Walk on the Water
John Bush is associate professor of applied mathematics at the
Massachusetts Institute of Technology. In his research, he uses
experimental and theoretical techniques to elucidate fundamental
problems in fluid dynamics. I first saw some of John's still
photographs of water responding to various forces and since then
have paid close attention to his stunning images. I am always
delighted to be reminded that research can be presented with
both mathematical and visual beauty.
F. F. Can you tell us what brought you to
investigating the motion of water striders?
J. B. Much of my recent work in fluid mechanics has
been focused on flows dominated by the influence of surface tension.
I have long been looking for outstanding problems in the biological
sciences in which surface tension is important. When I learned of
Denny's paradox—the assertion that infant water striders
should be unable to move—I realized that the dynamics of
water-walking insects was just such a problem.
F. F. "Denny's paradox?"
J. B. It was generally believed that water striders
relied on waves to transfer momentum to the underlying fluid. A
standard result from hydrodynamic theory indicates that, in order to
generate waves, an object moving at the surface must exceed the
minimum wave speed (about 23 centimeters per second at an air-water
interface). Infant water striders' peak leg speeds may be less than
this critical value. It was thus thought that they would be unable
to generate waves, unable to transfer momentum to the underlying
fluid, and so unable to move. The fact that infant water striders
can move resulted in the conundrum known as Denny's paradox.
F. F. How did you capture this particular still image?
J. B. It was shot by my students (David Hu and
Brian Chan) with our standard digital Sony still camera. The
2-centimeter-deep fluid layer was contained within a shallow
plexiglass tank placed on a light table, which gave the fluid its
apparent luminescence. We were hoping for the strider to follow a
straight line, and so leave a linear trail of vortices. The pattern
of the thymol blue, the path taken by the strider, and the resulting
lines were simply fortuitous. Needless to say, many such photos were
taken, but this was our favorite.
F. F. What kind of information do you get from
measuring the shape and size of the vortices?
J. B. The form of the vortices, in addition to
their speed, indicates the magnitude of the momentum that they
transfer. In order for water striders to move, they must transfer
momentum to the underlying fluid; it was previously thought that
they did so through waves. The point of our study was to show that
vortices rather than waves are responsible for the dominant momentum
transfer in the wake of the strider.
F. F. Much of your other work captures phenomena
through photography. Would you say that you are engaged both
visually and mathematically as you first approach a question ... or
does the math come later?
J. B. All of my research has its origins in our
laboratory, and is focused on elucidating new physical
(specifically, fluid mechanical) phenomena. Photography is the
simplest means by which to clearly present the flow of interest to
the reader. The mathematical modeling is both motivated and
constrained by our experimental observations, and the two typically
evolve in tandem. However, in my work the mathematical modeling is
rarely if ever as elegant as the phenomenon of interest.