphere of solar spicules, we solve the non-linear MHD equations in the x-z plane. Our simulations show that the damping is enhanced due to viscosity and resistivity gradients. Moreover, energy variations is influenced due to nonlinear terms in MHD equations.