  Context. Kink waves are routinely observed in coronal loops. Resonant
absorption is a well-accepted mechanism that extracts energy from kink waves.
Nonlinear kink waves are know to be affected by the Kelvin-Helmholtz
instability. However, all previous numerical studies consider linearly
polarized kink waves. Aims. We study the properties of circularly polarized
kink waves on straight plasma cylinders, for both standing and propagating
waves, and compare them to the properties of linearly polarized kink waves.
Methods. We use the code MPI-AMRVAC to solve the full 3D Magnetohydrodynamic
(MHD) equations for a straight magnetic cylinder, excited by both standing and
propagating circularly polarized kink (m = 1) modes. Results. The damping due
to resonant absorption is independent of the polarization state. The morphology
or appearance of the induced resonant flow is different for the two
polarizations, however, there are essentially no differences in the
forward-modeled Doppler signals. For nonlinear oscillations, the growth rate of
small scales is determined by the total energy of the oscillation rather than
the perturbation amplitude. We discuss possible implications and seismological
relevance.
