# Swell (ocean)

Breaking swell waves at Hermosa Beach, California
Swell near Lyttelton Harbour, New Zealand
Swell near the Whales Lighthouse, Île de Ré

A swell, in the context of an ocean, sea or lake, is the formation of long wavelength waves on the surface of the sea. These series of surface gravity waves are not generated by the local wind. Swell waves often have a long wavelength but this varies with the size of the water body, e.g. wavelengths are rarely more than 150 m in the Mediterranean. Swell wavelength, also, varies from event to event. Occasionally, swells which are longer than 700 m occur as a result of the most severe storms. Swells have a narrower range of frequencies and directions than the wind sea, because swell waves have dispersed from their generation area and have been dissipated.

## Swell dissipation

The dissipation of swell energy is much stronger for short waves, which is why swells from distant storms are only long waves. The dissipation of waves with periods larger than 13 s is very weak but still significant at the scale of the Pacific Ocean.[1] These long swells lose half of their energy over a distance that varies from over 20000 km (half the distance round the globe) to just over 2000 km. This variation was found to be a systematic function of the swell steepness: the ratio of the swell height to the wavelength. The reason for this behaviour is still unclear but it is possible that this dissipation is due to the friction at the air-sea interface.

## Swell dispersion and wave groups

Swells are often created by storms thousands of nautical miles away from the beach where they break, and the propagation of the longest swells is only limited by shorelines. For example swells generated in the Indian Ocean have been recorded in California after more than half a round-the-world trip.[2] This distance allows the waves comprising the swells to be better sorted and free of chop as they travel toward the coast. Waves generated by storm winds have the same speed and will group together and travel with each other, while others moving at even a fraction of a metre per second slower will lag behind, ultimately arriving many hours later due to the distance covered. The time of propagation from the source t is proportional to the distance X divided by the wave period T. In deep water it is $t = 4 \pi X /( g T)$ where g is the acceleration of gravity. For a storm located 10000 km away, swells with a period T=15 s will arrive 10 days after the storm, followed by 14 s swells another 17 hours later, and so forth.

This dispersive arrivals of swells, long periods first with a reduction in the peak wave period over time, can be used to tell the distance at which swells were generated.

Whereas the sea state in the storm has a frequency spectrum with more or less always the same shape (i.e. a well defined peak with dominant frequencies within plus or minus 7% of the peak), the swell spectra are more and more narrow, sometimes as 2% or less, as waves disperse further and further away. The result is that wave groups (called sets by surfers) can have a large number of waves. From about seven waves per group in the storm, this rises to 20 and more in swells from very distant storms.

## Swell and coastal impacts

Just like for all water waves the energy flux is proportional to the significant wave height squared times the group velocity. In deep water this group velocity is proportional to the wave period. Hence swells, with usually longer periods, can pack a lot more energy than shorter wind seas. Also, the amplitude of infragravity waves increases dramatically with the wave period (typically like the period squared), which results in higher run-up.

As swell waves typically have long wavelengths (and thus a deeper wave base), they begin the refraction process (see water waves) at greater distances offshore (in deeper water) than locally generated waves.

[3]

Since swell-generated waves are mixed with normal sea waves, they can be difficult to detect with the naked eye (particularly away from the shore) if they are not significantly larger than the normal waves. From a signal analysis point of view, swells can be thought of as a fairly regular (though not continual) wave signal existing in the midst of strong noise (i.e., normal waves and chop).