  We present the results of three-dimensional (3D) ideal magnetohydrodynamics
(MHD) simulations on the dynamics of a perpendicularly inhomogeneous plasma
disturbed by propagating Alfv\'enic waves. Simpler versions of this scenario
have been extensively studied as the phenomenon of phase mixing. We show that,
by generalizing the textbook version of phase mixing, interesting phenomena are
obtained, such as turbulence-like behavior and complex current-sheet structure,
a novelty in longitudinally homogeneous plasma excited by unidirectionally
propagating waves. This constitutes an important finding for turbulence-related
phenomena in astrophysics in general, relaxing the conditions that have to be
fulfilled in order to generate turbulent behavior.
