Azura at the US Navy’s Wave Energy Test Site (WETS) on Oahu
The AMOG Wave Energy Converter (WEC), in operation off SW England (2019)
The mWave converter by Bombora Wave Power
CalWave Power Technologies, Inc. wave energy converter in California
Wave Power Station using a pneumatic Chamber
Wave Power Station using a pneumatic Chamber

Wave power is the capture of energy of wind waves to do useful work – for example, electricity generation, water desalination, or pumping water. A machine that exploits wave power is a wave energy converter (WEC).

Waves are generated by wind passing over the surface of the sea. As long as the waves propagate slower than the wind speed just above the waves, there is an energy transfer from the wind to the waves. Both air pressure differences between the upwind and the lee side of a wave crest, as well as friction on the water surface by the wind, making the water to go into the shear stress causes the growth of the waves.[1]

Wave power is distinct from tidal power, which captures the energy of the current caused by the gravitational pull of the Sun and Moon. Waves and tides are also distinct from ocean currents which are caused by other forces including breaking waves, wind, the Coriolis effect, cabbeling, and differences in temperature and salinity.

Wave-power generation is not a widely employed commercial technology compared to other established renewable energy sources such as wind power, hydropower and solar power. However, there have been attempts to use this source of energy since at least 1890[2] mainly due to its high power density. As a comparison, the power density of photovoltaic panels is 1 kW/m2 at peak solar insolation, and the power density of the wind is 1 kW/m2 at 12 m/s; the average annual power density of the waves at e.g. San Francisco coast is 25 kW/m2.[3]

In 2000 the world's first commercial Wave Power Device, the Islay LIMPET was installed on the coast of Islay in Scotland and connected to the National Grid.[4] In 2008, the first experimental multi-generator wave farm was opened in Portugal at the Aguçadoura Wave Park.[5]

Testing is used to validate the performance and reliability of wave energy systems in open ocean. In 2021, CalWave Power Technologies, Inc.[6] commissioned its pilot unit device off the coast of San Diego. [7]

Physical concepts

Simplified design of Wave Power Station
Simplified design of Wave Power Station
When an object bobs up and down on a ripple in a pond, it follows approximately an elliptical trajectory.
When an object bobs up and down on a ripple in a pond, it follows approximately an elliptical trajectory.
Motion of a particle in an ocean wave. A = At deep water. The elliptical motion of fluid particles decreases rapidly with increasing depth below the surface. B = At shallow water (ocean floor is now at B).  The elliptical movement of a fluid particle flattens with decreasing depth. 1 = Propagation direction.  2 = Wave crest. 3 = Wave trough.
Motion of a particle in an ocean wave.
A = At deep water. The elliptical motion of fluid particles decreases rapidly with increasing depth below the surface.
B = At shallow water (ocean floor is now at B). The elliptical movement of a fluid particle flattens with decreasing depth.
1 = Propagation direction.
2 = Wave crest.
3 = Wave trough.
Photograph of the elliptical trajectories of water particles under a – progressive and periodic – surface gravity wave in a wave flume. The wave conditions are: mean water depth d = 2.50 ft (0.76 m), wave height H = 0.339 ft (0.103 m), wavelength λ = 6.42 ft (1.96 m), period T = 1.12 s.[8]
Photograph of the elliptical trajectories of water particles under a – progressive and periodic – surface gravity wave in a wave flume. The wave conditions are: mean water depth d = 2.50 ft (0.76 m), wave height H = 0.339 ft (0.103 m), wavelength λ = 6.42 ft (1.96 m), period T = 1.12 s.[8]

The interaction between ocean waves and energy converters is a complex high-order non linear phenomenon. Under specific conditions, this process can be simplified and described by simpler theories and models.

Potential flow theory

The potential flow theory has a fundamental relevance to wave study. It is based on the assumption of irrotational fluid, and given that the curl of a gradient vanishes, allows to express the water velocity in terms of velocity potential,[9]

with is the fluid velocity and the velocity potential. Furthermore, considering incompressible fluid (constant density) is a realistic approach for liquids and gives,

with the fluid mass density. Hence, the velocity potential must satisfy the Laplace equation,

If we consider an ideal flow, that is, in addition to be irrotational is frictionless, and considering that the only external force acting on the fluid is the earth gravity , the Navier-Stokes equation can be developed as follow,

with is the fluid viscosity, is the gravitational acceleration, and the pressure. Despite all fluids being viscous, in certain situation the effect of viscosity is sufficiently small to be neglected and hence the potential flow theory can be applied. This is the case for ocean waves and wave energy converter devices for small amplitude waves and body motion, where is taken equal to zero. However, when interacting with extreme waves, the body motion might become non linear and the potential theory can´t hold anymore.

After integration along spatial dimensions, the Bernoulli equation can be obtained,

Linear potential flow theory

When considering small amplitude waves and motions, the quadratic terms can be neglected, giving the linear Bernoulli equation,

Boundary constraints

At the free surface, that is , the pressure is approximately equal to and we consider the constant so that the linear potential flow equation at the free surface becomes,


with the elevation of the water free surface from equilibrium position.

This constraint lies on the idea that at the free surface, the fluid velocity is equal to the velocity of the surface itself. This condition, using the chain rule, takes the form,

, for .

Taking the time partial derivative of the above free surface dynamical constraint, and substituting with the former gives,


This boundary constraint simply states that fluid should not penetrate body, such as the sea bed. It is expressed as follow,


with the water depth.

Solution to linear potential flow theory

Given the Laplace equation, a solution of the following form is proposed,

where and are determined with the boundary constraints. One can find,

, and ,

where is the wave height, is the wave number, is the wavelength and is the angular frequency.

The surface elevation can then be simply derived as follow,

it describes a plane wave progressing along the x-axis direction.

Wave power formula

In deep water where the water depth is larger than half the wavelength, the wave energy flux is[a]

with P the wave energy flux per unit of wave-crest length, Hm0 the significant wave height, Te the wave energy period, ρ the water density and g the acceleration by gravity. The above formula states that wave power is proportional to the wave energy period and to the square of the wave height. When the significant wave height is given in metres, and the wave period in seconds, the result is the wave power in kilowatts (kW) per metre of wavefront length.[10][11][12][13]

Example: Consider moderate ocean swells, in deep water, a few km off a coastline, with a wave height of 3 m and a wave energy period of 8 s. Using the formula to solve for power, we get

meaning there are 36 kilowatts of power potential per meter of wave crest.

In major storms, the largest waves offshore are about 15 meters high and have a period of about 15 seconds. According to the above formula, such waves carry about 1.7 MW of power across each meter of wavefront.

An effective wave power device captures as much as possible of the wave energy flux. As a result, the waves will be of lower height in the region behind the wave power device.

Wave energy and wave-energy flux

In a sea state, the average(mean) energy density per unit area of gravity waves on the water surface is proportional to the wave height squared, according to linear wave theory:[1][14]


where E is the mean wave energy density per unit horizontal area (J/m2), the sum of kinetic and potential energy density per unit horizontal area. The potential energy density is equal to the kinetic energy,[1] both contributing half to the wave energy density E, as can be expected from the equipartition theorem. In ocean waves, surface tension effects are negligible for wavelengths above a few decimetres.

The waves propagate on the ocean surface, and the wave energy is also transported horizontally with the group velocity. The mean transport rate of the wave energy through a vertical plane of unit width, parallel to a wave crest, is called the wave energy flux (or wave power, which must not be confused with the actual power generated by a wave power device), and is equal to:[16][1]

with cg the group velocity (m/s).

Due to the dispersion relation for water waves under the action of gravity, the group velocity depends on the wavelength λ, or equivalently, on the wave period T. Further, the dispersion relation is a function of the water depth h. As a result, the group velocity behaves differently in the limits of deep and shallow water, and at intermediate depths:[1][14]

Deepwater corresponds with a water depth larger than half the wavelength, which is the common situation in the sea and ocean. In deep water, longer-period waves propagate faster and transport their energy faster. The deep-water group velocity is half the phase velocity. In shallow water, for wavelengths larger than about twenty times the water depth, as found quite often near the coast, the group velocity is equal to the phase velocity.[17]

Wave height is determined by wind speed, the duration of time the wind has been blowing, fetch (the distance over which the wind excites the waves) and by the depth and topography of the seafloor (which can focus or disperse the energy of the waves). A given wind speed has a matching practical limit over which time or distance will not produce larger waves. When this limit has been reached the sea is said to be "fully developed". In general, larger waves are more powerful but wave power is also determined by wave speed, wavelength, and water density.

Oscillatory motion is highest at the surface and diminishes exponentially with depth. However, for standing waves (clapotis) near a reflecting coast, wave energy is also present as pressure oscillations at great depth, producing microseisms.[1] These pressure fluctuations at greater depth are too small to be interesting from the point of view of wave power.


The first known patent to use energy from ocean waves dates back to 1799, and was filed in Paris by Girard and his son.[18] An early application of wave power was a device constructed around 1910 by Bochaux-Praceique to light and power his house at Royan, near Bordeaux in France.[19] It appears that this was the first oscillating water-column type of wave-energy device.[20] From 1855 to 1973 there were already 340 patents filed in the UK alone.[18]

Modern scientific pursuit of wave energy was pioneered by Yoshio Masuda's experiments in the 1940s.[21] He tested various concepts of wave-energy devices at sea, with several hundred units used to power navigation lights. Among these was the concept of extracting power from the angular motion at the joints of an articulated raft, which was proposed in the 1950s by Masuda.[22]

A renewed interest in wave energy was motivated by the oil crisis in 1973. A number of university researchers re-examined the potential to generate energy from ocean waves, among whom notably were Stephen Salter from the University of Edinburgh, and Johannes Falnes from Norwegian Institute of Technology (later merged into Norwegian University of Science and Technology), Michael E. McCormick from U.S. Naval Academy, David Evans from Bristol University, Michael French from University of Lancaster, Nick Newman and C. C. Mei from MIT.

Stephen Salter's 1974 invention became known as Salter's duck or nodding duck, although it was officially referred to as the Edinburgh Duck. In small scale controlled tests, the Duck's curved cam-like body can stop 90% of wave motion and can convert 90% of that to electricity giving 81% efficiency.[23]

In the 1980s, as the oil price went down, wave-energy funding was drastically reduced. Nevertheless, a few first-generation prototypes were tested at sea. More recently, following the issue of climate change, there is again a growing interest worldwide for renewable energy, including wave energy.[24]

The world's first marine energy test facility was established in 2003 to kick-start the development of a wave and tidal energy industry in the UK. Based in Orkney, Scotland, the European Marine Energy Centre(EMEC) has supported the deployment of more wave and tidal energy devices than at any other single site in the world. EMEC provides a variety of test sites in real sea conditions. Its grid-connected wave test site is situated at Billia Croo, on the western edge of the Orkney mainland, and is subject to the full force of the Atlantic Ocean with seas as high as 19 metres recorded at the site. Wave energy developers currently testing at the centre include Aquamarine Power, Pelamis Wave Power, and ScottishPower Renewables.

Wave energy converters (WECs)

Wave power converters are generally categorized by the method used to capture or harness the energy of the waves, by location and by the power take-off system. Locations are shoreline, nearshore and offshore. Types of power take-off include: hydraulic ram, elastomeric hose pump, pump-to-shore, hydroelectric turbine, air turbine,[25] and linear electrical generator. When evaluating wave energy as a technology type, it is important to distinguish between the four most common approaches: point absorber buoys, surface attenuators, oscillating water columns, and overtopping devices.

Generic wave energy concepts: 1. Point absorber, 2. Attenuator, 3. Oscillating wave surge converter, 4. Oscillating water column, 5. Overtopping device, 6. Submerged pressure differential, 7. Floating in-air converters.
Generic wave energy concepts: 1. Point absorber, 2. Attenuator, 3. Oscillating wave surge converter, 4. Oscillating water column, 5. Overtopping device, 6. Submerged pressure differential, 7. Floating in-air converters.

Point absorber buoy

This device floats on the surface of the water, held in place by cables connected to the seabed. The point-absorber is defined as having a device width much smaller than the incoming wavelength λ. A good point absorber has the same characteristics as a good wave-maker. The wave energy is absorbed by radiating a wave with destructive interference to the incoming waves. Buoys use the rise and fall of swells to generate electricity in various ways including directly via linear generators,[26] or via generators driven by mechanical linear-to-rotary converters[27] or hydraulic pumps.[28] Electromagnetic fields generated by electrical transmission cables and acoustics of these devices may be a concern for marine organisms. The presence of the buoys may affect fish, marine mammals, and birds as potential minor collision risk and roosting sites. Potential also exists for entanglement in mooring lines. Energy removed from the waves may also affect the shoreline, resulting in a recommendation that sites remain a considerable distance from the shore.[29]

Surface attenuator

These devices act similarly to the aforementioned point absorber buoys, with multiple floating segments connected to one another and are oriented perpendicular to incoming waves. A flexing motion is created by swells, and that motion drives hydraulic pumps to generate electricity. Environmental effects are similar to those of point absorber buoys, with an additional concern that organisms could be pinched in the joints.[29]

Oscillating wave surge converter

These devices typically have one end fixed to a structure or the seabed while the other end is free to move. Energy is collected from the relative motion of the body compared to the fixed point. Oscillating wave surge converters often come in the form of floats, flaps, or membranes. Environmental concerns include minor risk of collision, artificial reefing near the fixed point, electromotive force effects from subsea cables, and energy removal effecting sediment transport.[29] Some of these designs incorporate parabolic reflectors as a means of increasing the wave energy at the point of capture. These capture systems use the rise and fall motion of waves to capture energy.[30] Once the wave energy is captured at a wave source, power must be carried to the point of use or to a connection to the electrical grid by transmission power cables.[31]

Oscillating water column

Oscillating Water Column devices can be located onshore or in deeper waters offshore. With an air chamber integrated into the device, swells compress air in the chambers forcing air through an air turbine to create electricity.[32] Significant noise is produced as air is pushed through the turbines, potentially affecting birds and other marine organisms within the vicinity of the device. There is also concern about marine organisms getting trapped or entangled within the air chambers.[29]

Overtopping device

Overtopping devices are long structures that use wave velocity to fill a reservoir to a greater water level than the surrounding ocean. The potential energy in the reservoir height is then captured with low-head turbines. Devices can be either onshore or floating offshore. Floating devices will have environmental concerns about the mooring system affecting benthic organisms, organisms becoming entangled, or electromotive force effects produced from subsea cables. There is also some concern regarding low levels of turbine noise and wave energy removal affecting the nearfield habitat.[29]

Submerged pressure differential

Submerged pressure differential based converters are a comparatively newer technology [33] utilizing flexible (usually reinforced rubber) membranes to extract wave energy. These converters use the difference in pressure at different locations below a wave to produce a pressure difference within a closed power take-off fluid system. This pressure difference is usually used to produce flow, which drives a turbine and electrical generator. Submerged pressure differential converters frequently use flexible membranes as the working surface between the ocean and the power take-off system. Membranes offer the advantage over rigid structures of being compliant and low mass, which can produce more direct coupling with the wave's energy. Their compliant nature also allows for large changes in the geometry of the working surface, which can be used to tune the response of the converter for specific wave conditions and to protect it from excessive loads in extreme conditions.

A submerged converter may be positioned either on the seafloor or in midwater. In both cases, the converter is protected from water impact loads which can occur at the free surface. Wave loads also diminish in non-linear proportion to the distance below the free surface. This means that by optimizing the depth of submergence for such a converter, a compromise between protection from extreme loads and access to wave energy can be found. Submerged WECs also have the potential to reduce the impact on marine amenity and navigation, as they are not at the surface.

Floating in-air converters

The recognised need for increased reliability in wave energy converter technology has spawned this group of concepts. Floating in-air converters offer potential increased reliability of machinery components as they are located above the sea-water where easy inspection and maintenance is afforded. Examples of different concepts of floating in-air converters are shown in #7 of the figure. 7a) roll damping type energy extraction systems with turbines in compartments containing sloshing fresh water; 7b) horizontal axis pendulum systems; 7c) vertical axis pendulum systems.

Environmental effects

Further information: Environmental impact of electricity generation § Wave

Common environmental concerns associated with marine energy developments include:

The Tethys database provides access to scientific literature and general information on the potential environmental effects of wave energy.[34]


The worldwide resource of coastal wave energy has been estimated to be greater than 2 TW.[35] Locations with the most potential for wave power include the western seaboard of Europe, the northern coast of the UK, and the Pacific coastlines of North and South America, Southern Africa, Australia, and New Zealand. The north and south temperate zones have the best sites for capturing wave power. The prevailing westerlies in these zones blow strongest in winter.

Estimates have been made by the National Renewable Energy Laboratory (NREL) for various nations around the world in regards to the amount of energy that could be generated from wave energy converters (WECs) on their coastlines. For the United States in particular, it is estimated that the total energy amount that could be generated along its coastlines is equivalent to 1170 TWh per year, which would account to approximately 10 kWh per United States citizen per day. That's almost 5% of the overall energy consumption per average citizen, including transport and industry.[36] While this sounds promising, the coastline along Alaska accounted for approx. 50% of the total energy created within this estimate. Considering this, there would need to be the proper infrastructure in place to transfer this energy from Alaskan shorelines to the mainland United States in order to properly capitalize on meeting United States energy demands. However, these numbers show the great potential these technologies have if they are implemented on a global scale to satisfy the search for sources of renewable energy.

WECs have gone under heavy examination through research, especially relating to their efficiencies and the transport of the energy they generate. NREL has shown that these WECs can have efficiencies near 50%.[36] This is a phenomenal efficiency rating among renewable energy production. For comparison, efficiencies above 10% in solar panels are considered viable for sustainable energy production.[37] Thus, a value of 50% efficiency for a renewable energy source is extremely viable for the future development of renewable energy sources to be implemented across the world. Additionally, research has been conducted examining smaller WECs and their viability, especially relating to power output. One piece of research showed great potential with small devices, reminiscent of buoys, capable of generating upwards of 6 MW of power in various wave conditions and oscillations and device size (up to a roughly cylindrical 21 kg buoy).[38] Even further research has led to the development of smaller, compact versions of current WECs that could produce the same amount of energy while using roughly one-half of the area necessary as current devices.[39]  

World wave energy resource map
World wave energy resource map


There is a potential impact on the marine environment. Noise pollution, for example, could have a negative impact if not monitored, although the noise and visible impact of each design varies greatly.[12] Other biophysical impacts (flora and fauna, sediment regimes and water column structure and flows) of scaling up the technology are being studied.[40] In terms of socio-economic challenges, wave farms can result in the displacement of commercial and recreational fishermen from productive fishing grounds, can change the pattern of beach sand nourishment, and may represent hazards to safe navigation.[41] Furthermore, supporting infrastructure, such as offshore grid connections, is not widely available.[42] Offshore deployments of WECs and underwater substations undergo complicated procedures, which can put excessive stress in companies working in these applications. In 2019, for example, the Swedish production subsidiary Seabased Industries AB was liquidated due to "extensive challenges in recent years, both practical and financial".[43]

Wave farms

Main article: Wave farm

A group of wave energy devices deployed in the same location is called wave farm, wave power farm or wave energy park. Wave farms represent a solution to achieve larger electricity production. The devices of a park are going to interact with each other hydrodynamically and electrically, according to the number of machines, the distance among them, the geometric layout, the wave climate, the local geometry, the control strategies. The design process of a wave energy farm is a multi-optimization problem with the aim to get a high power production and low costs and power fluctuations.[44]

Wave farm projects



Gibraltar Wave Farm



United Kingdom

United States

Main article: Wave power in the United States


See also


  1. ^ The energy flux is with the group velocity, see Herbich, John B. (2000). Handbook of coastal engineering. McGraw-Hill Professional. A.117, Eq. (12). ISBN 978-0-07-134402-9. The group velocity is , see the collapsed table "Properties of gravity waves on the surface of deep water, shallow water and at intermediate depth, according to linear wave theory" in the section "Wave energy and wave energy flux" below.
  2. ^ Here, the factor for random waves is 116, as opposed to 18 for periodic waves – as explained hereafter. For a small-amplitude sinusoidal wave with wave amplitude the wave energy density per unit horizontal area is or using the wave height for sinusoidal waves. In terms of the variance of the surface elevation the energy density is . Turning to random waves, the last formulation of the wave energy equation in terms of is also valid (Holthuijsen, 2007, p. 40), due to Parseval's theorem. Further, the significant wave height is defined as , leading to the factor 116 in the wave energy density per unit horizontal area.
  3. ^ For determining the group velocity the angular frequency ω is considered as a function of the wavenumber k, or equivalently, the period T as a function of the wavelength λ.


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Further reading