![Early 90's Bangs](https://upload.wikimedia.org/wikipedia/commons/d/d2/Early_90%27s_Bangs.jpg)
A swell, also sometimes referred to as ground swell, in the context of an
ocean
The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wo ...
,
sea
The sea, connected as the world ocean or simply the ocean, is the body of salty water that covers approximately 71% of the Earth's surface. The word sea is also used to denote second-order sections of the sea, such as the Mediterranean Sea, ...
or
lake
A lake is an area filled with water, localized in a basin, surrounded by land, and distinct from any river or other outlet that serves to feed or drain the lake. Lakes lie on land and are not part of the ocean, although, like the much large ...
, is a series of
mechanical waves that propagate along the interface between water and air under the predominating influence of gravity, and thus are often referred to as
surface gravity waves. These surface gravity waves have their origin as
wind waves
In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of t ...
, but are the consequence of dispersion of wind waves from distant
weather systems
Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmosphere, the tr ...
, where wind blows for a duration of time over a
fetch
Fetch may refer to:
Books
* ''Fetch'', a 2012 book by Alan MacDonald and David Roberts
* ''The Fetch'', a 2006 book by Chris Humphreys
* ''The Fetch'', a 2009 book by Laura Whitcomb
* ''The Fetch'', a 1991 book by Robert Holdstock
* ''Fazbear ...
of water, and these waves move out from the source area at speeds that are a function of wave period and length. More generally, a swell consists of wind-generated waves that are not greatly affected by the local wind at that time. Swell waves often have a relatively long
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
, as short wavelength waves carry less energy and
dissipate
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
faster, but this varies due to the size, strength, and duration of the weather system responsible for the swell and the size of the water body, and varies from event to event, and from the same event, over time. Occasionally, swells that are longer than 700m occur as a result of the most severe storms.
Swell direction is the direction from which the swell is moving. It is given as a geographical direction, either in degrees, or in
points of the compass, such as NNW or SW swell, and like winds, the direction given is generally the direction the swell is coming from. Swells have a narrower range of
frequencies and directions than locally generated wind waves, because they have dispersed from their generation area and over time tend to sort by speed of propagation with the faster waves passing a distant point first. Swells take on a more defined shape and direction and are less random than locally generated wind waves.
Formation
![Easterly swell, Lyttelton Harbour, 29 July 2008](https://upload.wikimedia.org/wikipedia/commons/e/e0/Easterly_swell%2C_Lyttelton_Harbour%2C_29_July_2008.jpg)
Large breakers observed on a shore may result from distant weather systems over the ocean. Five factors work together to determine the size of wind waves which will become ocean swell:
*
Wind speed
In meteorology, wind speed, or wind flow speed, is a fundamental atmospheric quantity caused by air moving from high to low pressure, usually due to changes in temperature. Wind speed is now commonly measured with an anemometer.
Wind speed ...
– the wind must be moving faster than the wave crest (in the direction in which the wave crest travels) for net energy transfer from air to water; stronger prolonged winds create larger waves
* The uninterrupted distance of open water over which the wind blows without significant change in direction (called the ''
fetch
Fetch may refer to:
Books
* ''Fetch'', a 2012 book by Alan MacDonald and David Roberts
* ''The Fetch'', a 2006 book by Chris Humphreys
* ''The Fetch'', a 2009 book by Laura Whitcomb
* ''The Fetch'', a 1991 book by Robert Holdstock
* ''Fazbear ...
'')
* Width of water surface in the fetch
* Wind duration – the time over which the wind has blown over the fetch
* Water depth
A wave is described using the following dimensions:
*
Wave height
In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighboring trough. ''Wave height'' is a term used by mariners, as well as in coastal, ocean and naval engineering.
At sea, the te ...
(from
trough to
crest
Crest or CREST may refer to:
Buildings
*The Crest (Huntington, New York), a historic house in Suffolk County, New York
*"The Crest", an alternate name for 63 Wall Street, in Manhattan, New York
*Crest Castle (Château Du Crest), Jussy, Switzerla ...
)
*
Wave length
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
(from crest to crest)
*
Wave period
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is e ...
(time interval between arrival of consecutive crests at a stationary point)
*
Wave propagation
Wave propagation is any of the ways in which waves travel. Single wave propagation can be calculated by 2nd order wave equation ( standing wavefield) or 1st order one-way wave equation.
With respect to the direction of the oscillation relative to ...
direction
Wave length is a function of period, and of water depth for depths less than approximately half the wave length, where the wave motion is affected by friction with the bottom.
![Deep water wave](https://upload.wikimedia.org/wikipedia/commons/4/4a/Deep_water_wave.gif)
A fully developed sea has the maximum wave size theoretically possible for a wind of a specific strength and fetch. Further exposure to that specific wind would result in a loss of energy equal to the energy input giving a steady state, due to the energy dissipation from viscosity and breaking of wave tops as "whitecaps".
Waves in a given area typically have a range of heights. For weather reporting and for scientific analysis of wind wave statistics, their characteristic height over a time interval is usually expressed as ''
significant wave height
In physical oceanography, the significant wave height (SWH, HTSGW or ''H''s)
is defined traditionally as the mean ''wave height'' ( trough to crest) of the highest third of the waves (''H''1/3). Nowadays it is usually defined as four times the ...
''. This figure represents an average height of the highest one-third of the waves in a given time period (usually chosen somewhere in the range from 20 minutes to twelve hours), or in a specific wave or storm system. The significant wave height is also the value a "trained observer" (e.g. from a ship's crew) would estimate from visual observation of a sea state. Given the variability of wave height, the largest individual waves are likely to be somewhat less than twice the significant wave height.
Sources of wind-wave generation
Wind waves are generated by wind. Other kinds of disturbances such as
seismic
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
events, can also cause gravity waves, but they are not wind waves, and do not generally result in swell. The generation of wind waves is initiated by the disturbances of the crosswind field on the surface of the water.
For initial conditions of a flat water surface (
Beaufort Scale 0) and abrupt crosswind flows on the surface of the water, the generation of surface wind waves can be explained by two mechanisms, which are initiated by normal pressure fluctuations of turbulent winds and parallel wind shear flows.
Surface wave generation by winds
![Sjyang waveGeneration](https://upload.wikimedia.org/wikipedia/commons/4/4b/Sjyang_waveGeneration.png)
From "wind fluctuations": Wind wave formation is started by a random distribution of normal pressure acting on the water from the wind. By this mechanism, proposed by
O.M. Phillips in 1957, the water surface is initially at rest, and the generation of the wave is
initiated by turbulent wind flows and then by fluctuations of the wind, normal pressure acting on the water surface. Due to this pressure fluctuation arise normal and tangential stresses that generate wave behavior on the water surface.
The assumptions of this mechanism are as follows:
* The water is originally at rest;
* The water is
inviscid;
* The water is
irrotational
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of any path between two points does not c ...
;
* The normal pressure to the water surface from the turbulent wind is randomly distributed; and
* Correlations between air and water motions are neglected.
[Phillips, O. M. (1957), "On the generation of waves by turbulent wind", Journal of Fluid Mechanics 2 (5): 417–445, , ]
From "wind shear forces": In 1957,
John W. Miles suggested a surface wave generation mechanism that is initiated by turbulent wind shear flows,
, based on the inviscid
Orr-Sommerfeld equation. He found that the energy transfer from wind to water surface as a wave speed,
, is proportional to the curvature of the velocity profile of wind,
, at the point where the mean wind speed is equal to the wave speed (
, where
is the mean turbulent wind speed). Since the wind profile,
, is logarithmic to the water surface, the curvature,
, has a negative sign at point
. This relation shows the wind flow transferring its kinetic energy to the water surface at their interface, and thence arises wave speed,
. The growth-rate can be determined by the curvature of the winds (
) at the steering height (
) for a given wind speed,
.
The assumptions of this mechanism are:
* 2-dimensional, parallel shear flow,
.
* Incompressible, inviscid water/wind.
* Irrotational water.
* Small slope of the displacement of the surface.
Generally, these wave formation mechanisms occur together on the ocean surface, giving rise to wind waves that eventually grow into fully developed waves. If one supposes a very flat sea surface (Beaufort number, 0), and sudden wind flow blows steadily across it, the physical wave generation process would be like this:
# Turbulent wind flows form random pressure fluctuations at the sea surface. Small waves with a few centimeters order of wavelengths are generated by the pressure fluctuations (Phillips mechanism).
# The cross wind keeps acting on the initially fluctuated sea surface. Then the waves become larger, and as they do so, the pressure differences increase, and the resulting shear instability expedites wave growth exponentially (Miles mechanism).
# The interaction among the waves on the surface generates longer waves (Hasselmann et al., 1973) and this interaction transfers energy from the shorter waves generated by the Miles mechanism to those that have slightly lower frequencies than at the peak wave magnitudes. Ultimately, the wave speed becomes higher than that of the cross wind (Pierson & Moskowitz).
*(Note: Most of the wave speeds calculated from the wavelength divided by the period are proportional to the square root of the length. Thus, except for the shortest wavelength, the waves follow the deep water theory described in the next section. The 8.5 m long wave must be either in shallow water or between deep and shallow.)
Development
Long swell waves develop from and take energy from the shorter wind waves. The process was first described by
Klaus Hasselmann
Klaus Ferdinand Hasselmann (, born 25 October 1931) is a German oceanographer and climate modeller. He is Professor Emeritus at the University of Hamburg and former Director of the Max Planck Institute for Meteorology. He was awarded the 2021 ...
(2021 Nobel prize winner) after investigating the non-linear effects that are most pronounced near the peaks of the highest waves. He showed that, through these non-linearities, two wave trains in deep water can interact to generate two new sets of waves, one generally of longer and the other of shorter wavelength.
The equation that Hasselmann developed to described this process is now used in the sea state models (for example Wavewatch III) used by all the major weather and climate forecasting centres. This is because both the wind sea and the swell have significant effects on the transfer of heat from the ocean to atmosphere. This affects both large scale climate systems, like the
El Niño
El Niño (; ; ) is the warm phase of the El Niño–Southern Oscillation (ENSO) and is associated with a band of warm ocean water that develops in the central and east-central equatorial Pacific (approximately between the International Date ...
, and smaller scale systems, such as the atmospheric depressions that develop near the edges of the
Gulf Stream.
A good physical description of the Hasselmann process is hard to explain, but the non-linear effects are largest near the peaks of the highest waves and the short waves, which often break near the same position, can be used as an analogy.
This is because each small breaking wave gives a small push to the longer wave on which it is breaking. From the point of view of the long wave, it is receiving a small push on each of its crests just like a swing being given a small push at just the right time. There is also no comparable effect in the wave's trough - a term which would tend to reduce the size of the long wave.
From the point of view of a physicist this effect is of extra interest because it shows how, what starts as a random wave field, can generate the order of a long train of swell waves at the cost of the energy losses and increased disorder affecting all the small breaking waves. The sorting of sand grain sizes, often seen on a beach, is a similar process (as is a lot of
life).
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 seconds is very weak but still significant at the scale of the Pacific Ocean. These long swells lose half of their energy over a distance that varies from over 20,000 km (half the distance round the globe) to just over 2,000 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 behavior 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 shores where they break, and the propagation of the longest swells is primarily 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. 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 meter 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
where g is the acceleration of gravity. For a storm located 10,000 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.
The dispersed arrival of swells, starting with the longest period, with a reduction in the
peak wave period over time, can be used to calculate the distance at which swells were generated.
Whereas the sea state in the storm has a
frequency spectrum
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...
with more or less 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.
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 longer periods can transfer more energy than shorter wind waves. Also, the amplitude of
infragravity waves increases dramatically with the wave period (approximately the square of the period), 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
In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of ...
) at greater distances offshore (in deeper water) than locally generated waves.
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
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, di ...
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).
Navigation
Swells were used by
Micronesia
Micronesia (, ) is a subregion of Oceania, consisting of about 2,000 small islands in the western Pacific Ocean. It has a close shared cultural history with three other island regions: the Philippines to the west, Polynesia to the east, and ...
n navigators to maintain course when no other clues were available, such as on foggy nights.
See also
*
Surfing
References
External links
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{{Underwater diving, scidiv
Surfing
Water waves
Oceanographical terminology