Magnetohydrodynamic kink waves naturally form as a consequence of perturbations to a structured
medium, for example transverse oscillations of coronal loops. Linear theory has provided many insights
in the evolution of linear oscillations, and results from these models are often applied to infer information about the solar corona ...
Magnetohydrodynamic kink waves naturally form as a consequence of perturbations to a structured
medium, for example transverse oscillations of coronal loops. Linear theory has provided many insights
in the evolution of linear oscillations, and results from these models are often applied to infer information about the solar corona from observed wave periods and damping times. However, simulations
show that nonlinear kink waves can host the Kelvin-Helmholtz instability (KHi) which subsequently
creates turbulence in the loop, dynamics which are beyond linear models. In this paper we investigate
the evolution of KHi-induced turbulence on the surface of a flux tube where a non-linear fundamental
kink-mode has been excited. We control our numerical experiment so that we induce the KHi without
exciting resonant absorption. We find two stages in the KHi turbulence dynamics. In the first stage, we
show that the classic model of a KHi turbulent layer growing ∝ t is applicable. We adapt this model to
make accurate predictions for damping of the oscillation and turbulent heating as a consequence of the
KHi dynamics. In the second stage, the now dominant turbulent motions are undergoing decay. We
find that the classic model of energy decay proportional to t−2 approximately holds and provides an
accurate prediction of the heating in this phase. Our results show that we can develop simple models
for the turbulent evolution of a non-linear kink wave, but the damping profiles produced are distinct
from those of linear theory that are commonly used to confront theory and observations.