Space Grant Consortium - University of Wisconsin - Green Bay

Vortex ring reflection. Similarly, the right column of Fig. 5 depicts representative trajectories
for vortex rings launched at larger incidence angles: θi = 72 (row a) and 82 degrees
(row b). And the left column depicts the corresponding depth dependence of A/F . Notice
that at each incidence angle, the rapidly moving vortices (squares and circles) penetrate the
interface. But the slowly moving vortex (triangles) is reflected from the interface. Also, in
row (a), the reflected vortex exhibits one cycle of damped oscillations prior to disintegrating.
This is likely due to entrainment of the surrounding fluid, which leads to alternating upward
and downward forces on the ring.
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Figure 5: Right column: Trajectories for vortex rings when launched at incidence angles 72 (row a)
and 82 degrees (row b). Left column: The depth dependence of log(A/F ) for each vortex launch.
A summary of the dimensionless quantities calculated from the trajectory data represented
by various symbols in Figs. 4 and 5 is provided in Tab. 1. There, the listed values of the
dimensionless length scale, w/l, Froude number, F and interface strength, A/F , indicate
their values an instant before the vortex ring strikes the interface. The refraction angle is
only provided in cases where refraction is clearly discernible. As revealed in the final two
columns of Tab. 1, a simplistic application of the law of refraction cannot account for the
data. In particular, the ratio of the sines of the angles of incidence and refraction differs
significantly from the ratio of the average values of the velocities measured above, and below
the interface.
On the one hand, it may seem intuitively clear that a vortex ring would experience refraction
when striking an interface. After all, it is an extended structure, the different components of
which can travel at different velocities, similar to a wavefront. On the other hand, a theory
of vortex ring refraction would likely need to account for vortex ring tension, which offers
resistance to deformation of its structure. A generalized form of the law of refraction may
also need to explicitly incorporate the Froude and Atwood numbers, or a ratio of the two.
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