Focus: Waves of Depression

Published October 29, 2002  |  Phys. Rev. Focus 10, 20 (2002)  |  DOI: 10.1103/PhysRevFocus.10.20

Observation of Depression Solitary Surface Waves on a Thin Fluid Layer

Éric Falcon, Claude Laroche, and Stéphan Fauve

Published October 23, 2002
Figure 1
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.

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

Subject Areas

New in Physics