  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.
