Torsional Alfven waves are a type of magnetohydrodynamic waves in a non-uniform plasma, that travel at the Alfven speed along the magnetic field. In a straight field-aligned magnetic flux tube, these waves are azimuthal perturbations of the plasma that are accompanied by an azimuthal component of the magnetic field. The torsional waves are important because they may play role in coronal heating, efficiently transferring energy from lower solar atmosphere layers to corona (Ofman, 2005; Murawski 2015) and the wind acceleration.
A series of theoretical studies of coronal heating and solar wind acceleration by Alfven waves were carried out by many authors (e.g. Suzuki, 2011; Verdini et al. 2012) in 1D, i.e. for plane waves. A key ingredient of the models is the nonlinear cascade of the wave energy from low-frequency injection range to higher frequencies, where it becomes subject to dissipation by MHD and kinetic mechanisms. In Alfven waves this effect becomes possible because of the non-linear interaction of the waves with the (nonlinearly) induced compressive perturbation. Vasheghani Farahani et al. (2011) and Vashehgani Farahani et al. (2012) studied nonlinear long-wavelength torsional Alfven wave in magnetic flux tube analytically in terms of the second order thin flux tube approximation (Zhugzhda, 1996). Compressive perturbations induced by axisymmetric torsional waves were found to oscillate at twice the frequency of the torsional wave. The back-reaction of the nonlinearly induced compressive perturbations resulted in the deformation of the axial wave profile, thus transferring energy to higher frequencies. In the weakly nonlinear regime, the evolution of the wave profile is described by Cohen-Kulsrud equation.
We performed a numerically study the behaviour of a nonlinear torsional Alfven waves in a straight magnetic flux tube, aiming to verify the analytical findings and extend them on the strongly nonlinear regime. We used the Lare3D code, set up an equilibrium magnetic flux tube with a finite-beta plasma and simulated the evolution of standing and propagating torsional Alfven waves, paying attention to the nonlinear cascade, the wave front deformation, and compressive perturbations. Nonlinear torsional Alfven waves were found to be consistent with main features found in the asymptotic analytical consideration.