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J.C. Eilbeck
and D.B. Duncan/Heriot-Watt Univ.
Unstoppable
wave. Solitary waves can travel long distances without changing
shape. Their discovery in a canal in 1834 was re-enacted in
1995 (above, click for
larger image ). New experiments with mercury demonstrate that they
can also exist as "depression" waves.
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A research team has created the first laboratory
example of a depression solitary wave on a liquid surface. Solitary
waves maintain a constant shape as they travel with little dissipation,
but only "elevation" waves have been made in fluids in the past.
Depression waves were predicted over a century ago but require special
conditions to produce. The team used a new magnetic inductive sensor
technique to detect the waves on liquid mercury and reports the results
in the 11 November print issue of PRL .
Unlike the up-and-down, sinusoidal behavior of a
normal wave, a solitary wave--or soliton--travels through a material as
only an "up" or a "down" wave. It keeps its shape, even at large
amplitudes, because the speed of waves in the medium depends on
frequency in just the right way.
Éric Falcon and his colleagues at
École Normale Supérieure in Paris and Lyon originally set
up their inductance measurement technique as an improved way to study
fluid turbulence. The induction sensor detects motion of a nearby
conductor the same way an electric guitar pick-up senses vibrating
metal strings: The sensor generates an electromagnetic field and
detects the degree to which that field is disrupted.
While studying elevation solitons in mercury to
test the new system, Falcon came across an 1895 prediction of the
existence of depression solitons, but only in fluids of extremely
shallow depth. "It was a surprise to me," he recalls. "When I was a
student I followed lectures and read course books that stated that
solitary waves cannot be depression waves." So he took on the creation
of depression waves as a challenge.
One of the biggest experimental hurdles involved
spreading an ultrathin, even layer of mercury in the shallow plastic
test channel, Falcon says. The metal is so cohesive that it tends to
pull back from the sides of a container to form large drops. The
ultimate solution, devised by
team member Claude Laroche, was to dig grooves into the sides of the
channel bottom, running parallel to the desired wave direction, to
anchor the mercury in place.
The researchers vibrated a rectangular wave maker
in horizontal pulses across the surface of the mercury. Though the
depression solitons were eventually damped by viscosity, they
maintained the shape and velocity required by the standard soliton
equations as they traveled across the channel.
Surajit Sen, of the State University of New York
at Buffalo, calls the achievement "a commendable feat, given that
surface tension, density, gravity, and channel height must conspire to
make a sustainable depression possible." Chris Eilbeck, a mathematician
at Heriot-Watt University in Edinburgh, remarks that "It's nice to see
careful experiments, since much soliton research is purely
theoretical." He is glad to see "a new twist to the soliton story."
--Pam Frost Gorder
Pam Frost Gorder is a freelance
science writer in Columbus, OH.
Observation of Depression Solitary Surface Waves on
a Thin Fluid Layer
Éric Falcon, Claude Laroche, and Stéphan Fauve
Phys. Rev. Lett. 89,
204501
(print issue of 11 November 2002)
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