Swella

Meet Swella, a long ocean swell who races ahead of the small choppy waves.

Waves on deep water do not all travel at the same speed. Water counts as deep when it is more than about half a wavelength deep, and there the speed depends on the wavelength λ, v = √(gλ/2π). Longer waves travel faster.

A swell with a wavelength of 100 m moves at about √(9.81 × 100 / 6.28) ≈ 12.5 m/s, roughly 45 km/h. A shorter wave of 25 m travels at about 6.25 m/s, only half as fast, because the speed depends on the square root of the wavelength.

This is called dispersion. A distant storm makes waves of many lengths, and the long ones outrun the short ones, so the first swell to reach a far coast has the longest wavelength.

In shallow water the rule changes. The speed then depends on the depth instead of the wavelength, which is why waves slow down and pile up as they reach the beach.