Propagating coupled Alfvén and kink oscillations in an arbitrary inhomogeneous corona

Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low
β plasma. We consider the cases of distorted cylindrical flux tubes and a randomly generated inhomogeneous medium. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of
the kink mode to the Alfvén mode. The decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. In all cases considered, modest changes in density were capable of efficiently converting
energy from the driving footpoint motion to localized Alfv´en modes. We have demonstrated that mode coupling efficiently couples propagating kink perturbations to Alfvén modes in an arbitrary inhomogeneous medium. This
has the consequence that transverse footpoint motions at the base of the corona will deposit energy to Alfvén modes in the corona.