Estimating the energy flux of transverse waves associated with Kelvin-Helmholtz instability in solar coronal loops

Context. The energy flux of kink waves in coronal loops has been estimated in previous studies. Recent numerical simulations have revealed that kink oscillations can induce a Kelvin-Helmholtz Instability (KHI) in magnetic flux tubes. This non-linear process breaks the assumptions that have typically been included in previous eigenmode analyses. Therefore, the current analytical expressions of energy flux need to be re-examined.Aims. In the present work, we aim to compare our numerical energy flux with previous analytical formulae and establish modifications to the estimation of the energy flux of kink waves in coronal loops.Methods. Working within the framework of ideal magnetohydrodynamics (MHD), we conducted three-dimensional (3D) simulations of kink oscillations in coronal cylinders. Forward models were also employed to translate our numerical results into observables using the FoMo code.Results. We find that the previous estimation of the energy flux of kink waves is reasonable up to the point before the KHI is fully developed. However, as small vortices develop, the energy flux derived from the analytical formula becomes smaller than the total Poynting flux calculated from our numerical results. Furthermore, when degrading the original numerical resolution to match a realistic instrumental resolution, for instance, the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO), the energy flux becomes much smaller than the numerical value.Conclusions. The energy flux calculated from the analytical formula should be modified by multiplying it by a factor of about 2. When it comes to the energy flux estimation based on SO/EUI observations, this factor should be between about 3 and 4.