  It is widely accepted in the MHD turbulence community that the nonlinear
cascade of wave energy requires counter-propagating Alfv\'enic wave-packets,
along some mean magnetic field. This fact is an obvious outcome of the MHD
equations under the assumptions of incompressibility and homogeneity. Despite
attempts to relax these assumptions in the context of MHD turbulence, the
central idea of turbulence generation persists. However, once the assumptions
of incompressiblity and homogeneity break down, the generally accepted picture
of turbulent cascade generation is not universal. In this paper, we show that
perpendicular inhomogeneities (across the mean magnetic field) lead to
propagating wave solutions which are necessarily described by co-propagating
Els\"asser fields, already in the incompressible case. One simple example of
these wave solutions is the surface Alfv\'en wave on a planar discontinuity
across the magnetic field. We show through numerical simulations how the
nonlinear self-deformation of these unidirectionally propagating waves leads to
a cascade of wave energy across the magnetic field. The existence of this type
of unidirectional cascade might have an additional strong effect on the
turbulent dissipation rate of dominantly outward propagating Alfv\'enic waves
in structured plasma, as in the solar corona and solar wind.
