Rogue waves captured

Freak waves that swallow ships whole have been re-created in a tank of water. Though these tiny terrors are only centimeters high, a devilishly difficult mathematical equation describing their shape may help to explain the origins of massive rogue waves at sea..

Sailors have long swapped stories about walls of water leaping up in the open ocean — even in calm water — without warning or obvious cause. But for centuries, rogue waves were little more than talk; no one had ever measured one with scientific instruments.

Then on New Year’s Eve of 1995, a laser on an oil rig off Norway’s coast recorded one of these rare events: a wave 26 meters from bottom to top, flanked by deep troughs on either side.

This wave and others measured since look like breather waves, says Amin Chabchoub, a mathematician at the Hamburg University of Technology in Germany. A breather wave is an anomaly in a series of waves that sucks in the energy of its neighbors and puffs itself up to a great height.

The nonlinear interactions that allow for this energy theft were described by mathematician Howell Peregrine in 1983. His solutions of nonlinear Schrödinger equations showed that pulselike waves called Peregrine solitons can pop out of sine waves under certain conditions.  

“For a long time, nobody really thought this mathematics would be applicable to the ocean,” says Al Osborne, a physicist at the University of Turin in Italy. “Not only is it applicable, but we’re now undergoing a paradigm shift in understanding ocean waves.”

To make a Peregrine soliton, Chabchoub wobbled a paddle back and forth at the end of a long water tank. Regularly spaced waves about a centimeter high emerged and rolled across the surface. Then he gave the paddle a precise jerk – introducing an anomaly.

“It’s possible that the wind could generate a similar modulation or perturbation in the open sea,” says Chabchoub, who describes the experiment in a paper in the May 20 Physical Review Letters.

In the 15-meter tub, this spot grew to a height of about 3 centimeters before dying down — hardly enough to make a rubber ducky quack in fear. Flanked by two deep troughs, the rising peak moved half as fast as the background waves. It satisfied both Peregrine’s mathematics and a common statistical view that a rogue wave is something at least two to three times the size of the tallest one-third of the other waves averaged.

In theory, the toy waves in the water tank should scale up to oceanic proportions. But oceans are much messier than water tanks. Normal ocean waves come in a variety of sizes and speeds, and other nonlinear effects may play a role in creating rogue waves.

“You add an almost imperceptible amount of noise, and all sorts of wacky and unexpected things can happen,” says Daniel Solli, a physicist at UCLA who created the first Peregrine soliton in light waves.

Chabchoub and his colleagues are exploring ways to introduce a little more mess into their tank to see what other wacky conditions can give rise to freak waves.