A few surf spots on Earth are so legendary that surfers dream their whole  lives of catching a wave there.

Like, there’s Peʻahi in Maui, Hawaiʻi, which has one of the fastest and  largest waves in the Pacific Ocean. It’s so extreme that its nickname  is Jaws, after the movie.

Then there’s Praia do Norte in Nazaré, Portugal. It has the largest waves ever surfed. These monsters can get 30 meters high and don’t even look real in  some of the photos of them.

All of these waves are made by physics, of course. And scientists are trying to decode  the secrets of exactly how they form. Because many of the best surf spots are currently threatened by environmental changes.

And understanding that formula could  help scientists preserve them … or even allow for us to design  some sick waves from scratch. [♪ INTRO] When you think of a surfable wave,  you might picture something like this. The top, or crest, of the wave curls  over to create what’s called the barrel. And when the wave crashes in on itself,  you get that foamy whitewater spray.

Surfers generally surf on the shoulder  of the wave in front of the barrel or, if they’re skilled enough, in it! That’s called getting tubed. And while it’s easy to define a wave’s anatomy, it’s trickier to say what  makes a surfing wave good.

For one, it depends on the surfer’s skill level. And every surfer’s gonna  have their own preferences. So rather than using language  to define a perfect wave, scientists use a different tool: math.

To be clear, they’re not trying to define  the singular, platonic ideal of a wave. Rather, they want to use math to define a  range of waves that surfers deem “good”. One approach distills waves into  four fundamental parameters: the height, defined by measuring the  wave from its crest to its trough; the length, that’s the horizontal  distance of a single breaking wave; the peel angle, which is the angle  between the crest and the whitewater; and the breaking intensity, ranked in one paper on a scale from medium to extreme.

Love that the wimpy waves don’t  even get to be in the study. We don’t care. From here, you can determine  a wave’s “surf-worthiness” by considering what kinds of surf maneuvers are possible for waves created  with different parameter ranges.

And within a “surf-worthy”  range of wave parameters, scientists can get to work reverse-engineering the physics factors that lead to those good waves. This is complicated by the fact that  waves are kinda like snowflakes: no two break exactly alike. But waves in the same location  with similar formation conditions tend to look a lot alike, so  scientists can still trace backwards to discover the factors that  made them in the first place.

To find these baby waves, we must  venture far out to the open ocean in super deep water, thousands  of kilometers away from shore. Now, far from shore, in the deep open ocean, water picks up the energy  that eventually forms waves. Most waves start when wind blows across the water, creating small pockets of underwater  circulation that slowly march forward.

This is called trochoidal  motion, and it’s also what makes buoys or ducks bob on the water. Stronger winds, say from a storm, can transfer more energy to the water and create bigger waves. This is why, when there’s a  hurricane that’s like just far enough off the coast, surfers  will decide to go to the beach.

Once the waves accrue enough  energy, they graduate to swells. Swells have a wavelength of about 300 meters. That’s like three soccer  fields, or like… 100 longboards.

These swells, with their long wavelengths, can actually outrun choppy  waves with shorter wavelengths, helping them survive the long  trek to the nearest coast. The fun stuff happens when the  swells finally get to the coast and hit water that’s about half  as deep as the swell’s wavelength. So like… 1.5 soccer fields  or, like, 50 longboards deep.

This is probably not helpful. When the water gets shallow,  the bottom of the wave drags along the seafloor and slows down. But the top of the wave keeps all  its momentum and continues forward, which causes it to trip over itself,  eventually forming crests that break.

If we’re lucky, the wave will break  in just the right way to be surfable. But that depends on the shape of  the seafloor, called bathymetry. To be surfable, a wave  needs a non-zero peel angle.

Otherwise it’s called a “closeout”,  where it breaks all at once. To avoid closeouts, the beach needs to be uneven, so that one side of the wave breaks  first, creating a peel angle. This is why so many famous surf  beaches are also coral reefs.

Basically if you want an interesting  wave, you need an interesting beach! Scientists looked at the bathymetry of  34 locations known to have good surfing waves, and they identified the seafloor  configurations that created them. Then, using computer simulations,  the scientists studied how these configurations affected  wave direction, speed, and shape.

For example, they found that dips in the seafloor can make waves faster or more intense. And the angle of the seafloor  slope relative to the coast can affect whether or not waves travel  in the optimal direction for surfing. So thanks to that data, scientists have  basically solved the mystery of how bathymetry leads to good waves.

But it’s still only one part of the equation. To get a great wave, everything  else needs to be just right, too. That includes wind speed and direction, swell period and height, and tide conditions.

So over time, experienced  surfers develop intuition for the weather and water conditions  that forecast the waves they like. But those conditions are rapidly changing, as more surf breaks are threatened  by rising seas, coastal erosion, and coastline development, all of which affect the bathymetry and coastline shape. A 2017 study found that California, for example, could lose 34% of its surf  breaks by the end of the century.

Unfortunately, the same  strategies that protect coastlines can inadvertently ruin great surf breaks. Like replenishing an eroding  coastline with extra sediment can change the bathymetry enough that  waves break in totally unsurfable ways. That’s why these mathematical models  of surf breaks are so important.

Scientists can help design interventions that preserve both coastlines and surf breaks. One way is to arrange special sand bags, rock, or concrete into underwater structures that  direct sand to settle in certain patterns. These structures can reduce  erosion to protect the coast and shape the bathymetry so that waves  break in surf-worthy fashion.

Narrowneck Reef in Australia tried this  strategy in 1999 and got it to work. Scientists could even someday use  these surf break models to turn unsurfable beaches into  top-tier surfing destinations. For example, Middleton Beach in Albany, Australia used to only generate  closeout waves on its shores.

Until July 2025, when the beach  debuted an artificial reef. They leveraged beach measurements  and computer simulations to modify the seafloor so that it funnels waves in just the right way for them to  break at just the right speed. These discoveries are certainly  making waves in the physics community.

And while surfers will continue to debate  the definition of a “perfect” wave, at least now they can format their  arguments in mathematical terms. [♪ OUTRO]