Surf

Intro

When you paddle into a wave, you are riding energy that may have left a storm days earlier and crossed half an ocean. Understanding how that happens makes you better at reading forecasts, choosing spots and knowing when to go.

This article explains the physics in plain language, with a few simple formulas for those who want them. The figures come from oceanography sources, mainly Wikipedia's well-referenced article on wind waves, lecture notes from the Scripps Institution of Oceanography (UC San Diego), SMHI and Portugal's Instituto Hidrográfico, all linked at the bottom.

1. Wind makes waves

Almost all surfable waves are wind waves. When wind blows over water, friction and pressure differences push the surface into small ripples. The ripples give the wind something to push against, so they grow, and the bigger they get, the more energy they can take from the wind.

For wind to keep feeding a wave, the wind has to move faster than the wave. How large the waves become depends on:

• Wind speed: how hard it blows.
• Duration: how long it blows.
• Fetch: the distance of open water the wind blows over.
• Fetch width and water depth also play a part.

If the wind blows long enough over a long enough fetch, the sea reaches a fully developed state, where waves are as big as that wind can make them. Wikipedia's article on wind waves gives these examples:

The lesson for surfers: big swell needs strong wind over a huge area for a long time. That is why the best swells come from large storms far out at sea, not from a windy day at the beach.

2. From messy sea to clean swell

Inside the storm, the sea is chaotic: waves of many sizes and directions on top of each other. Surfers call the local version of this wind swell or windswell. It is short-period, bumpy and weak.

Once waves leave the storm area, they become swell. Short waves lose energy quickly, but longer waves can travel thousands of kilometres, because water's viscosity is very low, as SMHI explains. Over that journey the swell sorts itself out, for a simple reason:

In deep water, longer waves travel faster.

So the longest, most powerful waves race ahead and arrive at the coast first, followed by shorter ones. This sorting is called dispersion. It turns a messy storm sea into the clean, evenly spaced lines of groundswell that surfers dream about. It is also why forecasters can predict when a swell will arrive: the first sign is usually a rise in the period, before the size builds.

3. Period: the number to watch

Wave period is the time, in seconds, between two wave crests passing a fixed point. On a forecast it is often more important than height.

• Short period (under about 8 s): usually local windswell. Weak, crumbly waves, close together.
• Medium period (about 9–12 s): decent swell.
• Long period (13 s and up): powerful groundswell from distant storms. Waves are far apart, travel fast, and feel the bottom earlier, so they grow more when they reach the coast.

These bands are a common rule of thumb rather than precise physical limits, but the principle is solid: a longer period means a longer wavelength, more speed and more energy reaching the coast. A 1.5 m swell at 16 seconds is a very different thing from a 1.5 m swell at 7 seconds.

According to Wikipedia, wind waves in deep water can reach periods of up to about 20 seconds. The Scripps lecture notes give an example: a 17-second swell needs a wind of about 27 m/s (around 100 km/h) to form.

4. How fast does swell travel?

Ocean waves behave differently depending on how deep the water is compared with their wavelength (the distance between crests):

• Deep water: depth greater than half the wavelength. The wave does not feel the bottom.
• Shallow water: depth less than 1/20 of the wavelength. The bottom controls the wave.
• Transitional water: in between.

In deep water

Speed depends only on the period (T, in seconds):

Wave speed ≈ 1.56 × T metres per second

Wavelength ≈ 1.56 × T² metres

These come from the standard formulas c = gT/2π and L = gT²/2π, where g is gravity. A few examples:

There is a twist. The energy of a swell, which is what actually arrives at your beach, travels at the group velocity, which in deep water is half the speed of the individual crests. So a 16-second swell carries its energy at roughly 45 km/h, or about 1,000 km per day. That is why a storm several thousand kilometres away may take a few days to deliver its swell.

In shallow water

Near the coast the speed depends only on depth (d, in metres):

Wave speed ≈ √(g × d) ≈ 3.1 × √d metres per second

In 4 m of water a wave moves at roughly 6 m/s. In 1 m, about 3 m/s. The period stays the same, so as the wave slows down its wavelength shrinks.

5. Refraction: why waves bend

Because waves slow down in shallower water, any part of a wave crest over shallow water slows while the part over deeper water keeps going. The crest bends, just as light bends when it passes from air into water. This is refraction.

Refraction explains a lot of what surfers see:

• Waves tend to swing around to face the beach, even when the swell arrives at an angle.
• Reefs and points that stick out focus wave energy onto them, so they get bigger waves than the bays beside them.
• Deep channels next to a reef spread energy out, so the water there is calmer. That is often where you paddle out.
• Submarine canyons can focus energy dramatically. At Nazaré in Portugal, the Instituto Hidrográfico explains that waves travel faster over the deep canyon than over the shelf beside it, so the crests bend and converge at Praia do Norte. Their simulations suggested a 10 m wave could grow to about 20 m there.

Long-period swells feel the bottom earlier (their wavelength is longer, so the "deep water" limit is deeper), which means they refract more. That is why some spots only work on a long-period groundswell.

6. Shoaling: why waves grow

As a wave enters shallower water and slows down, the energy it carries gets squeezed into a shorter, slower wave. The result is that the wave grows taller. This is called shoaling. Together with refraction, it is why a swell that measured 2 m at an offshore buoy can produce bigger waves at a reef that focuses the energy, and smaller ones at a sheltered beach.

The energy in a wave grows with the square of its height. A wave twice as high carries roughly four times the energy, which is why a small change in forecast size can make a big difference in the water.

7. Breaking: when and how

A wave breaks when it can no longer support its own shape:

• In deep water, waves break when they become too steep: when height is more than about 1/7 of the wavelength (a steepness of about 0.14 to 0.17, depending on the source). This creates whitecaps on a windy day.
• In shallow water, a wave breaks roughly when its height reaches about 0.8 times the water depth. Put the other way, as the Scripps notes do, a wave breaks in water about 1.3 times as deep as its height. A 2 m wave breaks in about 2.5 m of water.

Three types of breaking wave

How a wave breaks depends mostly on how quickly the bottom rises:

That is the basic reason why reef breaks and some beach breaks are hollow and powerful, while long, flat beaches tend to give softer waves.

8. Sets and why waves come in groups

Surfers know waves come in sets, with lulls in between. When swells of slightly different periods travel together, they add up where their crests line up and partly cancel where they do not. The result is groups of larger waves followed by smaller ones. Waiting for the set, rather than taking the first wave that comes, is basic surf physics.

9. Measuring waves: significant height

Forecasts and buoys report significant wave height: the average height of the highest third of the waves. SMHI notes that this matches what an experienced observer would estimate by eye. It is not the biggest wave you will see. Individual waves can reach about twice the significant height, which is worth remembering before you paddle out.

10. Wind at the beach

Finally, the local wind decides the quality of the waves:

• Offshore wind (blowing from the land to the sea) holds up the face of the wave and makes it clean and hollow.
• Onshore wind (from the sea) makes waves crumble and break early.
• No wind gives "glassy" conditions, often in the early morning.

How to use this in practice

• Look at period and direction on the forecast, not just height.
• Long-period groundswell plus offshore wind is the classic recipe for good surf.
• Know which way your spot faces and what the bottom is like. Refraction and bottom shape decide what the same swell does at different spots.
• Check offshore buoys. They show what is really arriving, and a rising period is the first sign a new swell is on its way.

We go further into forecast websites and buoys in our guide to surf forecasting, and into the biggest waves of all in Nazaré and Mavericks.

Sources

• Wikipedia: Wind wave
• Scripps Institution of Oceanography (UC San Diego): Ocean waves lecture notes (PDF)
• SMHI: Wind waves
• Instituto Hidrográfico (Portugal): Why are the waves at Nazaré so big?
• Coastal Engineering Manual, Part II, Chapter 4: Surf zone hydrodynamics
• Surfer Today: The mechanics of the Nazaré canyon wave