  Kink oscillations are ubiquitously observed in solar coronal loops, their
understanding being crucial in the contexts of coronal seismology and
atmospheric heating. We study kink modes supported by a straight coronal loop
embeded in an asymmetric environment using three-dimensional
magnetohydrodynamic (MHD) simulations. We implement the asymmetric effect by
setting different exterior densities below and above the loop interior, and
initiate the simulation using a kink-like velocity perturbation perpendicular
to the loop plane, mimicking the frequently measured horizontally polarized
kink modes. We find that the external velocity fields show fan blade structures
propagating in the azimuthal direction as a result of the successive excitation
of higher azimuthal Fourier modes. Resonant absorption and phase mixing can
still occur despite an asymmetric environment, leading to the development of
small scales at loop boundaries. These small scales nonetheless develop
asymmetrically at the upper and lower boundaries due to the different gradients
of the Alfven speed. These findings enrich our understanding of kink modes in
coronal loops embedded within an asymmetric environment, providing insights
helpful for future high-resolution observations.
