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Panel (a): a large scale schematic diagram of an oscillating flux tube rooted in the solar photosphere. The black dashed lines show the magnetic field lines and the black arrows show the direction of oscillation. The shaded region represents dense material in the tube. The red line marks the position of the cross-section displayed in panel (b). Panel (b): image of the cross-section of the flux tube with flow patterns. The lines and arrows show: (i) a snapshot in time of the streamlines of the dipole flow formed around a kink-oscillating flux-tube (instability in this setting was investigated numerically by Terradas et al. 2008), note that the direction of the flow arrows will reverse periodically with the wave motion, and (ii) the shear-flow in a flux tube associated with surface Alfvén waves (instability in this setting was investigated numerically by Antolin et al. 2015). The blue boxes show the local region modelled in this paper as shown in panel (c). Panel (c): diagram of the local Cartesian model investigated in this paper with different densities and magnitudes of the velocity field in the regions above and below the density jump. Both regions have a velocity field that oscillates in phase at the same frequency and have the same magnetic field strength, both in the x-direction.

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The Kelvin–Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the osc...

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... flux tubes (an example of such a situation is shown in Panel (a) of Fig. 1). There are a number of possible flow profiles associated with oscillations of a flux tube, two are shown in the cross-sections shown in Panel (b) of Fig. 1. However, this is a complicated configuration which would be difficult to treat analytically. In this paper, we investigate a simpler problem that provides a good approximation to ...
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... flux tubes (an example of such a situation is shown in Panel (a) of Fig. 1). There are a number of possible flow profiles associated with oscillations of a flux tube, two are shown in the cross-sections shown in Panel (b) of Fig. 1. However, this is a complicated configuration which would be difficult to treat analytically. In this paper, we investigate a simpler problem that provides a good approximation to the relevant dynamics of this system. We perform a local Cartesian analysis looking at the apex of the flux tube, where the amplitude of the velocity shear ...
Context 3
... a simpler problem that provides a good approximation to the relevant dynamics of this system. We perform a local Cartesian analysis looking at the apex of the flux tube, where the amplitude of the velocity shear driven by the fundamental kink mode is largest, and the side of the flux tube with strong oscillatory shear flow with a setup shown in Fig. (1) panel (c). Thus in this model we have an oscillatory shear flow in the presence of a uniform horizontal magnetic field. Note that we neglect variations of the flow around and along the tube to allow us to make analytical progress. We also neglect the spatial and temporal variation of the magnetic field that would be associated with the ...

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