Online Material

Appendix C: Animations

We provide three animated GIF files showing the simulated evolution of perturbed flux tubes, available on-line.

The animation frict_inst.gif shows the final phases of the development of the friction-induced instability in the overshoot region, between t=700 d and t=1100 d (Sect. 2.2). A snapshot from the animation is shown in Fig. C.1. The asterisk signs represent selected mass elements, which all move rightwards in the initial phases, owing to the internal equilibrium flow. We assume that  G, , and the initial radial perturbation amplitude is  km. The initial location is the middle of the overshoot region.

	Figure C.1: The shape of a flux tube with  G, and  km at t=1030 d, in the plane. The horizontal lines mark the boundaries of the overshoot region.
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The animation files TF60.gif and TF180.gif show the evolution of a flux tube subject to a radial downflow with a duration of 60 and 120 days, respectively, until t=300 days (Sect. 3.2.2). Two snapshots are shown in Figs. C.2 and C.3, corresponding to the time when the downflow ceases in each case, i.e., at t=60 d and t=180 d. Note that for the longer-duration flow, the flux tube is radially more disturbed when the action of the downflow is finished.

	Figure C.2: The shape of a flux tube with  G, , at t=60 d, when the transient downflow (  m s-1) ceases. The horizontal lines mark the boundaries of the overshoot region and the vertical line denote the azimuthal location of the centre of the downflow.
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	Figure C.3: Same as Fig. C.2, at t=180 d, when the transient downflow ceases.
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frict_inst.gif

TF180.gif

TF60.gif