Coherent nonlinear oscillations in magnetohydrodynamic plasma

Single fluid magnetohydrodynamic (MHD) equations have been studied through direct numerical simulations (DNS) using pseudo-spectral methods in two as well as three spatial dimensions. At Alfv\'en resonance, a reversible periodic exchange of energy between kinetic and magnetic variables is observed. The oscillations are identified as nonlinear dispersionless Alfv\'en waves that have been predicted earlier on theoretical grounds but not observed in large scale numerical simulations. A systematic study of their occurrence for various initial conditions and a range of Alfven velocities is carried out. An analysis based on a finite mode representation of the incompressible single fluid MHD equations in two spatial dimensions reproduces the essential features of these oscillations.