The Kelvin-Helmholtz Instability in Oscillating

Coronal LoopsThomas Howson

Ineke De Moortel Patrick Antolin

Coronal WavesWaves are abundant in the solar atmosphere.

Coronal WavesWaves are abundant in the solar atmosphere.

Could power coronal heating. However energy dissipation is very slow.

Small length scales, (e.g. from turbulence), enhance heating rates. How could these

small scales form? And do they?

Key TermsMagnetic Tension Force - acts to straighten magnetic field lines. It is the restoring force in the oscillations we model.

Kelvin-Helmholtz Instability - can occur when a velocity shear exists within a fluid. Think wind moving across water generating waves.

Magnetic diffusivity and Viscosity - dissipate wave energy as heat.

Our ModelCore

Shell

External

X Z

Y

Straight, dense magnetic flux tube

Our ModelCore

Shell

External

X Z

Y

Straight, dense magnetic flux tube

Initial perturbation

Generates standing wave

Lare3D, what happens next?

Kink Wave

Vertical Cross-Section

Model a standing kink wave - transverse oscillation with ends held fixed.

Maximum displacement occurs at loop ‘apex’.

Wave damping occurs despite no dissipation of kinetic/magnetic energy -Resonant Absorption.

Wave DampingTracking the loop centre gives damping profile.

Enclosed by Gaussian (not exponential) curves.

Evidence of Resonant Absorption - (ideal) transfer of energy from the kink mode to Alfvénic modes in the loop shell.

Resonant AbsorptionInitial velocity profile concentrated in loop core.

Resonant absorption creates flows within the loop shell - subject to phase mixing.

Creates large velocity shear within the loop K-H instability?

Resonant Absorption

Wave energy becomes concentrated in the loop’s shell region.

Density Evolution

Magnetic EnergyConcentration of magnetic (and kinetic) energy in the loop shell.

KHI enhances this effect and generates smaller length scales. Small length scales enhance wave energy dissipation. More heating.

Heating requires viscosity and/or magnetic diffusivity to be greater than 0.

Large transport coefficients suppress the instability.

Can get faster heating rate with locally enhanced transport coefficients.

But …

ConclusionsEnergy transferred from a standing kink mode to Alfvénic waves in the loop shell.

This generates small length scales and therefore heating.

It also encourages the development of the KHI.

KHI generates small length scales and enhanced heating rate. 

However it is suppressed for large transport coefficients.