  Aims. We investigate the formation of small scales and the dissipation of MHD
wave energy through non-linear interactions of counter-propagating, phase-mixed
Alfvenic waves in a complex magnetic field. Methods. We conducted fully 3-D,
non-ideal MHD simulations of transverse waves in complex magnetic fields.
Continuous wave drivers were imposed on the foot points of magnetic field lines
and the system was evolved for several Alfven travel times. Phase-mixed waves
were allowed to reflect off the upper boundary and the interactions between the
resultant counter-streaming wave packets were analysed. Results. The complex
nature of the background magnetic field encourages the development of phase
mixing, leading to a growth in currents and vorticities. Counter-propagating
phase-mixed waves induce a cascade of energy to small scales and result in more
efficient energy dissipation. This effect is enhanced in simulations with more
complex magnetic fields. High-frequency drivers excite localised field line
resonances and produce efficient wave heating. However, this relies on the
formation of large amplitude oscillations on resonant field lines. Drivers with
smaller frequencies than the fundamental frequencies of field lines are not
able to excite resonances and thus do not inject sufficient Poynting flux to
power coronal heating. Even in the case of high-frequency oscillations, the
rate of dissipation is likely too slow to balance coronal energy losses, even
within the quiet Sun. Conclusions. For the generalised phase-mixing presented
here, complex background field structures enhance the rate of wave energy
dissipation. However, it remains difficult for realistic wave drivers to inject
sufficient Poynting flux to heat the corona. Indeed, significant heating only
occurs in cases which exhibit amplitudes that are much larger than those
currently observed in the solar atmosphere.
