Space Grant Consortium - University of Wisconsin - Green Bay

frames in the upper left corner, which lack transecting lines, were identified by hand so as
to seed the automated vortex ring tracking code. The horizontal dotted line indicates the
position of the fluid density interface. Notable in Fig. 3 is a slight change in the trajectory
and orientation of the vortex ring just after penetrating the fluid density interface. These
changes are accompanied by a slight change in its velocity and diameter.
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Figure 3: A montage depicting the position, and orientation, of a vortex ring launched from the
upper left corner of the image at an angle of 45 degrees with respect to a normal to the horizontal
density interface (dotted line).
Results and Discussion
Vortex ring refraction. In the right column of Fig. 4 are shown nine representative
trajectories of vortex rings when launched at incidence angles θi = 35 (row a), 45 (row b),
and 60 degrees (row c). In each row, three separate launches are shown, represented from
right to left by triangles, squares and circles. The precise value of θi for each launch is
determined by fitting a line to the data which lies above the interface (the horizontal axis).
It is then measured with respect to a normal to the fluid density interface.
In the left column of Fig. 4 is shown the depth dependence of A/F for each launch. A
logarithmic scale has been used on the abscissa to facilitate depiction of a wide range of
data. Notice that in each row, the rightmost vortex strikes the interface with the smallest
velocity, and hence the largest value of A/F . In such cases, once below the interface, the
vortex begins to curve upward. This suggests that for small Froude numbers, the buoyancy,
rather than inertia, determines its trajectory. Proceeding leftward in each row, the vortices
strike the interface with diminishing values of A/F . In particular, notice that the leftmost
trajectory (circles) exhibits a distinct downward deflection, as emphasized by a broken line
fit to the data beneath the interface. Such refraction occurs at relatively large values of the
Froude number, when A/F � 0.004.
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