Ocean Waves: Dynamics, Dispersion & Breaking

simulator intermediate ~9 min
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λ ≈ 100 m, Hs ≈ 2.5 m — moderate ocean swell

With 10 m/s wind over 200 km fetch, the dominant waves have approximately 100 m wavelength, 8 s period, and 2.5 m significant wave height. These are typical mid-ocean swell conditions.

Formula

Deep water phase speed: c = g·T/(2π) ≈ 1.56·T (m/s)
Deep water wavelength: λ = g·T²/(2π) ≈ 1.56·T² (m)
Shallow water speed: c = √(g·d) where d = depth
Significant wave height: Hs ≈ 0.0246 × U² × √(F/g) (simplified)

Born from Wind

Every ocean wave begins as a small ripple. Wind blowing across the water surface creates tiny perturbations through friction and pressure differences. Once formed, these ripples present a larger surface for the wind to push against, growing into wavelets and eventually into fully developed waves. The wave height depends on three factors: wind speed, duration, and fetch — the unobstructed distance over which the wind blows. The open Southern Ocean, with its endless fetch, produces the largest waves on Earth.

Deep Water Dispersion

In deep water (depth greater than half the wavelength), waves travel at speeds proportional to their period: longer waves move faster. This dispersion means that a storm-generated mixture of wave frequencies gradually separates as it propagates. Long-period swell outruns shorter waves, arriving at distant coasts as clean, evenly spaced lines — the perfect surf that arrives days after a distant storm, having traveled thousands of kilometers across open ocean.

Shallow Water Transformation

When waves enter water shallower than about half their wavelength, the seafloor begins to influence their motion. Waves slow down, their wavelength decreases, and their height increases — a process called shoaling. If the bottom is sloped, different parts of the wave crest travel at different speeds, causing the wave to bend (refract) and align roughly parallel to shore. This is why waves almost always appear to approach the beach head-on, regardless of the offshore wave direction.

Breaking and Energy

As a shoaling wave steepens, it eventually becomes unstable and breaks. The wave's kinetic energy, accumulated over hundreds or thousands of kilometers of open ocean, is released in seconds in the surf zone. A single breaking wave can dissipate hundreds of kilowatts per meter of crest. This energy drives longshore currents, shapes beaches, and powers an emerging industry of wave energy converters that aim to harvest the ocean's relentless power.

FAQ

How are ocean waves formed?

Ocean waves are generated by wind blowing over the water surface. Wind transfers energy to the water through friction and pressure differences. Waves grow with stronger wind, longer duration, and greater fetch (the distance over which wind blows). Once formed, waves can travel thousands of kilometers as swell, long after leaving the generation area.

What is wave dispersion?

Dispersion is the phenomenon where waves of different wavelengths travel at different speeds. In deep water, longer waves travel faster than shorter ones (phase speed = √(gλ/2π)). This causes a mixed sea to sort itself by wavelength as it propagates — long-period swell arrives at distant shores before shorter waves.

Why do waves break near shore?

As waves enter shallow water (depth less than half the wavelength), the bottom slows the lower part of the wave while the top continues at higher speed. The wave steepens until the top outruns the base and the crest topples forward. Waves typically break when depth equals about 1.28 times the wave height.

What is significant wave height?

Significant wave height (Hs) is the average height of the highest one-third of waves, roughly matching what an experienced observer would estimate as 'the wave height.' It is the standard measure of sea state used in forecasting and engineering. The maximum wave in a storm can be 1.5-2 times the significant wave height.

Sources

Embed

<iframe src="https://homo-deus.com/lab/oceanography/wave-dynamics/embed" width="100%" height="400" frameborder="0"></iframe>
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