formed by the magnetic Rayleigh-Taylor instability in the Kippenhahn-Schlüter model. Panel (b) shows the time-distance diagram taken along the dashed line in panel (a). This allows the Mach number of the rise velocity of the plume to be calculated as $M=0.28$.[]{data-label="plumerise"}](figure4.eps){height="8cm"}

Panel (b) of Figure \[plumerise\] shows the time-distance plot taken along the slit in Panel (a). The constant rise velocity of the plumes, resulting from the force balance created at the head of the plume, is clearly shown [@HILL2012]. The rise velocity of the topmost plume was found to have a Mach number of $M=0.28$. We use the free-stream Mach number because if we transform the plume head to 0-velocity rest frame then the rise velocity transforms to a free-stream velocity of the dense material.

It can be instantly noticed in Figure \[plumerise\] that the plume is not perfectly circular. The first step of the transform is to change the coordinate size so that the size of the elliptical bubble is that of a unit ellipse (i.e. the area of the ellipse is $\pi$). This is achieved by dividing the $y$ and $z$ axis by $\sqrt{ab}$, where $a$ is the minor axis of the ellipse and $b$ is the 