![Porto Covo Outubro 2014-3](https://upload.wikimedia.org/wikipedia/commons/0/04/Porto_Covo_Outubro_2014-3.jpg)
In
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
, a wind wave, water wave, or wind-generated water wave, is a
surface wave
In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occu ...
that occurs on the
free surface
In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress,
such as the interface between two homogeneous fluids.
An example of two such homogeneous fluids would be a body of water (liquid) and the air in ...
of
bodies of water
A body of water or waterbody (often spelled water body) is any significant accumulation of water on the surface of Earth or another planet. The term most often refers to oceans, seas, and lakes, but it includes smaller pools of water such as p ...
as a result from the
wind
Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few hou ...
blowing over the water surface. The contact distance in the
direction of the wind is known as 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 Fr ...
''. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small
ripples
Ripple may refer to:
Science and technology
* Capillary wave, commonly known as ripple, a wave traveling along the phase boundary of a fluid
** Ripple, more generally a disturbance, for example of spacetime in gravitational waves
* Ripple (electri ...
, to waves over high, being limited by wind speed, duration, fetch, and water depth.
When directly generated and affected by local wind, a wind wave system is called a wind sea. Wind waves will travel in a
great circle route
Great-circle navigation or orthodromic navigation (related to orthodromic course; from the Greek ''ορθóς'', right angle, and ''δρóμος'', path) is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such rout ...
after being generated – curving slightly left in the southern hemisphere and slightly right in the northern hemisphere. After moving out of the area of fetch, wind waves are called ''
swells'' and can travel thousands of kilometers. A noteworthy example of this is waves generated south of Tasmania during heavy winds that will travel across the Pacific to southern California, producing desirable surfing conditions. Swell consists of wind-generated waves that are not significantly affected by the local wind at that time. They have been generated elsewhere and some time previously. Wind waves in the ocean are also called ocean surface waves, and are mainly ''
gravity waves
In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere ...
'', where
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
is the main equilibrium force.
Wind waves have a certain amount of
randomness
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rand ...
: subsequent waves differ in height, duration, and shape with limited predictability. They can be described as a
stochastic process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
, in combination with the physics governing their generation, growth, propagation, and decay – as well as governing the interdependence between flow quantities such as: the
water surface movements,
flow velocities and water
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
. The key
statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypo ...
s of wind waves (both seas and swells) in evolving
sea state
In oceanography, sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, p ...
s can be predicted with
wind wave model
In fluid dynamics, wind wave modeling describes the effort to depict the sea state and predict the evolution of the energy of wind waves using numerical techniques. These simulations consider atmospheric wind forcing, nonlinear wave interactions ...
s.
Although waves are usually considered in the water seas of Earth, the hydrocarbon seas of
Titan
Titan most often refers to:
* Titan (moon), the largest moon of Saturn
* Titans, a race of deities in Greek mythology
Titan or Titans may also refer to:
Arts and entertainment
Fictional entities
Fictional locations
* Titan in fiction, fictiona ...
may also have wind-driven waves.
Formation
![Ocean wave phases numbered](https://upload.wikimedia.org/wikipedia/commons/3/3d/Ocean_wave_phases_numbered.png)
The great majority of large breakers seen at a beach result from distant winds. Five factors influence the formation of the flow structures in wind waves:
#
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 ...
or strength relative to wave speed – the wind must be moving faster than the wave crest for energy transfer
# 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 Fr ...
'')
# Width of the area affected by fetch (at a right angle to the distance)
# Wind duration – the time for which the wind has blown over the water.
# Water depth
All of these factors work together to determine the size of the water waves and the structure of the flow within them.
The main dimensions associated with
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 ...
are:
*
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 term ' ...
(vertical distance 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, tro ...
(distance from crest to crest in the direction of propagation)
*
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 eq ...
(time interval between arrival of consecutive crests at a stationary point)
* Wave direction or
azimuth
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.
Mathematicall ...
(predominantly driven by
wind direction
Wind direction is generally reported by the direction from which it originates. For example, a ''north'' or ''northerly'' wind blows from the north to the south. The exceptions are onshore winds (blowing onto the shore from the water) and offsho ...
)
A fully developed sea has the maximum wave size theoretically possible for a wind of specific strength, duration, and fetch. Further exposure to that specific wind could only cause a dissipation of energy due to the breaking of wave tops and formation of "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 period of time 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 st ...
''. This figure represents an
average
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...
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 reported significant wave height for a particular day or storm.
Wave formation on an initially flat water surface by wind is started by a random distribution of normal pressure of turbulent wind flow over the water. This pressure fluctuation produces normal and tangential stresses in the surface water, which generates waves. It is assumed that:
# The water is originally at rest.
# The water is not viscous.
# 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 ...
.
# There is a random distribution of normal pressure to the water surface from the turbulent wind.
# Correlations between air and water motions are neglected.
The second mechanism involves wind shear forces on the water surface.
John W. Miles suggested a surface wave generation mechanism that is initiated by turbulent wind shear flows based on the inviscid Orr-Sommerfeld equation in 1957. He found the energy transfer from the wind to the water surface is proportional to the curvature of the velocity profile of the wind at the point where the mean wind speed is equal to the wave speed. Since the wind speed profile is logarithmic to the water surface, the curvature has a negative sign at this point. This relation shows the wind flow transferring its kinetic energy to the water surface at their interface.
Assumptions:
# two-dimensional parallel shear flow
# incompressible, inviscid water and wind
# irrotational water
# slope of the displacement of the water surface is small
Generally, these wave formation mechanisms occur together on the water surface and eventually produce fully developed waves.
For example, if we assume a flat sea surface (Beaufort state 0), and a sudden wind flow blows steadily across the sea surface, the physical wave generation process follows the sequence:
# Turbulent wind forms random pressure fluctuations at the sea surface. Ripples with wavelengths in the order of a few centimeters are generated by the pressure fluctuations. (The
Phillips mechanism
)
# The winds keep acting on the initially rippled sea surface causing the waves to become larger. As the waves grow, the pressure differences get larger causing the growth rate to increase. Finally, the shear instability expedites the wave growth exponentially. (The Miles mechanism
)
# The interactions between the waves on the surface generate longer waves and the interaction will transfer wave energy from the shorter waves generated by the Miles mechanism to the waves which have slightly lower frequencies than the frequency at the peak wave magnitudes, then finally the waves will be faster than the crosswind speed (Pierson & Moskowitz).
Types
![Porto Covo pano April 2009-4](https://upload.wikimedia.org/wikipedia/commons/c/c7/Porto_Covo_pano_April_2009-4.jpg)
Three different types of wind waves develop over time:
*
Capillary wave
A capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics and phase velocity are dominated by the effects of surface tension.
Capillary waves are common in nature, and are often referred to as ripples. The w ...
s, or ripples, dominated by surface tension effects.
*
Gravity waves
In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere ...
, dominated by gravitational and inertial forces.
** Seas, raised locally by the wind.
*
Swells, which have traveled away from where they were raised by the wind, and have to a greater or lesser extent dispersed.
Ripples appear on smooth water when the wind blows, but will die quickly if the wind stops. The restoring force that allows them to propagate is
surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...
. Sea waves are larger-scale, often irregular motions that form under sustained winds. These waves tend to last much longer, even after the wind has died, and the restoring force that allows them to propagate is gravity. As waves propagate away from their area of origin, they naturally separate into groups of common direction and wavelength. The sets of waves formed in this manner are known as swells. The
Pacific Ocean
The Pacific Ocean is the largest and deepest of Earth's five oceanic divisions. It extends from the Arctic Ocean in the north to the Southern Ocean (or, depending on definition, to Antarctica) in the south, and is bounded by the continen ...
is 19,800km from
Indonesia
Indonesia, officially the Republic of Indonesia, is a country in Southeast Asia and Oceania between the Indian and Pacific oceans. It consists of over 17,000 islands, including Sumatra, Java, Sulawesi, and parts of Borneo and New Guine ...
to the coast of
Colombia
Colombia (, ; ), officially the Republic of Colombia, is a country in South America with insular regions in North America—near Nicaragua's Caribbean coast—as well as in the Pacific Ocean. The Colombian mainland is bordered by the Car ...
and, based on an average wavelength of 76.5m, would have ~258,824 swells over that width.
Individual "
rogue wave
Rogue waves (also known as freak waves, monster waves, episodic waves, killer waves, extreme waves, and abnormal waves) are unusually large, unpredictable, and suddenly appearing surface waves that can be extremely dangerous to ships, even to lar ...
s" (also called "freak waves", "monster waves", "killer waves", and "king waves") much higher than the other waves in the
sea state
In oceanography, sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, p ...
can occur. In the case of the
Draupner wave
Rogue waves (also known as freak waves, monster waves, episodic waves, killer waves, extreme waves, and abnormal waves) are unusually large, unpredictable, and suddenly appearing surface waves that can be extremely dangerous to ships, even to la ...
, its height was 2.2 times the
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 st ...
. Such waves are distinct from
tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravity, gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another.
Tide t ...
s, caused by the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
and
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
's
gravitational pull
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
,
tsunami
A tsunami ( ; from ja, 津波, lit=harbour wave, ) is a series of waves in a water body caused by the displacement of a large volume of water, generally in an ocean or a large lake. Earthquakes, volcanic eruptions and other underwater explo ...
s that are caused by underwater
earthquake
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from ...
s or
landslide
Landslides, also known as landslips, are several forms of mass wasting that may include a wide range of ground movements, such as rockfalls, deep-seated grade (slope), slope failures, mudflows, and debris flows. Landslides occur in a variety of ...
s, and waves generated by
underwater explosion
An underwater explosion (also known as an UNDEX) is a chemical or nuclear explosion that occurs under the surface of a body of water. While useful in anti-ship and submarine warfare, underwater bombs are not as effective against coastal facilities. ...
s or the fall of
meteorite
A meteorite is a solid piece of debris from an object, such as a comet, asteroid, or meteoroid, that originates in outer space and survives its passage through the atmosphere to reach the surface of a planet or Natural satellite, moon. When the ...
s—all having far longer
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, tro ...
s than wind waves.
The largest ever recorded wind waves are not rogue waves, but standard waves in extreme sea states. For example, high waves were recorded on the
RRS Discovery
The RRS ''Discovery'' is a barque-rigged auxiliary steamship built in Dundee, Scotland for Antarctic research. Launched in 1901, she was the last traditional wooden three-masted ship to be built in the United Kingdom. Her first mission was th ...
in a sea with significant wave height, so the highest wave was only 1.6 times the significant wave height.
The biggest recorded by a buoy (as of 2011) was high during the
2007 typhoon Krosa near Taiwan.
Spectrum
![Munk ICCE 1950 Fig1](https://upload.wikimedia.org/wikipedia/commons/d/db/Munk_ICCE_1950_Fig1.svg)
Ocean waves can be classified based on: the disturbing force that creates them; the extent to which the disturbing force continues to influence them after formation; the extent to which the restoring force weakens or flattens them; and their wavelength or period. Seismic sea waves have a period of about 20 minutes, and speeds of . Wind waves (deep-water waves) have a period of about 20 seconds.
The speed of all ocean waves is controlled by gravity, wavelength, and water depth. Most characteristics of ocean waves depend on the relationship between their wavelength and water depth. Wavelength determines the size of the orbits of water molecules within a wave, but water depth determines the shape of the orbits. The paths of water molecules in a wind wave are circular only when the wave is traveling in deep water. A wave cannot "feel" the bottom when it moves through water deeper than half its wavelength because too little wave energy is contained in the small circles below that depth. Waves moving through water deeper than half their wavelength are known as deep-water waves. On the other hand, the orbits of water molecules in waves moving through shallow water are flattened by the proximity of the sea surface bottom. Waves in water shallower than 1/20 their original wavelength are known as shallow-water waves. Transitional waves travel through water deeper than 1/20 their original wavelength but shallower than half their original wavelength.
In general, the longer the wavelength, the faster the wave energy will move through the water. The relationship between the wavelength, period and velocity of any wave is:
:::
where C is speed (celerity), L is the wavelength, and T is time, or period (in seconds). Thus the speed of the wave derives from the functional dependence
of the wavelength on the period (the
dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
).
The speed of a deep-water wave may also be approximated by:
:::
where g is the acceleration due to gravity, per second squared. Because g and π (3.14) are constants, the equation can be reduced to:
:::
when C is measured in meters per second and L in meters. Note that in both formulas the wave speed is proportional to the square root of the wavelength.
The speed of shallow-water waves is described by a different equation that may be written as:
:::
where C is speed (in meters per second), g is the acceleration due to gravity, and d is the depth of the water (in meters). The period of a wave remains unchanged regardless of the depth of water through which it is moving. As deep-water waves enter the shallows and feel the bottom, however, their speed is reduced, and their crests "bunch up," so their wavelength shortens.
Spectral models
Sea state
In oceanography, sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, p ...
can be described by the sea wave spectrum or just wave spectrum
. It is composed of a wave height spectrum (WHS)
and a wave direction spectrum (WDS)
. Many interesting properties about the sea state can be found from the wave spectra.
WHS describes the
spectral density
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, o ...
of
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 term ' ...
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...
("power") versus
wave frequency
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 eq ...
, with
dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
.
The relationship between the spectrum
and the wave amplitude
for a wave component
is:
:
Some WHS models are listed below.
* The International Towing Tank Conference (ITTC) recommended spectrum model for fully developed sea (ISSC spectrum/modified
Pierson-Moskowitz spectrum):
::
* ITTC recommended spectrum model for limited
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 Fr ...
(
JONSWAP spectrum)
::
:where
::