In a previous paper, we computed the energy density and the non-linear energy cascade rate for transverse kink waves using Elsässer variables. In this paper, we focus on the standing kink waves, which are impulsively excited in coronal loops by external perturbations. We present an analytical calculation to compute the damping time due to the non-linear development of the Kelvin-Helmholtz instability. The main result is that the damping time is inversely proportional to the oscillation amplitude. We compare the damping times from our formula with the results of numerical simulations and observations. In both cases we find a reasonably good match. The comparison with the simulations show that the non-linear damping dominates in the high amplitude regime, while the low amplitude regime shows damping by resonant absorption. In the comparison with the observations, we find a power law inversely proportional to the amplitude η −1 as an outer envelope for our Monte Carlo data points.

We investigated a shear instability of the Kelvin-Helmholtz (KH) type in a plasma with temperature anisotropy under the MHD approximation. To solve the problem, a system of 16-moment MHD transport equations is used in a collisionless Bi-Maxwellian plasma, including the various components of the heat fluxes along the magnetic field. We consider supersonic flows of two semiinfinite anisotropic and homogeneous plasma layers with different physical parameters and velocities. For the general case, i.e. when the interface between these two flows is a transition layer with a finite thickness, we derived a general linear differential equation framework for determining the eigenmodes in the system. Furthermore, we considered thoroughly the limiting case of a zero thickness transition zone (contact discontinuity). The analysis enabled applying appropriate boundary conditions to derive the dispersion equation for interface waves. The obtained equation is analyzed in detail for the case when heat fluxes are absent along the discontinuity in the background state. It is shown that the shear flow excites the KH instability and "couples" the various branches of the free-plasma oscillations to each other. It is found that the region of mode interaction is determined by the resonance regions when the longitudinal phase velocities of the waves match. In the resonance flows with an average speed the KH instability occurs. The growth rates of the KH instability are calculated as a function of the parameters, including the degree of plasma anisotropy. It is found that in most cases the KH instability is dominant in the considered configuration. The obtained results are applied to the plasma conditions in the bimodal solar wind in the vicinity of the contact discontinuity between different flow patterns (fast and slow wind).

This investigation is concerned with uniturbulence associated with surface Alfvén waves that exist in a Cartesian equilibrium model with a constant magnetic field and a piece-wise constant density. The surface where the equilibrium density changes in a discontinuous manner are the source of surface Alfvén waves. These surface Alfvén waves create uniturbulence because of the variation of the density across the background magnetic field. The damping of the surface Alfvén waves due to uniturbulence is determined using the Elsässer formulation. Analytical expressions for the wave energy density, the energy cascade, and the damping time are derived. The study of uniturbulence due to surface Alfvén waves is inspired by the observation that (the fundamental radial mode of) kink waves behave similarly to surface Alfvén waves. The results for this relatively simple case of surface Alfvén waves can help us understand the more complicated case of kink waves in cylinders. We perform a series of 3D ideal MHD simulations for a numerical demonstration of the non-linearly self-cascading model of unidirectional surface Alfvén waves using the code MPI-AMRVAC. We show that surface Alfvén waves damping time in the numerical simulations follows well our analytical prediction for that quantity. Analytical theory and the simulations show that the damping time is inversely proportional to the amplitude of the surface Alfvén waves and the density contrast. This unidirectional cascade may play a role in heating the coronal plasma.

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The linear MHD Kelvin-Helmholtz instability (KHI) in an anisotropic plasma is studied. The governing equations obtained as the 16 moments of Boltzmann-Vlasov kinetic equations, including the heat flow, are applied. In the case of tangential discontinuity between the supersonic flows along the magnetic field calculated growth rates as functions of the anisotropic plasma properties allow us to conclude that quasi-transverse modes grow faster. Then dispersion equations for the KHI of quasi-transverse modes are derived considering the finite width of the transition zone with different velocity profiles. For these modes, when the role of heat flow is not important, the plasma parameters are controlled so that the fundamental plasma instabilities (firehose and mirror) do not affect the KHI. The problem is solved analytically, which will be helpful in verifying for numerical simulation. In contrast to the tangential discontinuity, the finite width of the transition layer confines KHI excitation as the wavenumber increases. In the general case of oblique propagation (when a heat flux complicates the problem), the boundary value problem is solved to determine the spectral eigenvalues. In particular, it is observed that fundamental plasma instabilities that arise in the transition zone between flows with a finite width can modify and considerably enhance KHI.