Ocean waves activity
Follow ocean waves from the storm that makes them to the beach where they break. Six stops. At each one, move the sliders, make a prediction, then test it.
A wave carries energy across the ocean, but the water itself mostly stays put. Watch the orange buoy: crests pass by, and the buoy just goes around in a loop. The white dots are bits of water below the surface.
Side view, drawn to scale. The ▼ markers ride along with the crests.
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Only the crest. The wave's shape and energy travel. The water loops in place. A floating bottle bobs up and down in nearly the same spot instead of riding the waves to shore.
About half a wavelength (the dashed line). The circles shrink quickly with depth. A submarine 50 m down would not feel these waves at all.
They flatten into a back-and-forth sway. If you have snorkeled near a beach, you have felt this surge. The wave now "feels the bottom", and that sets up everything at stops 3 and 4.
In deep water, waves of different lengths travel at different speeds. Scientists call this dispersion. Set up two waves, guess the winner, and race them.
A storm makes waves of every length at once, all jumbled together. Watch what dispersion does to that jumble as it travels, and what a faraway buoy feels.
Side view, deep water. Time runs 4× faster than real life. Wave heights are not to scale.
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The long wave, every time. In deep water, speed = √(g × wavelength ÷ 2π), where g is gravity (9.8 m/s²). A 100 m wave moves at about 12.5 m/s (28 mph), about as fast as the fastest human sprinter at full speed.
Four times longer. Speed depends on the square root of wavelength, so 25 m and 100 m will do it. To go three times faster you would need nine times the length.
Long rollers first, then shorter and shorter waves. Dispersion sorts the jumble by length. Surf forecasters watch real buoys for this. Very long-period swell means a distant storm's waves have started to arrive. The period shrinks over the next few days, and how fast it shrinks tells them how far away the storm was.
No. Crests appear at the back of a group, run forward through it, and fade out at the front. In deep water a group of waves, and the energy it carries, moves at half the speed of the crests inside it. So the 200 m waves take twice as long to reach the buoy as the race would suggest.
Once the water is shallower than about half a wavelength, a wave feels the bottom. It slows down, its crests bunch together, and it grows taller until it breaks. This is shoaling. Drag the orange probe to measure the wave anywhere along the way.
Side view. Heights are stretched about 25× so you can see them. Time runs 3× faster than real life.
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Speed and wavelength drop, and height climbs. The period never changes. If 6 crests per minute pass the deep end, 6 per minute must pass every other spot too, or crests would pile up somewhere.
Make the starting height bigger (a longer period or a gentler slope helps too). Waves break when their height reaches about ¾ of the water depth, so bigger waves break in deeper water, farther out. Big-wave surf spots break far offshore.
It's the same shoaling, pushed to the limit. With a wavelength that long, even the 4 km deep ocean counts as "shallow". So it races along at about 200 m/s, as fast as a jet. In 10 m of water it slows to about 10 m/s. All that energy gets squeezed into a much shorter, much taller wave.
No. It dips by about 4 percent first, then grows. Wave energy moves at the "group speed". That speed briefly rises as the wave starts to feel the bottom, stretching the energy out. Then the big slowdown squeezes it.
Now look down from above. The part of a crest over shallow water moves slower than the part over deep water, so the whole crest swings around. This is refraction, the same bending light does in a lens. Dark blue is deep, pale blue is shallow.
Bird's-eye view, 600 m wide. Orange rays show the path the wave energy follows. Time runs 10× faster than real life.
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Nearly straight-on. The shoreward end of each crest is always in shallower, slower water, so the crest keeps turning until it lines up with the beach. Waves at the beach almost always roll straight at you, whatever direction they started from.
Rays crowd together on the headland, so wave energy is focused there: bigger waves, good for surfing, bad for cliffs. Rays spread out in the bays, so waves are smaller there. Over centuries this wears headlands back and fills bays with sand.
It acts like a magnifying glass. Crests slow over the shallow hill and wrap inward, and the rays cross behind it. That spot gets extra-large waves even though the beach itself is perfectly straight.
Small. Waves move faster over the deep canyon, so crests bend away from it and the energy lands on either side. Black's Beach near San Diego gets its famously big surf this way, from Scripps Canyon just offshore.
Breaking waves push water over the sandbars toward the beach. That water has to get back out, and it escapes through gaps in the bars as a narrow, fast stream: a rip current. Rips cause most surf rescues. You are the orange swimmer, 55 m out and being pulled away from the sand. Pick a plan.
Bird's-eye view of 300 m of beach. Time runs 6× faster than real life. The currents are a simplified model of a real rip.
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The calm, dark gap looks like the safe spot, and it is the worst one. Waves don't break there because the channel is deeper, and that channel is exactly where the rip flows out. Turn on the pink dye to see it. Lifeguards spot rips this way: a darker gap in the line of breakers, sometimes with foam or sandy water streaming seaward.
In this model it does, but look at the numbers. Strong rips reach 2 m/s and more. An Olympic champion holds about that speed for 20 seconds, in a calm pool, with no waves. Everyone else goes nowhere and wears themselves out. Exhausted swimmers are the ones who drown. A rip carries you away from shore. It does not pull you under.
Swimming sideways, parallel to the beach. A rip is strong but narrow, often only 10 to 30 m wide. A short swim along the beach takes you out of it, and then the breaking waves over the sandbar help push you in. Floating works too: the rip fades out just beyond the breakers, and floating saves energy and lets you wave for help. If you can't tell which way to go, float, stay calm, and signal. Swim near a lifeguard.
It gets faster. Bigger breaking waves push more water over the bars, and all of it has to drain back out through the same gap. Rips also tend to be strongest near low tide, when the water over the bars is shallow and more waves break there.
Back to where waves begin. Almost every wave you have seen at a beach was made by wind blowing over water somewhere. Three things set how big they get. How fast the wind blows, how long it blows, and how much open water it crosses (the fetch).
Top: the sea at the downwind end of the fetch. The boat is 20 m long, and the label shows how much heights are stretched. Bottom: how wave height builds up along the way. "Wave height" here is the significant wave height, the average of the tallest third of the waves.
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Only about a meter. The waves run out of room before they can grow. A pond never has surf, no matter how windy it gets. Fetch is the limit.
Yes, after about a day. At first, time is the limit. Eventually the waves get long enough to travel about as fast as the wind itself, and the wind can't push them any more. Scientists call this a fully developed sea.
It goes up four times. In a fully developed sea, height grows with the square of wind speed. A gale is far worse than a breezy day. The strongest storms make waves as tall as buildings.
Here the Southern Ocean wins, about 10 m to 8 m. A hurricane is compact: its strongest winds cover only a couple hundred kilometers, so waves leave the windy patch before they finish growing. Around Antarctica, strong wind blows over thousands of kilometers of open water for days. Those waves then cross entire oceans as swell, sorted by dispersion just like at stop 2. (Real hurricanes can beat this estimate when the storm travels along with its own waves and keeps pushing them.)
Under the hood: stops 1 to 5 use linear wave theory, ω² = gk·tanh(kh). Stop 3 applies linear shoaling up to a breaking limit of H = 0.78h. The peaked crest shapes near breaking are drawn for looks. Stop 4 solves the time-dependent mild-slope equation on a 240 × 192 grid that repeats along the shore, so the wave direction moves in steps. Stop 5 runs the same solver over a barred beach. Its currents are a prescribed, mass-conserving rip cell scaled by wave height, plus an onshore push where waves break over the bar. The swimmer's energy budget is for illustration only. Stop 6 uses the JONSWAP fetch-limited growth curves, gH/U² = 0.0016 (gF/U²)^½ and gT/U = 0.286 (gF/U²)^⅓, capped at the Pierson-Moskowitz fully developed sea (gH/U² = 0.2433, gT/U = 8.134). The duration limit comes from the Shore Protection Manual, and the 10 m wind speed is used directly.