Estimating the Energy Dissipation from Kelvin–Helmholtz Instability Induced Turbulence in Oscillating Coronal Loops

Kelvin–Helmholtz instability induced turbulence is one promising mechanism by which loops in the solar corona can be heated by MHD waves. In this Letter we present an analytical model of the dissipation rate of Kelvin–Helmholtz instability induced turbulence εD, finding it scales as the wave amplitude (d) to the third power (εD ∝ d3). 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 are insufficient to turbulently heat the solar corona.