All Figures

$\begin{figure} \par\includegraphics[width=14.5cm,height=18cm,clip]{4499f01.eps} \end{figure}$ Figure 1: The structure of the wake below the rising flux tube depends on the Reynolds number of the flow. The four panels show the distribution of the longitudinal magnetic field at Reynolds numbers ranging from 25 to 2600.
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In the text

$\begin{figure} \par\includegraphics[width=14.5cm,height=18cm,clip]{4499f02.eps} \end{figure}$ Figure 2: Same as Fig. 1 but for the zcomponent of the vorticity. At low Reynolds numbers - see cases with $\rm Re=25$ and $\rm Re=140$ - the wake consists of two vortex rolls with vorticity of opposite sign. At sufficiently high Reynolds numbers - see cases with $\rm Re=630$ and $\rm Re=2600$ - the vortex rolls break up and the shedding of vorticity into the wake occurs in a more intermittent fashion.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{4499f03.ps} \end{figure}$ Figure 3: Magnetic flux retained in the main tube as a function of the effective Reynolds number. The diamonds plot the values from simulations A1 to A4. If the amount of flux lost scaled as $O({\rm Re}^{-1/2})$ , it would follow the solid curve.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4499f04.ps}\end{figure}$ Figure 4: The change of $M/\Phi$ (ratio of enclosed mass and enclosed magnetic flux in the main tube) as a function of the Reynolds number.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{4499f05.ps}\end{figure}$ Figure 5: The dependence of the fraction of flux retained in the main tube as a function of the twist parameter $\lambda$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{4499f06.ps} \end{figure}$ Figure 6: The relationship between the tube's effective radius and its twist $\lambda$ . The solid line shows the linear relation given by Eq. (21). Diamonds denote the evolution of the mean twist $\langle \lambda \rangle$ of the main tube in run A4. This good match indicates that the main tube expands homologously over most of the tube rise.
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{4499f07.ps} \end{figure}$ Figure 7: Comparison between the simulation (run A4) and the thin flux tube model. Diamonds indicate values of the physical quantities at the tube centre in the simulation and the solid lines show the predictions from the thin tube model (Eqs. (29)-(33)).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4499f08.ps}\end{figure}$ Figure 8: Rise velocity ( upper panel) of the main tube and its height ( lower panel), both as functions of time. Diamonds indicate values from the MHD simulation (run A4). The solid line shows the velocity profile calculated with the thin flux tube model, with C_D=2.0 and I=2.0.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{4499f09.ps}\end{figure}$ Figure 9: The trajectory of the main tube in run B. The circles indicate the position of the main tube at different times during the simulation. The effective radius of the main tube at different instances is given by the size of the circles in the plot. The dashed line shows the trajectory from a thin flux tube calculation, taking into account the aerodynamic lift force.
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In the text

$\begin{figure} \par\subfigure{\includegraphics[width=8cm,clip]{4499f10.ps} }\end{figure}$ Figure 10: The distribution of the vorticity at t=280 for run B. In this simulation, the flux tube had an initial net vorticity. Aerodynamic lift causes the flux tube to rise in a zigzag fashion, leaving behind a vortex street in its wake.
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In the text

$\begin{figure} \par\subfigure{\includegraphics[width=7.1cm,clip]{4499f11a.eps} } \subfigure{\includegraphics[width=7.1cm,clip]{4499f11b.eps} } \end{figure}$ Figure 11: Evolution of a large flux tube (Run C). Shown in color is the longitudinal field. Each of the five circular green contours represent a magnetic field line projected onto the plane. Every contour encloses a certain amount of flux, which defines a flux roll. Table 2 gives the flux and initial radius of each flux roll.
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In the text

$\begin{figure} \par\subfigure{\includegraphics[width=6cm,clip]{4499f12a.ps} } \p... ...ce*{2mm} \subfigure{\includegraphics[width=6cm,clip]{4499f12d.ps} } \end{figure}$ Figure 12: Comparison between thin flux tube calculations with average quantities inside the flux rolls (Run C). The different symbols correspond to quantities in the different flux rolls (see Table 2). As the effective radius of the flux tube approaches the local pressure scale height H_p, the discrepancy between the simulation results and the thin flux tube predictions grows.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{4499f13.ps}\end{figure}$ Figure 13: Variation of the average twist of the flux rolls as a function of their effective radii. The different symbols show the average twist of the five flux rolls (Run C). The solid line shows the relation given by Eq. (21). The good match between the simulation results and relation (21) indicates that the flux rolls expand homologously.
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In the text

$\begin{figure} \par\includegraphics[width=14.5cm,height=18cm,clip]{4499f01.eps} \end{figure}$	Figure 1: The structure of the wake below the rising flux tube depends on the Reynolds number of the flow. The four panels show the distribution of the longitudinal magnetic field at Reynolds numbers ranging from 25 to 2600.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{4499f03.ps} \end{figure}$	Figure 3: Magnetic flux retained in the main tube as a function of the effective Reynolds number. The diamonds plot the values from simulations A1 to A4. If the amount of flux lost scaled as $O({\rm Re}^{-1/2})$ , it would follow the solid curve.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{4499f04.ps}\end{figure}$	Figure 4: The change of $M/\Phi$ (ratio of enclosed mass and enclosed magnetic flux in the main tube) as a function of the Reynolds number.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{4499f05.ps}\end{figure}$	Figure 5: The dependence of the fraction of flux retained in the main tube as a function of the twist parameter $\lambda$ .
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$\begin{figure} \par\includegraphics[width=7cm,clip]{4499f06.ps} \end{figure}$	Figure 6: The relationship between the tube's effective radius and its twist $\lambda$ . The solid line shows the linear relation given by Eq. (21). Diamonds denote the evolution of the mean twist $\langle \lambda \rangle$ of the main tube in run A4. This good match indicates that the main tube expands homologously over most of the tube rise.
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$\begin{figure} \par\includegraphics[width=6.5cm,clip]{4499f07.ps} \end{figure}$	Figure 7: Comparison between the simulation (run A4) and the thin flux tube model. Diamonds indicate values of the physical quantities at the tube centre in the simulation and the solid lines show the predictions from the thin tube model (Eqs. (29)-(33)).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{4499f08.ps}\end{figure}$	Figure 8: Rise velocity ( upper panel) of the main tube and its height ( lower panel), both as functions of time. Diamonds indicate values from the MHD simulation (run A4). The solid line shows the velocity profile calculated with the thin flux tube model, with C_D=2.0 and I=2.0.
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$\begin{figure} \par\includegraphics[width=7cm,clip]{4499f09.ps}\end{figure}$	Figure 9: The trajectory of the main tube in run B. The circles indicate the position of the main tube at different times during the simulation. The effective radius of the main tube at different instances is given by the size of the circles in the plot. The dashed line shows the trajectory from a thin flux tube calculation, taking into account the aerodynamic lift force.
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$\begin{figure} \par\subfigure{\includegraphics[width=8cm,clip]{4499f10.ps} }\end{figure}$	Figure 10: The distribution of the vorticity at t=280 for run B. In this simulation, the flux tube had an initial net vorticity. Aerodynamic lift causes the flux tube to rise in a zigzag fashion, leaving behind a vortex street in its wake.
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$\begin{figure} \par\subfigure{\includegraphics[width=7.1cm,clip]{4499f11a.eps} } \subfigure{\includegraphics[width=7.1cm,clip]{4499f11b.eps} } \end{figure}$	Figure 11: Evolution of a large flux tube (Run C). Shown in color is the longitudinal field. Each of the five circular green contours represent a magnetic field line projected onto the plane. Every contour encloses a certain amount of flux, which defines a flux roll. Table 2 gives the flux and initial radius of each flux roll.
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$\begin{figure} \par\subfigure{\includegraphics[width=6cm,clip]{4499f12a.ps} } \p... ...ce*{2mm} \subfigure{\includegraphics[width=6cm,clip]{4499f12d.ps} } \end{figure}$	Figure 12: Comparison between thin flux tube calculations with average quantities inside the flux rolls (Run C). The different symbols correspond to quantities in the different flux rolls (see Table 2). As the effective radius of the flux tube approaches the local pressure scale height H_p, the discrepancy between the simulation results and the thin flux tube predictions grows.
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$\begin{figure} \par\includegraphics[width=7cm,clip]{4499f13.ps}\end{figure}$	Figure 13: Variation of the average twist of the flux rolls as a function of their effective radii. The different symbols show the average twist of the five flux rolls (Run C). The solid line shows the relation given by Eq. (21). The good match between the simulation results and relation (21) indicates that the flux rolls expand homologously.
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