Space Grant Consortium - University of Wisconsin - Green Bay

Reflection and Refraction of Vortex Rings ∗
Kerry Kuehn, Matthew Moeller, Michael Schulz and Daniel Sanfelippo
Department of Physical Sciences
Wisconsin Lutheran College, Milwaukee, WI
Abstract
We have experimentally studied the impact of a planar axisymmetric vortex ring,
incident at an oblique angle, upon a sharp gravity-induced interface separating two
fluids of differing densities. After impact, the vortex ring was found to exhibit a variety
of subsequent trajectories, which we have organized according to both the incidence
angle, and the ratio of the Atwood and Froude numbers, A/F . For relatively small
angles of incidence, the vortices tended to penetrate the interface. In such cases, the
more slowly moving vortices, having values of A/F � 0.004, tended to subsequently
curve back up toward the interface. Quickly moving vortices, on the other hand, tended
to refract downward, similar to a light ray entering a medium having a higher refractive
index. A simplistic application of Snell’s law of refraction cannot, however, account
for the observed trajectories. For grazing angles of incidence, fast moving vortices
tended to penetrate the interface, whereas slower vortices tended to reflect from the
interface. In some cases, the reflected vortices executed damped oscillations before
finally disintegrating.
Introduction
One of the early successes of the wave theory of light was its ability to explain the law of
refraction by appealing to the variation of the speed of light when crossing a boundary separating
media of different densities [Huygens, 1952]. Early models of light which emphasized
its corpuscular nature proved less convincing in explaining refraction, largely because these
models required that light travel more rapidly when entering a denser media, such as water
or glass, an ostensibly counterintuitive postulate which was later rejected on experimental
grounds [Smith, 1987].
With the advent of Hamilton-Jacobi theory [Wolf and Born, 1965], and later wave mechanics
[Schrödinger, 1964], the refraction of light was eventually reconciled with a corpuscular
nature, albeit only in a statistical sense. Quantum theory, of course, makes no predictions
as to the trajectory of an individual photon. Nonetheless, recent experiments in high energy
physics and quantum optics have revived a significant amount of speculation as to the
nature, and even the structure, of the photon [Nisius, 2000, Tiwari, 2002].
tium.
∗ This work was supported by a Research Infrastructure Grant from the Wisconsin Space Grant Consor-
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