What if waves came from a faraway storm?

Waves are usually made by wind.

But sometimes big waves roll in on a calm, sunny day. Where do they come from?

Most ocean waves are made by wind blowing over the water. But surfers know a puzzle: sometimes big, smooth waves roll onto a beach when there's hardly any wind at all.

Those waves are swells, and they can come from a storm thousands of kilometers away. In this lab you can change the time between waves, called the wave period, from short, choppy waves to long, slow swells, and see how much harder they hit an island's coast.

Waves generated by local wind form a confused sea of short-period waves. Waves that leave the storm that made them become swell: organized trains with longer periods that can cross ocean basins.

This lab asks how wave period, at a fixed height, changes the energy reaching a coast. It uses the erosion model's deep-water power formula and a rule-based erosion index on a bare sand island, so you can compare short-period wind waves with long-period swell directly.

Wind blows over the sea and makes ripples. The ripples grow into waves.

Waves carry energy across the water to the beach.

NOAA explains that waves carry energy, not water, across the ocean. As wind blows over calm water it makes ripples, and if it keeps blowing, the ripples grow into waves. The University of Hawaiʻi's Exploring Our Fluid Earth lists three things that make waves bigger: stronger wind, wind that blows for longer, and wind that blows over a longer stretch of water, called the fetch.

Near the storm, waves are jumbled, coming from many directions at different heights. That mix is called a sea.

Wind-driven surface waves form through friction between wind and water (NOAA). Their growth depends on wind speed, duration and fetch; the University of Hawaiʻi gives an example in which 25-knot winds blowing for 60 hours over a 510-nautical-mile fetch produce a significant wave height of 4.3 m with an 8.2-second period.

Near the generating area the sea state is mixed, with waves of different heights and directions. Waves transmit energy, not water, and if unobstructed can cross an entire ocean basin (NOAA).

In the lab, the waves are the same height. But now they come slowly, with lots of time between them.

These long waves are like the ones from a faraway storm. They hit the island much harder!

In the model, start with choppy waves 1.5 meters high, one every 6 seconds. Each meter of coast receives about 6.6 kilowatts of wave power, and after 50 model years about 78 percent of the bare sand island is left.

Now keep the height the same but make the waves arrive every 14 seconds, like swell from a distant storm. The power jumps to about 15.5 kilowatts per meter, about 2.3 times as much, and only about 58 percent of the island is left after 50 model years.

Model, H = 1.5 m, no plants, sand: T = 6 s gives 6.6 kW/m and an erosion index of 75; T = 14 s gives 15.5 kW/m and an index of 175. Because P ∝ H²T, the ratio is simply 14/6, about 2.3.

After 50 model years the island keeps about 78 percent at 6 s and about 58 percent at 14 s. To match the 14-second swell with 6-second waves you would need them about 2.3 m high: 15.6 kW/m and an index of 176. The numbers are model results; only wave power is a calculated physical quantity.

Taller waves carry more energy. Long, slow waves carry more too.

They bring their energy to the beach faster, so the sand washes away faster.

The energy a wave carries depends on its height: the University of Hawaiʻi notes that a wave twice as tall carries four times as much energy for each square meter of sea. The lab's formula adds one more thing: longer waves carry that energy forward faster, so more of it reaches each meter of coast every second.

That's why, in the model, waves 14 seconds apart deliver more power than equally tall waves 6 seconds apart. The model then turns more power into faster erosion of the sand.

Wave energy per unit surface area scales with H² (University of Hawaiʻi). In linear deep-water theory, which the model's formula P = ρg²H²T/(64π) ≈ 0.49 H²T kW/m comes from, that energy travels at a group speed proportional to period, so power per meter of crest scales as H²T (EPRI's 2011 wave resource assessment for DOE, Appendix A, gives P = ρg²H²T/(64π), about 0.49 H²T kW/m).

The model's limits: it uses the deep-water formula all the way to the shore, ignoring shoaling, refraction and breaking; its erosion index is a rule (power × softness × plant factor), not a measured rate; waves come from one side only; and no sand returns. Its model years show a pattern, not real dates.

Waves from storms near Alaska travel all the way to Hawaiʻi.

Some waves from near Antarctica even reach Alaska!

Once swells form, they don't need wind to keep going. The University of Hawaiʻi explains that swells can carry a storm's energy thousands of kilometers. Big winter waves on Hawaiʻi's North Shore come from storms near Alaska, and swells formed near Antarctica can travel all the way to Alaska.

As waves travel away from a storm, their wavelengths get longer. When they finally reach shallow water near a coast, they slow, grow steeper and break, releasing their energy on the shore.

Swells are waves that have gained enough energy to travel beyond their fetch without further wind; storm swells can carry energy thousands of kilometers, from North Pacific storms to Hawaiʻi's North Shore and from the Antarctic to Alaska (University of Hawaiʻi). Wavelengths increase as waves travel, so distant storms deliver longer waves.

Swells are deep-water waves until the depth falls below half a wavelength; then friction with the bottom steepens and breaks them. The U.S. Energy Information Administration estimates the theoretical U.S. wave energy potential at up to 2.64 trillion kWh a year.