Nonlinear Damping of Standing Kink Waves Computed With Elsässer Variables

Doorsselaere, Tom Van; Goossens, Marcel; Magyar, Norbert; Рудерман, М. С.; Ismayilli, Rajab

doi:10.3847/1538-4357/abe630

Cited by 35 publications

(24 citation statements)

References 63 publications

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“…The attenuation is mainly due to the process of resonant absorption (see e.g., Ionson 1978;Ruderman & Roberts 2002). There is also a small contribution due to the non-linear generation of modes with high azimuthal wavenumber (Ruderman & Goossens 2014; Soler 2017), and the development of the KHI (Terradas et al 2018;Van Doorsselaere et al 2021). We found that the damping times also decrease as the longitudinal density ratio of the tube is increased.…”

Section: Summary and Future Workmentioning

confidence: 66%

“…The main reason for this attenuation is the linear process of resonant absorption, which causes a transfer of energy from the global kink oscillation to localised Alfvén modes in the transverse inhomogeneous layer (Ionson 1978;Ruderman & Roberts 2002;Arregui et al 2008;Soler et al 2010a). The non-linear excitation of fluting modes (see e.g., Ruderman & Goossens 2014;Soler 2017) and the triggering of the KHI (Terradas et al 2018;Van Doorsselaere et al 2021) also contribute to the damping of the oscillation.…”

Section: Example Simulationsmentioning

confidence: 99%

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Transverse kink oscillations of inhomogeneous prominence threads: numerical analysis and H$α$ forward modelling

Martínez-Gómez,

Soler,

Terradas

et al. 2021

Preprint

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Context. Prominence threads are very long and thin flux tubes which are partially filled with cold plasma. Observations have shown that transverse oscillations are frequent in these solar structures. The observations are usually interpreted as the fundamental kink mode, while the detection of the first harmonic remains elusive. Aims. The properties of oscillations in threads are greatly affected by the density distribution along the flux tube.Here, we aim to study how the density inhomogeneity in the longitudinal and radial directions modify the periods and damping times of kink oscillations, and how this effect would be reflected in the observations. Methods. We solve the ideal magnetohydrodynamics equations through two different methods: a) performing 3D numerical simulations, and b) solving a 2D generalised eigenvalue problem. We study the dependence of the periods, damping times and amplitudes of transverse kink oscillations on the ratio between the densities at the centre and at the ends of the tube, and also on the average density. We apply forward modelling on our 3D simulations to compute synthetic Hα profiles.Results. We confirm that the ratio of the period of the fundamental oscillation mode to the period of the first harmonic increases as the ratio of the central density to the footpoint density is increased or as the averaged density of the tube is decreased. We find that the damping times due to resonant absorption decrease as the central to footpoint density ratio increases. Contrary to the case of longitudinally homogeneous tubes, we find that the damping time to period ratio also increases as the density ratio is increased or the average density is reduced. We present snapshots and time-distance diagrams of the emission in the Hα line. Conclusions. The results presented here have implications for the field of prominence seismology. While the Hα emission can be used to detect the fundamental mode, the first harmonic is barely detectable in Hα. This may explain the lack of detections of the first harmonic. A combination of different spectral lines is required to get information about the period ratio and to use it to infer physical properties of the threads.

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Section: Summary and Future Workmentioning

confidence: 66%

Section: Example Simulationsmentioning

confidence: 99%

Transverse kink oscillations of inhomogeneous prominence threads: numerical analysis and H$α$ forward modelling

Martínez-Gómez,

Soler,

Terradas

et al. 2021

Preprint

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“…These studies have emphasised the importance of the perpendicular structuring on the energy cascade and, thus, the wave heating rate. This analytic approach has also been extended to compute the damping rates for standing modes accounting for the non-linear evolution of the KHI [158]. In this study, the authors showed that the wave damping time is inversely proportional to the amplitude of the kink mode.…”

Section: Propagating Wavesmentioning

confidence: 97%

How Transverse Waves Drive Turbulence in the Solar Corona

Howson

2022

Symmetry

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Oscillatory power is pervasive throughout the solar corona, and magnetohydrodynamic (MHD) waves may carry a significant energy flux throughout the Sun’s atmosphere. As a result, over much of the past century, these waves have attracted great interest in the context of the coronal heating problem. They are a potential source of the energy required to maintain the high-temperature plasma and may accelerate the fast solar wind. Despite many observations of coronal waves, large uncertainties inhibit reliable estimates of their exact energy flux, and as such, it remains unclear whether they can contribute significantly to the coronal energy budget. A related issue concerns whether the wave energy can be dissipated over sufficiently short time scales to balance the atmospheric losses. For typical coronal parameters, energy dissipation rates are very low and, thus, any heating model must efficiently generate very small-length scales. As such, MHD turbulence is a promising plasma phenomenon for dissipating large quantities of energy quickly and over a large volume. In recent years, with advances in computational and observational power, much research has highlighted how MHD waves can drive complex turbulent behaviour in the solar corona. In this review, we present recent results that illuminate the energetics of these oscillatory processes and discuss how transverse waves may cause instability and turbulence in the Sun’s atmosphere.

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“…Furthermore, transverse standing waves have been extensively studied numerically, where it was revealed that standing transverse oscillations are the decisive point of developing Kelvin-Helmholtz instability (KHI) non-linearly (Terradas et al, 2008;Antolin et al, 2016). Lately, Van Doorsselaere et al (2021) developed a nonlinear damping model for standing kink waves and showed that the damping time is inversely proportional to the oscillation amplitude, where they also found a notable match with the observation (Nechaeva et al, 2019). Compared to standing transverse oscillations, propagating kink waves have received little attention (Thurgood et al, 2014;Morton et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Damping of Surface Alfvén Waves Due to Uniturbulence

Ismayilli

Doorsselaere

Goossens

et al. 2022

Front. Astron. Space Sci.

Self Cite

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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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Nonlinear Damping of Standing Kink Waves Computed With Elsässer Variables

Cited by 35 publications

References 63 publications

Transverse kink oscillations of inhomogeneous prominence threads: numerical analysis and H$α$ forward modelling

Transverse kink oscillations of inhomogeneous prominence threads: numerical analysis and H$α$ forward modelling

How Transverse Waves Drive Turbulence in the Solar Corona

Non-Linear Damping of Surface Alfvén Waves Due to Uniturbulence

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