A 127-year-old enigma solved

He solved on paper a 127-year-old physics problem and proved that eccentric wakes could exist. Five years later, practical experiences proved him right.

"Seeing images appear on the computer screen has been the best workday of my life," said Simen Ådnøy Ellingsen, associate professor in the Energy and Process Department of NTNU.

It was the day the Ph.D. Candidate Benjamin Keeler Smeltzer and the Master's student Eirik Æsøy had shown at the lab that Ellingsen was right and sent him the photos of the experiment. Five years ago, Ellingsen challenged the accepted knowledge as early as 1887, armed with a pen and paper, and won it.

He solved a problem regarding the so-called Kelvinangle in the wake of boats, which has been unchallenged for 127 years. The wake of the boat is the v-shaped pattern that a boat or canoe makes when moving in the water. You certainly saw one at some point.

39 degrees

It has long been assumed that the V-wake angle behind a boat should always be just below 39 degrees, provided the water is not too deep. Be it behind a supertanker or a duck, this should always be true. Or not. Because, as so many accepted facts, it turns out to be wrong, or at least not always. Ellingsen showed it.

"For me, it was a totally new field and no one told me it was difficult," Ellingsen explained during his first discovery.

The wakes of the boat may actually have a completely different angle in certain circumstances, and may even be off-center with respect to the direction of the boat. This can occur when there are different currents in different layers of water, called shear flows. For shear flow, Kelvin's boat wake theory does not apply

"It took the genius of people like Cauchy, Poisson and Kelvin to solve these wave problems for the first time, even in the simplest case of calm water without currents." It's much easier for us to understand later more general cases, as we've finished here, "says Ellingsen.

Oblong rings

Ringing waves also act funny under certain circumstances. If you throw a pebble into a lake on a peaceful summer day, the waves pattern will be perfect, concentric circles. But not if there is a shear flow. Then the rings could become oval. Ellingsen also predicted it, developing the theory of Cauchy and Poisson from 1815.

"After making the first calculations, I was on a beach in the Netherlands and I watched the water come back after a wave.I did some rings in the water and took some water. Looking at them later, they seemed oblong, and I'm pretty excited, it was not science, of course, but now it's there! "Ellingsen said.

Laboratory research saves calculations

That's how Ellingsen ended up on the cover of the Journal of Fluid Mechanics. But all his calculations had been made on paper and had not yet been observed empirically.

Now, however, laboratory research is supporting his work, thanks to the doctorate. Candidate and Master's student able to conduct experiments in a research tank specially developed under the supervision of Ellingsen.

Eirik Æsøy has a technician training, which has saved time and money in the construction of the laboratory. It took about six months for everything to be operational.

"Æsøy and I set up all the equipment to create the currents we needed," says Smeltzer. Their results were also published in the Journal of Fluid Mechanics.

"It is quite remarkable that the experiments of our small wave pool are being published there," Smeltzer said.

Practical applications

The results of their research on the Kelvin angle could have real practical consequences, such as the potential reduction in fuel consumption of ships. Much of the fuel from ships is used to make waves.

"Fuel consumption can double if the boat moves downstream compared to the upstream," Ellingsen said.

These calculations are based on currents located at the mouth of the Columbia River in Oregon in the United States. Currents are strong and boats are numerous.

Research on boats and ships in different currents is therefore important for anyone interested in reducing fuel consumption and, consequently, emissions.

Wake of the boat in front of the boat

Ellingsen insists that their results do not contradict Kelvin's theory, but extend it. The Kelvin angle remains valid as long as there are no layers of current beneath the surface when the water is deep.

But as soon as there is a movement between the layers of water, so that different layers move at different speeds, the angle changes. Sometimes by a lot. In theory, with extremely strong currents moving perpendicular to the direction of the boat, the wake can end in front of the boat on one side.

"In that case, you should probably go sailing somewhere else," says Ellingsen.