Non-Linear Damping of Surface Alfvén Waves Due to Uniturbulence

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.

Weak Damping of Propagating MHD Kink Waves in the Quiescent Corona

Propagating transverse waves are thought to be a key transporter of Poynting flux throughout the Sun’s atmosphere. Recent studies have shown that these transverse motions, interpreted as the magnetohydrodynamic kink mode, are prevalent throughout the corona. The associated energy estimates suggest the waves carry enough energy to meet the demands of coronal radiative losses in the quiescent Sun. However, it is still unclear how the waves deposit their energy into the coronal plasma. We present the results from a large-scale study of propagating kink waves in the quiescent corona using data from the Coronal Multi-channel Polarimeter (CoMP). The analysis reveals that the kink waves appear to be weakly damped, which would imply low rates of energy transfer from the large-scale transverse motions to smaller scales via either uniturbulence or resonant absorption. This raises questions about how the observed kink modes would deposit their energy into the coronal plasma. Moreover, these observations, combined with the results of Monte Carlo simulations, lead us to infer that the solar corona displays a spectrum of density ratios, with a smaller density ratio (relative to the ambient corona) in quiescent coronal loops and a higher density ratio in active-region coronal loops.

Bäcklund transformations, Lax pair and solutions of a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves

Burgers-type equations are considered as the models of certain phenomena in plasma astrophysics, ocean dynamics, atmospheric science and so on. In this paper, a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves is studied. Based on the Painlevé-Bäcklund equations, one auto-Bäcklund transformation and two hetero-Bäcklund transformations are derived. Motivated by the Burgers hierarchy, a Lax pair is given. Via two hetero-Bäcklund transformations with different constant seed solutions, we find some multiple-kink solutions, complex periodic solutions, hybrid solutions composed of the lump, periodic and multiple kink waves. Then we discuss the influence of the coefficients of the above equation on such solutions. Via the auto-Bäcklund transformation with the nontrivial seed solutions, we obtain certain lump-type solutions, kink-type solutions and recurrence relation of the above equation.

Bifurcations of Nonlinear Waves in the Generalized KdV–mKdV-Like Equation

Using bifurcation analytic method of dynamical systems, we investigate the nonlinear waves and their bifurcations of the generalized KdV–mKdV-like equation. We obtain the following results : (i) Three types of new explicit expressions of nonlinear waves are obtained. They are trigonometric expressions, exp-function expressions, and hyperbolic expressions. (ii) Under different parameteric conditions, these expressions represent different waves, such as solitary waves, kink waves, 1-blow-up waves, 2-blow-up waves, smooth periodic waves and periodic blow-up waves. (iii) Two kinds of new interesting bifurcation phenomena are revealed. The first phenomenon is that the single-sided periodic blow-up waves can bifurcate from double-sided periodic blow-up waves. The second phenomenon is that the double-sided 1-blow-up waves can bifurcate from 2-blow-up waves. Furthermore, we show that the new expressions encompass many existing results.

Kink Oscillations of Coronal Loops

Kink oscillations of coronal loops, i.e., standing kink waves, is one of the most studied dynamic phenomena in the solar corona. The oscillations are excited by impulsive energy releases, such as low coronal eruptions. Typical periods of the oscillations are from a few to several minutes, and are found to increase linearly with the increase in the major radius of the oscillating loops. It clearly demonstrates that kink oscillations are natural modes of the loops, and can be described as standing fast magnetoacoustic waves with the wavelength determined by the length of the loop. Kink oscillations are observed in two different regimes. In the rapidly decaying regime, the apparent displacement amplitude reaches several minor radii of the loop. The damping time which is about several oscillation periods decreases with the increase in the oscillation amplitude, suggesting a nonlinear nature of the damping. In the decayless regime, the amplitudes are smaller than a minor radius, and the driver is still debated. The review summarises major findings obtained during the last decade, and covers both observational and theoretical results. Observational results include creation and analysis of comprehensive catalogues of the oscillation events, and detection of kink oscillations with imaging and spectral instruments in the EUV and microwave bands. Theoretical results include various approaches to modelling in terms of the magnetohydrodynamic wave theory. Properties of kink oscillations are found to depend on parameters of the oscillating loop, such as the magnetic twist, stratification, steady flows, temperature variations and so on, which make kink oscillations a natural probe of these parameters by the method of magnetohydrodynamic seismology.

Hybrid solutions of a (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation in an incompressible fluid

Incompressible fluids are studied in such disciplines as ocean engineering, astrophysics and aerodynamics. Under investigation in this paper is a [Formula: see text]-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation in an incompressible fluid. Based on the known bilinear form, BLMP hybrid solutions comprising a lump wave, a periodic wave and two kink waves, and hybrid solutions comprising a breather wave and multi-kink waves are derived. We observe the interaction among a lump wave, a periodic wave and two kink waves. Fission of a kink wave is observed: A kink wave divides into a breather wave and three kink waves. On the contrary, we see the fusion among a breather wave and three kink waves: The breather wave and three kink waves merge into a kink wave. Finally, we observe the interaction among a breather wave and four kink waves.