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

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 ${\epsilon }_{\mathrm{D}}$, finding it scales as the wave amplitude ($d$) to the third power (${\epsilon }_{\mathrm{D}}\propto d^3$). 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.

arXiv comment6 pages, 1 figure, published in ApJL

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• Non-linear damping of standing kink waves computed with Elsasser variables
• Weak damping of propagating MHD kink waves in the quiescent corona
• High frequency decayless waves with significant energy in Solar Orbiter/EUI observations
• Transition to turbulence in nonuniform coronal loops driven by torsional Alfven waves
• Characteristics and Energy Flux Distributions of Decayless Transverse Oscillations Depending on Coronal Regions
• Kelvin-Helmholtz instability and heating in oscillating loops perturbed by power-law transverse wave drivers
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• Quasimodes in the cusp continuum in nonuniform magnetic flux tubes
• Damping of coronal oscillations in self-consistent 3D radiative MHD simulations of the solar atmosphere
• Stability of solar atmospheric structures harboring standing slow waves: An analytical model in a compressible plasma
• Magnetic reconnection and the Kelvin-Helmholtz instability in the solar corona