Estimating the energy dissipation {from Kelvin-Helmholtz instability induced} turbulence in oscillating coronal loops}

TL;DR

This paper develops an analytical model for energy dissipation due to Kelvin-Helmholtz instability in oscillating coronal loops, showing it scales with wave amplitude cubed, and assesses its role in coronal heating.

Contribution

The paper introduces a new analytical model for turbulence dissipation in coronal loops, linking wave amplitude to energy dissipation and validating it against numerical simulations.

Findings

Dissipation rate scales as the cube of wave amplitude.

Steady-state turbulence can match energy injection in coronal loops.

Observed decayless kink waves are insufficient for coronal heating.

Abstract

Kelvin-Helmholtz {instability induced} turbulence is one promising mechanism by which loops in the solar corona can be heated by MHD waves. In this paper we present an analytical model of the dissipation rate of {Kelvin-Helmholtz instability induced} turbulence $\varepsilon_{\rm D}$, finding it scales as the wave amplitude ($d$) to the third power ($\varepsilon_{\rm D}\propto d^3$). Based on the concept of steady-state turbulence, we expect the turbulence heating throughout the volume of {the} loop to match the total energy injected through its footpoints. In situations where this holds, the wave amplitude has to vary as the cube-root of the injected energy. Comparing the analytic results with those of simulations shows that our analytic formulation captures the key aspects of the turbulent dissipation from the numerical work. Applying this model to the observed characteristics of decayless kink waves we predict that the amplitudes of these observed waves is insufficient to turbulently heat the solar corona.