# Tidal resonance

In oceanography, a tidal resonance occurs when the tide excites one of the resonant modes of the ocean.[1] The effect is most striking when a continental shelf is about a quarter wavelength wide. Then an incident tidal wave can be reinforced by reflections between the coast and the shelf edge, the result producing a much higher tidal range at the coast.

Famous examples of this effect are found in the Bay of Fundy, where the world's highest tides are reportedly found, and in the Bristol Channel. Less well known is Leaf Bay, part of Ungava Bay near the entrance of Hudson Strait (Canada), which has tides similar to those of the Bay of Fundy.[2] Other resonant regions with large tides include the Patagonian Shelf and on the continental shelf of northwest Australia.[3]

Most of the resonant regions are also responsible for large fractions of the total amount of tidal energy dissipated in the oceans. Satellite altimeter data shows that the M2 tide dissipates approximately 2.5 TW, of which 261 GW is lost in the Hudson Bay complex, 208 GW on the European Shelves (including the Bristol Channel), 158 GW on the North-west Australian Shelf, 149 GW in the Yellow Sea and 112 GW on the Patagonian Shelf.[4]

Tides at Portishead Dock in the Bristol Channel. An example of tidal resonance.

## Scale of the resonances

The speed of long waves in the ocean is given, to a good approximation, by ${\displaystyle \scriptstyle {\sqrt {gh}}}$, where g is the acceleration of gravity and h is the depth of the ocean.[5][6][7] For a typical continental shelf with a depth of 100 m, the speed is approximately 30 m/s. So if the tidal period is 12 hours, a quarter wavelength shelf will have a width of about 300 km.

With a narrower shelf, there is still a resonance but it is mismatched to the frequency of the tides and so has less effect on tidal amplitudes. However the effect is still enough to partly explain why tides along a coast lying behind a continental shelf are often higher than at offshore islands in the deep ocean (one of the additional partly explanations being Green's law). Resonances also generate strong tidal currents and it is the turbulence caused by the currents which is responsible for the large amount of tidal energy dissipated in such regions.

In the deep ocean, where the depth is typically 4000 m, the speed of long waves increases to approximately 200 m/s. The difference in speed, when compared to the shelf, is responsible for reflections at the continental shelf edge. Away from resonance this can reduce tidal energy moving onto the shelf. However near a resonant frequency the phase relationship, between the waves on the shelf and in the deep ocean, can have the effect of drawing energy onto the shelf.

The increased speed of long waves in the deep ocean means that the tidal wavelength there is of order 10,000 km. As the ocean basins have a similar size, they also have the potential of being resonant.[8][9] In practice deep ocean resonances are difficult to observe, probably because the deep ocean loses tidal energy too rapidly to the resonant shelves.

## References

1. ^ Platzman, G.W. (1991), "Tidal Evidence for Ocean Normal Modes", in Parker, B.P. (ed.), Tidal Hydrodynamics, New York: John Wiley & Sons, p. 883
2. ^ O'Reilly, C.T.; Solvason, R.; Solomon, C. (2005). J. Ryan (ed.). "Where are the World's Largest Tides". BIO Annual Report: 2004 in Review. Biotechnol. Ind. Org., Washington, D. C.: 44–46.
3. ^ Webb, D.J. (1976). "A Model of Continental-shelf Resonances". Deep-Sea Research. 23: 1–15. Bibcode:1976DSROA..23....1W. doi:10.1016/0011-7471(76)90804-4.
4. ^ Egbert, G.D.; Ray, R. (2001). "Estimates of M2 tidal dissipation from TOPEX/Poseidon altimeter data". Journal of Geophysical Research. 106 (C10): 22475–22502. Bibcode:2001JGR...10622475E. doi:10.1029/2000JC000699.
5. ^ Segar, D.A. (2007). Introduction to Ocean Science. New York: W.W. Norton. pp. 581+.
6. ^ Knauss, J.A. (1997). Introduction to Physical Oceanography. Long Grove, USA: Waveland Press. p. 309.
7. ^ Defant, A. (1961). Introduction to Physical Oceanography. II. Oxford: Pergamon Press. p. 598.
8. ^ Platzman, G.W.; Curtis, G.A.; Hansen, K.S.; Slater, R.D. (1981). "Normal Modes of the World ocean. Part II: Description of Modes in the Period Range 8 to 80 Hours". Journal of Physical Oceanography. 11 (5): 579–603. Bibcode:1981JPO....11..579P. doi:10.1175/1520-0485(1981)011<0579:NMOTWO>2.0.CO;2.
9. ^ Webb, D.J. (1973). "Tidal Resonance in the Coral Sea". Nature. 243 (5409): 511. Bibcode:1973Natur.243..511W. doi:10.1038/243511a0.
Andrea Hamilton

Andrea Jarvis Hamilton (born in 1968) is a fine-art photographer known for her monumental lightboxes of natural phenomena like icebergs and for her candid portraits of London's creative personalities. Her work encompasses several photographic genres including portraiture, street photography and landscape, and questions subjects as varied as climate change, identity or place as they relate to other creative disciplines.

Hamilton has been short-listed for several notable photography prizes including the 7th Julia Margaret Cameron Award for Women Photographers, Chantel Paul’s Honorable Mention at The Centre for Fine Art Photography in Colorado, the 9th Arte Laguna Prize and the Judges Choice at the AOP Open Awards 2013.

Bahama Banks

The Bahama Banks are the submerged carbonate platforms that make up much of the Bahama Archipelago. The term is usually applied in referring to either the Great Bahama Bank around Andros Island, or the Little Bahama Bank of Grand Bahama Island and Great Abaco, which are the largest of the platforms, and the Cay Sal Bank north of Cuba. The islands of these banks are politically part of the Bahamas. Other banks are the three banks of the Turks and Caicos Islands, namely the Caicos Bank of the Caicos Islands, the bank of the Turks Islands, and wholly submerged Mouchoir Bank. Further southeast are the equally wholly submerged Silver Bank and Navidad Bank north of the Dominican Republic.

Bay of Fundy

The Bay of Fundy (French: Baie de Fundy) is a bay between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the US state of Maine. It has an extremely high tidal range. The name is likely a corruption of the French word Fendu, meaning "split".

Carbonate platform

A carbonate platform is a sedimentary body which possesses topographic relief, and is composed of autochthonic calcareous deposits. Platform growth is mediated by sessile organisms whose skeletons build up the reef or by organisms (usually microbes) which induce carbonate precipitation through their metabolism. Therefore, carbonate platforms can not grow up everywhere: they are not present in places where limiting factors to the life of reef-building organisms exist. Such limiting factors are, among others: light, water temperature, transparency and pH-Value. For example, carbonate sedimentation along the Atlantic South American coasts takes place everywhere but at the mouth of the Amazon River, because of the intense turbidity of the water there. Spectacular examples of present-day carbonate platforms are the Bahama Banks under which the platform is roughly 8 km thick, the Yucatan Peninsula which is up to 2 km thick, the Florida platform, the platform on which the Great Barrier Reef is growing, and the Maldive atolls. All these carbonate platforms and their associated reefs are confined to tropical latitudes. Today's reefs are built mainly by scleractinian corals, but in the distant past other organisms, like archaeocyatha (during the Cambrian) or extinct cnidaria (tabulata and rugosa) were important reef builders.

Index of physics articles (T)

The index of physics articles is split into multiple pages due to its size.

Index of wave articles

This is a list of Wave topics.

List of dynamical systems and differential equations topics

This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations.

List of submarine volcanoes

A list of active and extinct submarine volcanoes and seamounts located under the world's oceans. There are estimated to be 40,000 to 55,000 seamounts in the global oceans. Almost all are not well-mapped and many may not have been identified at all. Most are unnamed and unexplored. This list is therefore confined to seamounts that are notable enough to have been named and/or explored.

Mechanical resonance

Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings and airplanes. This is a phenomenon known as resonance disaster.

Avoiding resonance disasters is a major concern in every building, tower and bridge construction project. The Taipei 101 building relies on a 660-ton pendulum—a tuned mass damper—to modify the response at resonance. Furthermore, the structure is designed to resonate at a frequency which does not typically occur. Buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. In addition, engineers designing objects having engines must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other strongly oscillating parts.

Many resonant objects have more than one resonance frequency. It will vibrate easily at those frequencies, and less so at other frequencies. Many clocks keep time by mechanical resonance in a balance wheel, pendulum, or quartz crystal.

Oceanic plateau

An oceanic or submarine plateau is a large, relatively flat elevation that is higher than the surrounding relief with one or more relatively steep sides.There are 184 oceanic plateaus covering an area of 18,486,600 km2 (7,137,700 sq mi), or about 5.11% of the oceans. The South Pacific region around Australia and New Zealand contains the greatest number of oceanic plateaus (see map).

Oceanic plateaus produced by large igneous provinces are often associated with hotspots, mantle plumes, and volcanic islands — such as Iceland, Hawaii, Cape Verde, and Kerguelen. The three largest plateaus, the Caribbean, Ontong Java, and Mid-Pacific Mountains, are located on thermal swells. Other oceanic plateaus, however, are made of rifted continental crust, for example Falkland Plateau, Lord Howe Rise, and parts of Kerguelen, Seychelles, and Arctic ridges.

Plateaus formed by large igneous provinces were formed by the equivalent of continental flood basalts such as the Deccan Traps in India and the Snake River Plain in the United States.

In contrast to continental flood basalts, most igneous oceanic plateaus erupt through young and thin (6–7 km (3.7–4.3 mi)) mafic or ultra-mafic crust and are therefore uncontaminated by felsic crust and representative for their mantle sources.

These plateaus often rise 2–3 km (1.2–1.9 mi) above the surrounding ocean floor and are more buoyant than oceanic crust. They therefore tend to withstand subduction, more-so when thick and when reaching subduction zones shortly after their formations. As a consequence, they tend to "dock" to continental margins and be preserved as accreted terranes. Such terranes are often better preserved than the exposed parts of continental flood basalts and are therefore a better record of large-scale volcanic eruptions throughout Earth's history. This "docking" also means that oceanic plateaus are important contributors to the growth of continental crust. Their formations often had a dramatic impact on global climate, such as the most recent plateaus formed, the three, large, Cretaceous oceanic plateaus in the Pacific and Indian Ocean: Ontong Java, Kerguelen, and Caribbean.

Orbital resonance

In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly this relationship is found for a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, where the orbit and the swing both have a natural frequency, and the other body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i.e., their ability to alter or constrain each other's orbits. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large Solar System bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.

A binary resonance ratio in this article should be interpreted as the ratio of number of orbits completed in the same time interval, rather than as the ratio of orbital periods, which would be the inverse ratio. Thus the 2:3 ratio above means Pluto completes two orbits in the time it takes Neptune to complete three. In the case of resonance relationships among three or more bodies, either type of ratio may be used (in such cases the smallest whole-integer ratio sequences are not necessarily reversals of each other) and the type of ratio will be specified.

Physical oceanography

Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters.

Physical oceanography is one of several sub-domains into which oceanography is divided. Others include biological, chemical and geological oceanography.

Physical oceanography may be subdivided into descriptive and dynamical physical oceanography.Descriptive physical oceanography seeks to research the ocean through observations and complex numerical models, which describe the fluid motions as precisely as possible.

Dynamical physical oceanography focuses primarily upon the processes that govern the motion of fluids with emphasis upon theoretical research and numerical models. These are part of the large field of Geophysical Fluid Dynamics (GFD) that is shared together with meteorology. GFD is a sub field of Fluid dynamics describing flows occurring on spatial and temporal scales that are greatly influenced by the Coriolis force.

Resonance

Resonance describes the phenomena of amplification that occurs when the frequency of a periodically applied force is in harmonic proportion to a natural frequency of the system on which it acts. When an oscillating force is applied at the resonant frequency of another system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near the intrinsic resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy.

Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters).

The term resonance (from Latin resonantia, 'echo', from resonare, 'resound') originates from the field of acoustics, particularly observed in musical instruments, e.g., when strings started to vibrate and to produce sound without direct excitation by the player.

For example, electrical resonance occurs in a circuit with capacitors and inductors because the collapsing magnetic field of the inductor generates an electric current in its windings that charges the capacitor, and then the discharging capacitor provides an electric current that builds the magnetic field in the inductor. Once the circuit is charged, the oscillation is self-sustaining, and there is no external periodic driving action. This is analogous to a mechanical pendulum, where mechanical energy is converted back and forth between kinetic and potential, and both systems are forms of simple harmonic oscillators.

Severn Barrage

The Severn Barrage is any of a range of ideas for building a barrage from the English coast to the Welsh coast over the Severn tidal estuary. Ideas for damming or barraging the Severn estuary (and Bristol Channel) have existed since the 19th century. The building of such a barrage would constitute an engineering project comparable with some of the world's biggest. The purposes of such a project has typically been one, or several of: transport links, flood protection, harbour creation, or tidal power generation. In recent decades it is the latter that has grown to be the primary focus for barrage ideas, and the others are now seen as useful side-effects. Following the Severn Tidal Power Feasibility Study (2008–10), the British government concluded that there was no strategic case for building a barrage but to continue to investigate emerging technologies.

In June 2013 the Energy and Climate Change Select Committee published its findings after an eight-month study of the arguments for and against the Barrage. MPs said the case for the barrage was unproven. They were not convinced the economic case was strong enough and said the developer, Hafren Power, had failed to answer serious environmental and economic concerns.

Tidal barrage

A tidal barrage is a dam-like structure used to capture the energy from masses of water moving in and out of a bay or river due to tidal forces.Instead of damming water on one side like a conventional dam, a tidal barrage allows water to flow into a bay or river during high tide, and releases the water during low tide. This is done by measuring the tidal flow and controlling the sluice gates at key times of the tidal cycle. Turbines are placed at these sluices to capture the energy as the water flows in and out.Tidal barrages are among the oldest methods of tidal power generation, with tide mills being developed as early as the sixth century. In the 1960s the 1.7 megawatt Kislaya Guba Tidal Power Station in Kislaya Guba, Russia was built.

Tidal force

The tidal force is a force that stretches a body towards and away from the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field.

In celestial mechanics, the expression tidal force can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Earth), but is also perturbed by the gravitational effects of a third body (for example, the Moon). The perturbing force is sometimes in such cases called a tidal force (for example, the perturbing force on the Moon): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.

Tide

Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun, and the rotation of the Earth.

Tide tables can be used for any given locale to find the predicted times and amplitude (or "tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see Timing). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have a diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category.Tides vary on timescales ranging from hours to years due to a number of factors, which determine the lunitidal interval. To make accurate records, tide gauges at fixed stations measure water level over time. Gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to the reference (or datum) level usually called mean sea level.While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to forces such as wind and barometric pressure changes, resulting in storm surges, especially in shallow seas and near coasts.

Tidal phenomena are not limited to the oceans, but can occur in other systems whenever a gravitational field that varies in time and space is present. For example, the shape of the solid part of the Earth is affected slightly by Earth tide, though this is not as easily seen as the water tidal movements.

Undersea mountain range

Undersea mountain ranges are mountain ranges that are mostly or entirely underwater, and specifically under the surface of an ocean. If originated from current tectonic forces, they are often referred to as a mid-ocean ridge. In contrast, if formed by past above-water volcanism, they are known as a seamount chain. The largest and best known undersea mountain range is a mid-ocean ridge, the Mid-Atlantic Ridge. It has been observed that, "similar to those on land, the undersea mountain ranges are the loci of frequent volcanic and earthquake activity".

Wave base

The wave base, in physical oceanography, is the maximum depth at which a water wave's passage causes significant water motion. For water depths deeper than the wave base, bottom sediments and the seafloor are no longer stirred by the wave motion above.

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