Coastal physics: The mechanics of ocean waves

From Katsushika Hokusai’s print “The Great Wave off Kanagawa” to Otis Redding’s song “(Sittin’ On) The Dock of the Bay,” watching the tide roll away has long been a mainstay for beachgoers, inspiring timeless works of art.

But beyond the sea’s artistic allure, the motion of the ocean “has supplied science an equally generous source of inspiration,” says Arnold Mathijssen, an assistant professor in the Department of Physics and Astronomy in the School of Arts & Sciences whose lab studies fluid dynamics and how creatures move through liquids.

“For example,” Mathijssen says, “when Isaac Newton published the Principia in 1687, he used the rise and fall of the ocean as evidence that a single force governed both falling objects on Earth and bodies in space. The tides, Newton showed, are the moon and the sun pulling on the water by gravity.”

“What’s great about the beach is that it is often viewed as a place for simple relaxation, but it’s also actually a massive, open-air laboratory of everyday physics,” he adds. “From planetary-scale energy to the microscopic mechanics of glowing cells, the shore reveals the hidden machinery of our world.”

Small, big, and planet-sized

There are four major kinds of waves at any beach, Mathijssen says, and they scale.

Wind waves come first, driven directly by air currents, ranging from ripples to storm chop. Above them sit swell waves, which can travel for thousands of miles. Swells are predictable, which is why buoys and phone apps can alert surfers that a good one is inbound. Swells arriving from different directions combine and produce a “rogue wave”—like the one in the famous Hokusai print—far taller than either is on its own.
 

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Third are tsunamis, each of which packs enormous energy into a single wave whose wavelength can run for miles, which is why it goes almost unnoticed in deep water.

And then there are the tides, which are “basically waves that are the size of our planet,” Mathijssen says. The moon does most of the pulling, and the sun adds to it, raising two crests that sweep around the globe as Earth rotates underneath. The wavelength is roughly the diameter of the planet.

Waves can’t be stopped, only talked down

“You can deflect them, you can divert them, you can reduce impact,” Mathijssen says. “But you can’t really break a wave.”

Breakwaters work by making waves break early, transferring energy into friction and eddies before a wave reaches shore, he explains. But those eddies can still cause damage. Similarly, the deflected energy from seawalls often results in erosion further down the coast.

“The best wave-breakers are the ones nature made: reefs and coastal vegetation,” he notes. “They are actually incredibly effective at breaking this energy, which makes coral bleaching a coastal engineering problem as much as an ecological one.”

The wave is not the water

The actual water isn’t traveling, because water particles are going in circles, Mathijssen says. What travels is energy. And those circles don’t quite close either—each orbit ends a small distance from where it started, so anything floating creeps shoreward at about 1% of the wave’s speed. This is called Stokes drift.

“It’s also why plastic pollution sorts itself by size,” Mathijssen adds. “A big gallon jug of milk will come towards the beach, and you can clean it up, because the Stokes drift effect increases with the size of the floating object. Break it down a bunch, and the drift weakens. Microplastics stay out at sea, dispersed and far harder to collect.”

The surf that glows

Swim after sunset at the Jersey shore in August or September and, with some luck, the water sparkles wherever it is disturbed.

The source is a dinoflagellate, often Noctiluca scintillans—“scintillans, as in scintillating,” Mathijssen says. “It’s a very nice name.”

Inside are luciferin and luciferase, the same compound and enzyme that light fireflies. The trigger is mechanical: stretch the cell membrane with a breaking wave, a passing fish, or a hand, and mechanosensitive ion channels pull open, calcium floods in, and a biochemical cascade fires off a flash.

“It’s really magical,” Mathijssen says.