How One Physicist Solved a 127-Year-Old Wave Riddle

David Grossman
Photo credit: George Rose - Getty Images

From Popular Mechanics

  • For 127 years, science has held that in water, waves spread out in a triangle. this is known as a Kelvinangle.
  • But a Norwegian physicist recently challenged the theory. He discovered when there's a current underneath the water, the angle changes.
  • There could be a practical application for the discovery. When fueling up ships, waves are taken into account over how much power sailing through them will consume.

Anyone who has ever been on the stern (rear) of a boat has seen a familiar sight: waves rippling out in what's called a wake. Science has long assumed that there's a uniformity to this rippling, which takes a v-shape. No matter the vessel's size, speed, or motor's power, the v-shape would always form at exactly 39 degrees. That's been accepted science for 127 years. But now, a Norwegian professor has proven accepted science wrong.

Simen Ådnøy Ellingsen, an associate professor at the Norwegian University of Science and Technology's Department of Energy and Process Engineering, challenged what is known as the Kelvinangle in boat wakes. Named after famed Irish physicist William Thomson, later known as Lord Kelvin, the Kelvinangle shows that in water, waves spread out in a triangle.

In challenging Lord Kelvin's work, Ellingsen realized he was going against history.

"It took the genius of people like [Augustin-Louis] Cauchy, [Siméon Denis] Poisson and Kelvin to solve these wave problems for the first time, even for the simplest case of still water without currents," Ellingsen says in a press statement. It's far easier for us to figure out the more general cases later, like we've done here."

Ellingsen's focus was on a concept in fluid mechanics known as shear flow. In a shear flow, fluid flow is caused by forces, as opposed to the forces themselves.

Ellingsen was examining ring waves, the type of concentric circles created when a rock is plopped into the middle a calm pond. But if a shear flow is involved, those concentric circles aren't so circular. In fact, they look more like ovals.

Photo credit: NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY

"After I did the first calculations, I was on a beach in the Netherlands watching the water flow back out after a wave. I made some rings in the water and took some photos," he says. "Looking at them later, the rings looked oblong to me, and I got pretty excited. That wasn't science, of course, but now it is!"

Later, Ellingson was able to conduct lab work to back up his observations, observing experiments in a specially developed research tank while working with a Ph.D. candidate and a master's student. There findings were concrete: Kelvin's theory holds when there are no currents below deep water's surface. But when there's shear flow, a current underneath, the angle changes.

There could be a practical application for Ellingson's wave work. When fueling up ships, waves are taken into account over how much power sailing through them will consume.

"Fuel consumption can double if the vessel is traveling downstream compared to upstream," Ellingsen says. Anything that can reduce fuel consumption, from controlling waves with greater efficiency to robots, is worth considering.

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