Non-linear damping of standing kink waves computed with Elsasser variables

TL;DR

This paper derives an analytical model for the non-linear damping of standing kink waves in coronal loops, showing damping time inversely depends on oscillation amplitude, and validates it against simulations and observations.

Contribution

It provides a new analytical expression for damping time due to Kelvin-Helmholtz instability in standing kink waves, extending previous work on transverse waves.

Findings

Damping time is inversely proportional to oscillation amplitude.

Non-linear damping dominates at high amplitudes, resonant absorption at low.

Model matches numerical simulations and observational data reasonably well.

Abstract

In a previous paper, we computed the energy density and the non-linear energy cascade rate for transverse kink waves using Elsasser variables. In this paper, we focus on the standing kink waves, which are impulsively excited in coronal loops by external perturbations. We present an analytical calculation to compute the damping time due to the non-linear development of the Kelvin-Helmholtz instability. The main result is that the damping time is inversely proportional to the oscillation amplitude. We compare the damping times from our formula with the results of numerical simulations and observations. In both cases we find a reasonably good match. The comparison with the simulations show that the non-linear damping dominates in the high amplitude regime, while the low amplitude regime shows damping by resonant absorption. In the comparison with the observations, we find a power law inversely proportional to the amplitude $\eta^{-1}$ as an outer envelope for our Monte Carlo data points.