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57-497: The Pelamis Wave Energy Converter was a technology that used the motion of ocean surface waves to create electricity. The machine was made up of connected sections which flex and bend as waves pass; it is this motion which is used to generate electricity. Developed by the now defunct Scottish company Pelamis Wave Power (formerly Ocean Power Delivery), the Pelamis became the first offshore wave machine to generate electricity into

114-548: A 2011 heist. July 2023 the Orkney Island Council sought tenders for the disposal of the Pelamis 2 "Orkney Islands Council (OIC) invite you to submit a proposal to take ownership and remove and dispose of the wave energy converter known as “Pelamis” P2. The “Pelamis” is a Wave Energy Converter which was utilised to capture wave energy from the sea in the waters off the sea in Orkney. It became redundant and came into

171-399: A deep-water wave may also be approximated by: where g is the acceleration due to gravity, 9.8 meters (32 feet) 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. In both formulas the wave speed is proportional to the square root of the wavelength. The speed of shallow-water waves is described by

228-456: 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. Sea state can be described by

285-405: 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 . This figure represents an average height of the highest one-third of the waves in

342-429: 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

399-414: 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 usually assumed for the purpose of theoretical analysis that: The second mechanism involves wind shear forces on

456-473: A sudden wind flow blows steadily across the sea surface, the physical wave generation process follows the sequence: Three different types of wind waves develop over time: 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 . Sea waves are larger-scale, often irregular motions that form under sustained winds. These waves tend to last much longer, even after

513-406: Is called shoaling . Wave refraction is the process that occurs when waves interact with the sea bed to slow the velocity of propagation as a function of wavelength and period. As the waves slow down in shoaling water, the crests tend to realign at a decreasing angle to the depth contours. Varying depths along a wave crest cause the crest to travel at different phase speeds , with those parts of

570-495: Is concentrated as they converge, with a resulting increase in wave height. Because these effects are related to a spatial variation in the phase speed, and because the phase speed also changes with the ambient current—due to the Doppler shift —the same effects of refraction and altering wave height also occur due to current variations. In the case of meeting an adverse current the wave steepens , i.e. its wave height increases while

627-438: Is inevitable. Individual waves in deep water break when the wave steepness—the ratio of the wave height H to the wavelength λ —exceeds about 0.17, so for H  > 0.17  λ . In shallow water, with the water depth small compared to the wavelength, the individual waves break when their wave height H is larger than 0.8 times the water depth h , that is H  > 0.8  h . Waves can also break if

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684-406: 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: 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

741-503: Is measured in metres. This expression tells us that waves of different wavelengths travel at different speeds. The fastest waves in a storm are the ones with the longest wavelength. As a result, after a storm, the first waves to arrive on the coast are the long-wavelength swells. For intermediate and shallow water, the Boussinesq equations are applicable, combining frequency dispersion and nonlinear effects. And in very shallow water,

798-402: Is sometimes alleged that out of a set of waves, the seventh wave in a set is always the largest; while this isn't the case, the waves in the middle of a given set tend to be larger than those before and after them. Individual " rogue waves " (also called "freak waves", "monster waves", "killer waves", and "king waves") much higher than the other waves in the sea state can occur. In the case of

855-626: Is the main equilibrium force. Wind waves have a certain amount of randomness : subsequent waves differ in height, duration, and shape with limited predictability. They can be described as a stochastic process , 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 . The key statistics of wind waves (both seas and swells) in evolving sea states can be predicted with wind wave models . Although waves are usually considered in

912-627: Is the wave elevation, ϵ j {\displaystyle \epsilon _{j}} is uniformly distributed between 0 and 2 π {\displaystyle 2\pi } , and Θ j {\displaystyle \Theta _{j}} is randomly drawn from the directional distribution function f ( Θ ) : {\displaystyle {\sqrt {f(\Theta )}}:} As waves travel from deep to shallow water, their shape changes (wave height increases, speed decreases, and length decreases as wave orbits become asymmetrical). This process

969-665: The Draupner wave , its 25 m (82 ft) height was 2.2 times the significant wave height . Such waves are distinct from tides , caused by the Moon and Sun 's gravitational pull , tsunamis that are caused by underwater earthquakes or landslides , and waves generated by underwater explosions or the fall of meteorites —all having far longer wavelengths than wind waves. The largest ever recorded wind waves are not rogue waves, but standard waves in extreme sea states. For example, 29.1 m (95 ft) high waves were recorded on

1026-507: The RRS Discovery in a sea with 18.5 m (61 ft) 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 32.3 m (106 ft) high during the 2007 typhoon Krosa near Taiwan. 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;

1083-483: The intellectual property transferred to the Scottish Government body Wave Energy Scotland . Pelamis was an attenuating wave energy converter. The machine responded to the curvature of the waves (their shape) rather than the wave height. As waves can only reach a certain curvature before naturally breaking, this limits the range of motion through which the machine must move but maintains large motion at

1140-430: The sea wave spectrum or just wave spectrum S ( ω , Θ ) {\displaystyle S(\omega ,\Theta )} . It is composed of a wave height spectrum (WHS) S ( ω ) {\displaystyle S(\omega )} and a wave direction spectrum (WDS) f ( Θ ) {\displaystyle f(\Theta )} . Many interesting properties about

1197-412: The shallow water equations can be used. If the wavelength is very long compared to the water depth, the phase speed (by taking the limit of c when the wavelength approaches infinity) can be approximated by Lyness Lyness is a village on the east coast of the island of Hoy , Orkney , Scotland. The village is within the parish of Walls and Flotta, and is situated at the junction of

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1254-831: The B9047 and B9048. During the 1920s Lyness was briefly the headquarters of the metal salvage firm of Cox and Danks 's raising of the German High Seas Fleet , scuttled by the Germans on 21 June 1919 during the Armistice ( Scuttling of the German fleet in Scapa Flow ). During the Second World War it was home to HMS Proserpine , the main base for the naval fleet based at Scapa Flow . In 2010–2011

1311-596: The German utility company, E.ON , and was the UK's first commercial supply contract in the marine energy sector. The P2-001 machine was named Vágr Atferð , Old Norse for Wave Power. In March 2010 Pelamis Wave Power announced a second order for a P2 machine, from ScottishPower Renewables, part of Iberdrola Renovables . This second machine was first installed at EMEC in May 2012. The two utility companies announced that they will work together to share and collaborate in testing of

1368-1190: The Golden Wharf at Lyness Harbour was upgraded to host renewable energy projects, including the Pelamis Wave Energy Converter and the Wello Penguin . Today an Orkney Ferries Ro-Ro car ferry links it to Longhope on South Walls , the island of Flotta in Scapa Flow , and Houton on Mainland, Orkney . Lyness Royal Naval Cemetery was opened in 1915 primarily to serve the Scapa Flow base (which closed in 1946). Buried there are 445 Empire and Commonwealth service personnel, chiefly Royal Navy , from World War I (109 of whom are unidentified) and 200 from World War II (8 unidentified). There are also buried here 14 German Navy sailors and 4 other German service personnel including an unidentified Luftwaffe airman, and one Norwegian war grave. There are also 30 British non-war service burials (including 2 unidentified British Army soldiers). Major naval ship losses represented among

1425-577: The P2 Pelamis technology. When not being tested at the Billa Croo test site, the machines were maintained at Lyness Harbour on this island of Hoy, Orkney . The Golden Wharf at Lyness was upgraded in 2010–2011 to host renewable energy projects. Following the demise of the company, the P2-001 device was acquired by Wave Energy Scotland , having completed over 15,000 hours of operation. The device

1482-431: The Pelamis for some other purpose this should be explained in full detail including the method of preservation, security and protection of the environment. Ocean surface wave 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 after being generated – curving slightly left in the southern hemisphere and slightly right in

1539-471: The crest falling forward and down as it extends over the air ahead of the wave. Three main types of breaking waves are identified by surfers or surf lifesavers . Their varying characteristics make them more or less suitable for surfing and present different dangers. When the shoreline is near vertical, waves do not break but are reflected. Most of the energy is retained in the wave as it returns to seaward. Interference patterns are caused by superposition of

1596-464: The equilibrium of the water surface and transfer energy from the air to the water, forming waves. The initial formation of waves by the wind is described in the theory of Phillips from 1957, and the subsequent growth of the small waves has been modeled by Miles , also in 1957. In linear plane waves of one wavelength in deep water, parcels near the surface move not plainly up and down but in circular orbits: forward above and backward below (compared to

1653-475: 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 760 km/h (470 mph). Wind waves (deep-water waves) have a period up to 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

1710-546: The farm had an installed capacity of 2.25 MW and was the world's first multiple machine wave power project. The project was part funded by Portuguese utility Enersis , at the time owned by Australian global investment company Babcock & Brown . The farm first generated electricity in July 2008 but was taken offline in November 2008 at the same time as Babcock & Brown encountered financial difficulties. The P2 Pelamis design

1767-424: 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 the period (in seconds). Thus the speed of the wave derives from the functional dependence L ( T ) {\displaystyle L(T)} of the wavelength on the period (the dispersion relation ). The speed of

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1824-418: The formation of the flow structures in wind waves: 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 are: 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

1881-464: The grid, when it was first connected to the UK grid in 2004. Pelamis Wave Power then went on to build and test five additional Pelamis machines: three first-generation P1 machines, which were tested in a farm off the coast of Portugal in 2009, and two second-generation machines, the Pelamis P2, were tested off Orkney between 2010 and 2014. The company went into administration in November 2014, with

1938-460: The hyperbolic tangent approaches 1 {\displaystyle 1} , the speed c {\displaystyle c} approximates In SI units, with c deep {\displaystyle c_{\text{deep}}} in m/s, c deep ≈ 1.25 λ {\displaystyle c_{\text{deep}}\approx 1.25{\sqrt {\lambda }}} , when λ {\displaystyle \lambda }

1995-434: The incident and reflected waves, and the superposition may cause localized instability when peaks cross, and these peaks may break due to instability. (see also clapotic waves ) Wind waves are mechanical waves that propagate along the interface between water and air ; the restoring force is provided by gravity, and so they are often referred to as surface gravity waves . As the wind blows, pressure and friction perturb

2052-591: The joints in small waves. The Pelamis machine was an offshore wave energy converter, operating in water depths greater than 50m. The machine consisted of a series of semi-submerged cylindrical sections linked by hinged joints. As waves pass along the length of the machine, the sections move relative to one another. The wave-induced motion of the sections is resisted by hydraulic cylinders which pump high pressure oil through hydraulic motors via smoothing hydraulic accumulators . The hydraulic motors drive electrical generators to produce electricity. Electricity from all

2109-595: The joints is fed down a single umbilical cable to a junction on the sea bed . Several devices can be connected and linked to shore through a single seabed cable. Pelamis Wave Power tested their first full-scale prototype at the Billia Croo wave test site at the European Marine Energy Centre (EMEC) in Orkney , Scotland between 2004 and 2007. The machine, which was rated at 750 kW, was

2166-535: The northern hemisphere. After moving out of the area of fetch and no longer being affected by the local wind, 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. Wind waves in the ocean are also called ocean surface waves and are mainly gravity waves , where gravity

2223-411: The other hand, the orbits of water molecules in waves moving through shallow water are flattened by the proximity of the sea bottom surface. 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,

2280-563: The possession of OIC in 2017. It has been laid up at moorings off Lyness Wharf, Hoy, Orkney. Upon an agreed date which shall be within 7 days of signing acceptance to the agreement the Contractor shall take ownership of Pelamis, and the responsibility for the upkeep, maintenance and security of the “Pelamis” will become the Contractors responsibility. The Contractor will be required to have relevant and appropriate insurances in place at

2337-508: The sea state can be found from the wave spectra. WHS describes the spectral density of wave height variance ("power") versus wave frequency , with dimension { S ( ω ) } = { length 2 ⋅ time } {\displaystyle \{S(\omega )\}=\{{\text{length}}^{2}\cdot {\text{time}}\}} . The relationship between the spectrum S ( ω j ) {\displaystyle S(\omega _{j})} and

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2394-483: 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 water movement below that depth. Waves moving through water deeper than half their wavelength are known as deep-water waves. On

2451-471: The surface. The phase speed (also called the celerity) of a surface gravity wave is—for pure periodic wave motion of small- amplitude waves—well approximated by where In deep water, where d ≥ 1 2 λ {\displaystyle d\geq {\frac {1}{2}}\lambda } , so 2 π d λ ≥ π {\displaystyle {\frac {2\pi d}{\lambda }}\geq \pi } and

2508-405: The time of change of ownership. The contractor shall have the option to remove the Pelamis by sea to dismantle or dispose of the Pelamis at a regulated and certified recycling facility or to dismantle the Pelamis at Lyness Wharf and remove the components by road or by suitable marine transport and dispose of them at a regulated and certified recycling facility. Should the Contractor wish to re-use

2565-406: The water seas of Earth, the hydrocarbon seas of Titan may also have wind-driven waves. Waves in bodies of water may also be generated by other causes, both at the surface and underwater (such as watercraft , animals , waterfalls , landslides , earthquakes , bubbles , and impact events ). The great majority of large breakers seen at a beach result from distant winds. Five factors influence

2622-414: 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

2679-456: The wave amplitude A j {\displaystyle A_{j}} for a wave component j {\displaystyle j} is: Some WHS models are listed below. As for WDS, an example model of f ( Θ ) {\displaystyle f(\Theta )} might be: Thus the sea state is fully determined and can be recreated by the following function where ζ {\displaystyle \zeta }

2736-423: The wave amplitude (height), the particle paths do not form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as Stokes drift . As the depth below the free surface increases, the radius of the circular motion decreases. At a depth equal to half the wavelength λ, the orbital movement has decayed to less than 5% of its value at

2793-409: The wave in deeper water moving faster than those in shallow water . This process continues while the depth decreases, and reverses if it increases again, but the wave leaving the shoal area may have changed direction considerably. Rays —lines normal to wave crests between which a fixed amount of energy flux is contained—converge on local shallows and shoals. Therefore, the wave energy between rays

2850-464: The wave propagation direction). As a result, the surface of the water forms not an exact sine wave , but more a trochoid with the sharper curves upwards—as modeled in trochoidal wave theory. Wind waves are thus a combination of transversal and longitudinal waves. When waves propagate in shallow water , (where the depth is less than half the wavelength) the particle trajectories are compressed into ellipses . In reality, for finite values of

2907-400: The wavelength decreases, similar to the shoaling when the water depth decreases. Some waves undergo a phenomenon called "breaking". A breaking wave is one whose base can no longer support its top, causing it to collapse. A wave breaks when it runs into shallow water , or when two wave systems oppose and combine forces. When the slope, or steepness ratio, of a wave, is too great, breaking

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2964-404: The wind grows strong enough to blow the crest off the base of the wave. In shallow water, the base of the wave is decelerated by drag on the seabed. As a result, the upper parts will propagate at a higher velocity than the base and the leading face of the crest will become steeper and the trailing face flatter. This may be exaggerated to the extent that the leading face forms a barrel profile, with

3021-482: 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 is 19,800 km (12,300 mi) from Indonesia to the coast of Colombia and, based on an average wavelength of 76.5 m (251 ft), would have ~258,824 swells over that width. It

3078-491: The world's first offshore wave power machine to generate electricity into the grid system. The prototype was 120 metres (390 ft) long and 3.5 metres (11 ft) in diameter. It had four tube sections coupled by three power conversion modules. In 2008 Pelamis tested three first generation, P1 Pelamis waves at the Aguçadoura Wave Farm . Located off the northwest coast of Portugal near Póvoa de Varzim ,

3135-475: Was Pelamis Wave Power's second generation Pelamis machine. The Pelamis P2 is 180m long, 4m diameter and approximately 1350 tonnes in weight. Consisting of five tube sections and four flexible joints, the design is longer and fatter than the previous P1 design. In 2010, Pelamis Wave Power began tests of the first Pelamis P2 machine, again at the EMEC Billia Croo wave test site. The machine was owned by

3192-540: Was decommissioned in April 2016 and sold to the Orkney Island Council for £1. The other device, P2-002 was sold to the European Marine Energy Centre for use as a test rig. E.ON and ScottishPower Renewables announced plans to build larger projects using Pelamis machines in the waters off Orkney's west coast. Both companies won leases in 2010 from The Crown Estate , who own the seabed around the UK, for projects of up to 50 MW. The "Pentland Firth and Orkney Waters Leasing Round"

3249-512: Was the world's first commercial scale wave and tidal energy leasing opportunity. Pelamis platurus is a yellow-bellied sea snake that lives in tropical and subtropical waters. It prefers shallow inshore waters. The Hailong (Dragon) 1 is a Chinese wave energy machine reported to be a near perfect copy of the Pelamis which began testing in 2015 in the South China Sea . It was reported to have been based on IP stolen from Pelamis during

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