Transition to turbulence in nonuniform coronal loops driven by torsional Alfvén waves

Abstract

Both observations and numerical simulations suggest that Alfvénic waves may carry sufficient energy to sustain the hot temperatures of the solar atmospheric plasma. However, the thermalization of wave energy is inefficient unless very short spatial scales are considered. Phase mixing is a mechanism that can take energy down to dissipation lengths, but it operates over too long a timescale. Here, we study how turbulence, driven by the nonlinear evolution of phase-mixed torsional Alfvén waves in coronal loops, is able to take wave energy down to the dissipative scales much faster than the theory of linear phase mixing predicts. We consider a simple model of a transversely nonuniform cylindrical flux tube with a constant axial magnetic field. The flux tube is perturbed by the fundamental mode of standing torsional Alfvén waves. We solved the three-dimensional ideal magnetohydrodynamics equations numerically to study the temporal evolution. Initially, torsional Alfvén waves undergo the process of phase mixing because of the transverse variation of density. After only few periods of torsional waves, azimuthal shear flows generated by phase mixing eventually trigger the Kelvin-Helmholtz instability (KHi), and the flux tube is subsequently driven to a turbulent state. Turbulence is very anisotropic and develops transversely only to the background magnetic field. After the onset of turbulence, the effective Reynolds number decreases in the flux tube much faster than in the initial linear stage governed by phase mixing alone. We conclude that the nonlinear evolution of torsional Alfvén waves, and the associated KHi, is a viable mechanism for the onset of turbulence in coronal loops. Turbulence can significantly speed up the generation of small scales. Enhanced deposition rates of wave energy into the coronal plasma are therefore expected.