Internal wave

Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface.[1] To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical distance (as in the case of the thermocline in lakes and oceans or an atmospheric inversion), the waves propagate horizontally like surface waves, but do so at slower speeds as determined by the density difference of the fluid below and above the interface. If the density changes continuously, the waves can propagate vertically as well as horizontally through the fluid.

Internal waves, also called internal gravity waves, go by many other names depending upon the fluid stratification, generation mechanism, amplitude, and influence of external forces. If propagating horizontally along an interface where the density rapidly decreases with height, they are specifically called interfacial (internal) waves. If the interfacial waves are large amplitude they are called internal solitary waves or internal solitons. If moving vertically through the atmosphere where substantial changes in air density influences their dynamics, they are called anelastic (internal) waves. If generated by flow over topography, they are called Lee waves or mountain waves. If the mountain waves break aloft, they can result in strong warm winds at the ground known as Chinook winds (in North America) or Foehn winds (in Europe). If generated in the ocean by tidal flow over submarine ridges or the continental shelf, they are called internal tides. If they evolve slowly compared to the Earth's rotational frequency so that their dynamics are influenced by the Coriolis effect, they are called inertia gravity waves or, simply, inertial waves. Internal waves are usually distinguished from Rossby waves, which are influenced by the change of Coriolis frequency with latitude.

InternalWaves Gibraltar ISS009-E-09952 54
Internal waves (marked with arrows), caused by tidal flow through the Strait of Gibraltar and made visible by sea surface roughness enhance sunlight backscatter

Visualization of internal waves

An internal wave can readily be observed in the kitchen by slowly tilting back and forth a bottle of salad dressing - the waves exist at the interface between oil and vinegar.

Atmospheric internal waves can be visualized by wave clouds: at the wave crests air rises and cools in the relatively lower pressure, which can result in water vapor condensation if the relative humidity is close to 100%. Clouds that reveal internal waves launched by flow over hills are called lenticular clouds because of their lens-like appearance. Less dramatically, a train of internal waves can be visualized by rippled cloud patterns described as herringbone sky or mackerel sky. The outflow of cold air from a thunderstorm can launch large amplitude internal solitary waves at an atmospheric inversion. In northern Australia, these result in Morning Glory clouds, used by some daredevils to glide along like a surfer riding an ocean wave. Satellites over Australia and elsewhere reveal these waves can span many hundreds of kilometers.

Undulations of the oceanic thermocline can be visualized by satellite because the waves increase the surface roughness where the horizontal flow converges, and this increases the scattering of sunlight (as in the image at the top of this page showing of waves generated by tidal flow through the Strait of Gibraltar).

Buoyancy, reduced gravity and buoyancy frequency

According to Archimedes principle, the weight of an immersed object is reduced by the weight of fluid it displaces. This holds for a fluid parcel of density surrounded by an ambient fluid of density . Its weight per unit volume is , in which is the acceleration of gravity. Dividing by a characteristic density, , gives the definition of the reduced gravity:

If , is positive though generally much smaller than . Because water is much more dense than air, the displacement of water by air from a surface gravity wave feels nearly the full force of gravity (). The displacement of the thermocline of a lake, which separates warmer surface from cooler deep water, feels the buoyancy force expressed through the reduced gravity. For example, the density difference between ice water and room temperature water is 0.002 the characteristic density of water. So the reduced gravity is 0.2% that of gravity. It is for this reason that internal waves move in slow-motion relative to surface waves.

Whereas the reduced gravity is the key variable describing buoyancy for interfacial internal waves, a different quantity is used to describe buoyancy in continuously stratified fluid whose density varies with height as . Suppose a water column is in hydrostatic equilibrium and a small parcel of fluid with density is displaced vertically by a small distance . The buoyant restoring force results in a vertical acceleration, given by [2][3]

This is the spring equation whose solution predicts oscillatory vertical displacement about in time about with frequency given by the buoyancy frequency:

The above argument can be generalized to predict the frequency, , of a fluid parcel that oscillates along a line at an angle to the vertical:


This is one way to write the dispersion relation for internal waves whose lines of constant phase lie at an angle to the vertical. In particular, this shows that the buoyancy frequency is an upper limit of allowed internal wave frequencies.

Mathematical modeling of internal waves

The theory for internal waves differs in the description of interfacial waves and vertically propagating internal waves. These are treated separately below.

Interfacial waves

In the simplest case, one considers a two-layer fluid in which a slab of fluid with uniform density overlies a slab of fluid with uniform density . Arbitrarily the interface between the two layers is taken to be situated at The fluid in the upper and lower layers are assumed to be irrotational. So the velocity in each layer is given by the gradient of a velocity potential, and the potential itself satisfies Laplace's equation:

Assuming the domain is unbounded and two-dimensional (in the plane), and assuming the wave is periodic in with wavenumber the equations in each layer reduces to a second-order ordinary differential equation in . Insisting on bounded solutions the velocity potential in each layer is


with the amplitude of the wave and its angular frequency. In deriving this structure, matching conditions have been used at the interface requiring continuity of mass and pressure. These conditions also give the dispersion relation:[4]

in which the reduced gravity is based on the density difference between the upper and lower layers:

with the Earth's gravity. Note that the dispersion relation is the same as that for deep water surface waves by setting

Internal waves in uniformly stratified fluid

The structure and dispersion relation of internal waves in a uniformly stratified fluid is found through the solution of the linearized conservation of mass, momentum, and internal energy equations assuming the fluid is incompressible and the background density varies by a small amount (the Boussinesq approximation). Assuming the waves are two dimensional in the x-z plane, the respective equations are

in which is the perturbation density, is the pressure, and is the velocity. The ambient density changes linearly with height as given by and , a constant, is the characteristic ambient density.

Solving the four equations in four unknowns for a wave of the form gives the dispersion relation

in which is the buoyancy frequency and is the angle of the wavenumber vector to the horizontal, which is also the angle formed by lines of constant phase to the vertical.

The phase velocity and group velocity found from the dispersion relation predict the unusual property that they are perpendicular and that the vertical components of the phase and group velocities have opposite sign: if a wavepacket moves upward to the right, the crests move downward to the right.

Internal waves in the ocean

Internal Wave trains around Trinidad, as seen from space

Most people think of waves as a surface phenomenon, which acts between water (as in lakes or oceans) and the air. Where low density water overlies high density water in the ocean, internal waves propagate along the boundary. They are especially common over the continental shelf regions of the world oceans and where brackish water overlies salt water at the outlet of large rivers. There is typically little surface expression of the waves, aside from slick bands that can form over the trough of the waves.

Internal waves are the source of a curious phenomenon called dead water, first reported in 1893 by the Norwegian oceanographer Fridtjof Nansen, in which a boat may experience strong resistance to forward motion in apparently calm conditions. This occurs when the ship is sailing on a layer of relatively fresh water whose depth is comparable to the ship's draft. This causes a wake of internal waves that dissipates a huge amount of energy.[5]

Properties of internal waves

Internal waves typically have much lower frequencies and higher amplitudes than surface gravity waves because the density differences (and therefore the restoring forces) within a fluid are usually much smaller. Wavelengths vary from centimetres to kilometres with periods of seconds to hours respectively.

The atmosphere and ocean are continuously stratified: potential density generally increases steadily downward. Internal waves in a continuously stratified medium may propagate vertically as well as horizontally. The dispersion relation for such waves is curious: For a freely-propagating internal wave packet, the direction of propagation of energy (group velocity) is perpendicular to the direction of propagation of wave crests and troughs (phase velocity). An internal wave may also become confined to a finite region of altitude or depth, as a result of varying stratification or wind. Here, the wave is said to be ducted or trapped, and a vertically standing wave may form, where the vertical component of group velocity approaches zero. A ducted internal wave mode may propagate horizontally, with parallel group and phase velocity vectors, analogous to propagation within a waveguide.

At large scales, internal waves are influenced both by the rotation of the Earth as well as by the stratification of the medium. The frequencies of these geophysical wave motions vary from a lower limit of the Coriolis frequency (inertial motions) up to the Brunt–Väisälä frequency, or buoyancy frequency (buoyancy oscillations). Above the Brunt–Väisälä frequency, there may be evanescent internal wave motions, for example those resulting from partial reflection. Internal waves at tidal frequencies are produced by tidal flow over topography/bathymetry, and are known as internal tides. Similarly, atmospheric tides arise from, for example, non-uniform solar heating associated with diurnal motion.

Onshore transport of planktonic larvae

Cross-shelf transport, the exchange of water between coastal and offshore environments, is of particular interest for its role in delivering meroplanktonic larvae to often disparate adult populations from shared offshore larval pools.[6] Several mechanisms have been proposed for the cross-shelf of planktonic larvae by internal waves. The prevalence of each type of event depends on a variety of factors including bottom topography, stratification of the water body, and tidal influences.

Internal tidal bores

Similarly to surface waves, internal waves change as they approach the shore. As the ratio of wave amplitude to water depth becomes such that the wave “feels the bottom,” water at the base of the wave slows down due to friction with the sea floor. This causes the wave to become asymmetrical and the face of the wave to steepen, and finally the wave will break, propagating forward as an internal bore.[7][8] Internal waves are often formed as tides pass over a shelf break.[9] The largest of these waves are generated during springtides and those of sufficient magnitude break and progress across the shelf as bores.[10][11] These bores are evidenced by rapid, step-like changes in temperature and salinity with depth, the abrupt onset of upslope flows near the bottom and packets of high frequency internal waves following the fronts of the bores.[12]

The arrival of cool, formerly deep water associated with internal bores into warm, shallower waters corresponds with drastic increases in phytoplankton and zooplankton concentrations and changes in plankter species abundances.[13] Additionally, while both surface waters and those at depth tend to have relatively low primary productivity, thermoclines are often associated with a chlorophyll maximum layer. These layers in turn attract large aggregations of mobile zooplankton[14] that internal bores subsequently push inshore. Many taxa can be almost absent in warm surface waters, yet plentiful in these internal bores.[13]

Surface slicks

While internal waves of higher magnitudes will often break after crossing over the shelf break, smaller trains will proceed across the shelf unbroken.[11][15] At low wind speeds these internal waves are evidenced by the formation of wide surface slicks, oriented parallel to the bottom topography, which progress shoreward with the internal waves.[16][17] Waters above an internal wave converge and sink in its trough and upwell and diverge over its crest.[16] The convergence zones associated with internal wave troughs often accumulate oils and flotsam that occasionally progress shoreward with the slicks.[18][19] These rafts of flotsam can also harbor high concentrations of larvae of invertebrates and fish an order of magnitude higher than the surrounding waters.[19]

Predictable downwellings

Thermoclines are often associated with chlorophyll maximum layers.[14] Internal waves represent oscillations of these thermoclines and therefore have the potential to transfer these phytoplankton rich waters downward, coupling benthic and pelagic systems.[20][21] Areas affected by these events show higher growth rates of suspension feeding ascidians and bryozoans, likely due to the periodic influx of high phytoplankton concentrations.[22] Periodic depression of the thermocline and associated downwelling may also play an important role in the vertical transport of planktonic larvae.

Trapped cores

Large steep internal waves containing trapped, reverse-oscillating cores can also transport parcels of water shoreward.[23] These non-linear waves with trapped cores had previously been observed in the laboratory[24] and predicted theoretically.[25] These waves propagate in environments characterized by high shear and turbulence and likely derive their energy from waves of depression interacting with a shoaling bottom further upstream.[23] The conditions favorable to the generation of these waves are also likely to suspend sediment along the bottom as well as plankton and nutrients found along the benthos in deeper water.



  1. ^ "Caught on camera: Huge UNDERWATER wave spanning hundreds of miles observed from the International Space Station".
  2. ^ (Tritton 1990, pp. 208–214)
  3. ^ (Sutherland 2010, pp 141-151)
  4. ^ Phillips, O.M. (1977). The dynamics of the upper ocean (2nd ed.). Cambridge University Press. p. 37. ISBN 978-0-521-29801-8. OCLC 7319931.
  5. ^ (Cushman-Roisin and Beckers 2011, pp. 7)
  6. ^ Botsford LW, Moloney CL, Hastings A, Largier JL, Powell TM, Higgins K, Quinn JF (1994) The influence of spatially and temporally varying oceanographic conditions on meroplanktonic metapopulations. Deep-Sea Research Part II 41:107–145
  7. ^ Defant A (1961) Physical Oceanography, 2nd edn. Pergamon Press, New York
  8. ^ Cairns JL (1967) Asymmetry of internal tidal waves in shallow coastal waters. Journal of Geophysical Research 72:3563–3565
  9. ^ Rattray MJ (1960) On coastal generation of internal tides. Tellus 12:54–62
  10. ^ Winant CD, Olson JR (1976) The vertical structure of coastal currents. Deep-Sea Research 23:925–936
  11. ^ a b Winant CD (1980) Downwelling over the Southern California shelf. Journal of Physical Oceanography 10:791–799
  12. ^ Shanks AL (1995) Mechanisms of cross-shelf dispersal of larval invertebrates and fish. In: McEdward L (ed) Ecology of marine invertebrate larvae. CRC Press, Boca Raton, FL, p 323–336
  13. ^ a b Leichter JJ, Shellenbarger G, Genovese SJ, Wing SR (1998) Breaking internal waves on a Florida (USA) coral reef: a plankton pump at work? Marine Ecology Progress Series 166:83–97
  14. ^ a b Mann KH, Lazier JRN (1991) Dynamics of marine ecosystems. Blackwell, Boston
  15. ^ Cairns JL (1968) Thermocline strength fluctuations in coastal waters. Journal of Geophysical Research 73:2591–2595
  16. ^ a b Ewing G (1950) Slicks, surface films and internal waves. Journal of Marine Research 9:161–187
  17. ^ LaFond EC (1959) Sea surface features and internal waves in the sea. Indian Journal of Meteorology and Geophysics 10:415–419
  18. ^ Arthur RS (1954) Oscillations in sea temperature at Scripps and Oceanside piers. Deep-Sea Research 2:129–143
  19. ^ a b Shanks AL (1983) Surface slicks associated with tidally forces internal waves may transport pelagic larvae of benthic invertebrates and fishes shoreward. Marine Ecology Progress Series 13:311–315
  20. ^ Haury LR, Brisco MG, Orr MH (1979) Tidally generated internal wave packets in Massachusetts Bay. Nature 278:312–317
  21. ^ Haury LR, Wiebe PH, Orr MH, Brisco MG (1983) Tidally generated high-frequency internal wave-packets and their effects on plankton in Massachusetts Bay. Journal of Marine Research 41:65–112
  22. ^ Witman JD, Leichter JJ, Genovese SJ, Brooks DA (1993) Pulsed Phytoplankton Supply to the Rocky Subtidal Zone: Influence of Internal Waves. Proceedings of the National Academy of Sciences 90:1686–1690
  23. ^ a b Scotti A, Pineda J (2004) Observation of very large and steep internal waves of elevation near the Massachusetts coast. Geophysical Research Letters 31:1–5
  24. ^ Manasseh R, Chin CY, Fernando HJ (1998) The transition from density-driven to wave-dominated isolated flows. Journal of Fluid Mechanics 361:253–274
  25. ^ Derzho OG, Grimshaw R (1997) Solitary waves with a vortex core in a shallow layer of stratified fluid. Physics of Fluids 9:3378–3385


External links

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.

Coral reef

A coral reef is an underwater ecosystem characterized by reef-building corals. Reefs are formed of colonies of coral polyps held together by calcium carbonate. Most coral reefs are built from stony corals, whose polyps cluster in groups.

Coral belongs to the class Anthozoa in the animal phylum Cnidaria, which includes sea anemones and jellyfish. Unlike sea anemones, corals secrete hard carbonate exoskeletons that support and protect the coral. Most reefs grow best in warm, shallow, clear, sunny and agitated water.

Often called "rainforests of the sea", shallow coral reefs form some of Earth's most diverse ecosystems. They occupy less than 0.1% of the world's ocean area, about half the area of France, yet they provide a home for at least 25% of all marine species, including fish, mollusks, worms, crustaceans, echinoderms, sponges, tunicates and other cnidarians. Coral reefs flourish in ocean waters that provide few nutrients. They are most commonly found at shallow depths in tropical waters, but deep water and cold water coral reefs exist on smaller scales in other areas.

Coral reefs deliver ecosystem services for tourism, fisheries and shoreline protection. The annual global economic value of coral reefs is estimated between US$30–375 billion and 9.9 trillion USD. Coral reefs are fragile, partly because they are sensitive to water conditions. They are under threat from excess nutrients (nitrogen and phosphorus), rising temperatures, oceanic acidification, overfishing (e.g., from blast fishing, cyanide fishing, spearfishing on scuba), sunscreen use, and harmful land-use practices, including runoff and seeps (e.g., from injection wells and cesspools).

Deep Cove (New Zealand)

Deep Cove is an arm of Doubtful Sound, a deep indentation in the southwest coast of New Zealand's South Island. Along with the Hall Arm, which lies to the southwest of Deep Cove, it forms one of the two most remote parts of the sound from the Tasman Sea, with its mouth being 32 kilometres (20 mi) from the mouth of Doubtful Sound. Elizabeth Island lies close to the junction of Deep Cove and the Hall Arm. Deep Cove by itself is about four kilometres long and is home to several waterfalls, including Helena Falls and Lady Alice Falls.

Until the 1960s, Deep Cove was only accessible from the sea or via the Wilmot Pass walking track. In 1964, however, the cove saw the start of considerable activity as it became an important part of the Manapouri Hydroelectricity Project as the site of the tailrace tunnel from Lake Manapouri. A 10 kilometres (6.2 mi) tunnel connects the cove with the lake. The tunnel was completed in late 1969, with the power station became operational the following year. A second tunnel was started in 1997 and became operational in 2002.The discharge of clear fresh water has affected fauna and flora by letting light into the lower layers of the sound. Nevertheless, this is an area naturally high in fresh water inflows (7.6 metres of rain falls annually). In the 1980s an application was made to extract and ship the water overseas but the project did not proceed.

The strong salinity stratification generated by the freshwater layer has been the focus of a number of oceanographic expeditions using the cove as a natural laboratory. The research found that the riverine nature of the inflow gradually dissipated over a few km but that the underside of the freshwater plume sustains some of the sharpest stratification ever observed. The measurements detected internal wave motion both from the nearby river inlet and from the ocean 40 km away.

Today, Deep Cove serves as the starting point for Doubtful Sound cruises on tour boats stationed at a small wharf in Wanganella Cove, within Deep Cove. The full-day tours depart from Manapouri by boat to travel across Lake Manapouri, followed by a bus ride over Wilmot Pass, and return the same way after the boat tour in Doubtful Sound. The wharf in Deep Cove is also used for unloading large components such as transformers from barges, to be delivered to the Manapouri Power Station via Wilmot Pass, as there is no other road access to the power plant and these components would be too large to ferry across Lake Manapouri from the other side.

Hydraulic jump

A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface. The rapidly flowing liquid is abruptly slowed and increases in height, converting some of the flow's initial kinetic energy into an increase in potential energy, with some energy irreversibly lost through turbulence to heat. In an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shockwave forms.

It was first observed and documented by Leonardo da Vinci in 1500s. The mathematics were first described by Giorgio Bidone when he published a paper called Experiences sur le remou et sur la propagation des ondes.The phenomenon is dependent upon the initial fluid speed. If the initial speed of the fluid is below the critical speed, then no jump is possible. For initial flow speeds which are not significantly above the critical speed, the transition appears as an undulating wave. As the initial flow speed increases further, the transition becomes more abrupt, until at high enough speeds, the transition front will break and curl back upon itself. When this happens, the jump can be accompanied by violent turbulence, eddying, air entrainment, and surface undulations, or waves.

There are two main manifestations of hydraulic jumps and historically different terminology has been used for each. However, the mechanisms behind them are similar because they are simply variations of each other seen from different frames of reference, and so the physics and analysis techniques can be used for both types.

The different manifestations are:

The stationary hydraulic jump – rapidly flowing water transitions in a stationary jump to slowly moving water as shown in Figures 1 and 2.

The tidal bore – a wall or undulating wave of water moves upstream against water flowing downstream as shown in Figures 3 and 4. If considered from a frame of reference which moves with the wave front, you can see that this case is physically similar to a stationary jump.A related case is a cascade – a wall or undulating wave of water moves downstream overtaking a shallower downstream flow of water as shown in Figure 5. If considered from a frame of reference which moves with the wave front, this is amenable to the same analysis as a stationary jump.

These phenomena are addressed in an extensive literature from a number of technical viewpoints.

Index of physics articles (I)

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

To navigate by individual letter use the table of contents below.

Index of wave articles

This is a list of Wave topics.

Internal tide

Internal tides are generated as the surface tides move stratified water up and down sloping topography, which produces a wave in the ocean interior. So internal tides are internal waves at a tidal frequency. The other major source of internal waves is the wind which produces internal waves near the inertial frequency. When a small water parcel is displaced from its equilibrium position, it will return either downwards due to gravity or upwards due to buoyancy. The water parcel will overshoot its original equilibrium position and this disturbance will set off an internal gravity wave. Munk (1981) notes, "Gravity waves in the ocean's interior are as common as waves at the sea surface-perhaps even more so, for no one has ever reported an interior calm."


An isopycnal is a line connecting points of a specific density or potential density. Isopycnals are often displayed graphically to help visualize "layers" of water in the ocean or gases in the atmosphere in a similar manner to how contour lines are used in topographic maps to help visualize topography.

Kenneth M. Watson

Kenneth Marshall Watson (born September 7, 1921) is a theoretical physicist and physical oceanographer.Watson graduated in 1943 with BS in electrical engineering from Iowa State College. From 1943 to 1946 he was a researcher at the United States Naval Research Laboratory in Washington, D.C. During his work for the U.S. Navy he went to night school at George Washington University. He graduated from the University of Iowa with Ph.D. in 1948 with thesis The polarizability of the meson-charge cloud of a neutron in an external electrostatic field. He was from 1948 to 1949 an Atomic Energy Commission (AEC) Fellow at the Institute for Advanced Study and from 1949 to 1951 an AEC Fellow at the Berkeley Radiation Laboratory. He was from 1951 to 1954 an assistant professor of physics at Indiana University and from 1954 to 1957 an associate professor of physics at the University of Wisconsin, Madison. In 1953 he was elected a fellow of the American Physical Society. From 1957 to 1981 he was a staff member of Lawrence Berkeley National Laboratory, as well as a professor of physics at the University of California, Berkeley. In 1974 he was elected a member of the National Academy of Sciences. From 1981 to 1991 he was the director of the Marine Physical Laboratory, Scripps Institute of Oceanography, as well as a professor of physical oceanography at the University of California, San Diego. In 1991 he retired as professor emeritus. His doctoral students include Shang-keng Ma.Watson was an advisor to various United States organizations associated with the United States Department of Defense. In 1959 he worked with Marvin L. Goldberger, Keith Brueckner, and Murray Gell-Mann to join John A. Wheeler, Charles H. Townes, and others in forming the JASON group of government advisors. Watson remained in JASON until 1998. In 1971 he, with four others, formed the company Physical Dynamics, Inc. and then remained on the board of directors until 1981.He did research in the early 1950s on nuclear and pi meson physics, as well as quantum mechanical collision processes, and in the late 1950s on plasma physics

and controlled nuclear fusion.To quote Watson:

In the mid-1960’s I began a series of investigations, in collaboration with M. L. Goldberger of the observation of “entangled” quantum mechanical systems. We were concerned with sequential measurements and interference effects for correlated systems.

Watson did research in the early 1970s on atomic and molecular scattering and in the late 1970s on fluid mechanics related to oceanography. He worked in the early 1980s on applying methods of statistical mechanics to internal wave turbulence and in the early 1990’s on analyzing the coupling of surface and internal gravity waves.To quote Watson:

In the mid 1990’s my interest in nonlinear classical mechanics and ocean surface waves led to a study of capillary waves (few centimeter wavelengths) interacting with longer waves (10 cm to a meter wavelengths).

Ocean surface wave dynamics can be formulated as nonlinear interactions among a set of harmonic oscillators. The Hamiltonian formulation of this is mathematically very similar to the equations of classical and quantum mechanical field theory that I had encountered at the beginning of my career. I developed a canonical transformation technique which greatly simplified numerical integration of the equations. Calculations of the “long wave effect” agreed with observations of the radar scattering.

He married in 1946 and is the father of two sons. His father was Louis Erwin Watson (1884–1957) and his mother was Irene Marshall Watson (born 1886 in Roanoke, Illinois).

Ocean acoustic tomography

Ocean acoustic tomography is a technique used to measure temperatures and currents over large regions of the ocean. On ocean basin scales, this technique is also known as acoustic thermometry. The technique relies on precisely measuring the time it takes sound signals to travel between two instruments, one an acoustic source and one a receiver, separated by ranges of 100–5000 km. If the locations of the instruments are known precisely, the measurement of time-of-flight can be used to infer the speed of sound, averaged over the acoustic path. Changes in the speed of sound are primarily caused by changes in the temperature of the ocean, hence the measurement of the travel times is equivalent to a measurement of temperature. A 1 °C change in temperature corresponds to about 4 m/s change in sound speed. An oceanographic experiment employing tomography typically uses several source-receiver pairs in a moored array that measures an area of ocean.

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.

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.

Poor Knights Islands

The Poor Knights Islands are a group of islands off the east coast of the Northland Region of the North Island of New Zealand. They lie 50 kilometres (31 mi) to the north-east of Whangarei, and 22 kilometres (14 mi) offshore halfway between Bream Head and Cape Brett. Uninhabited since the 1820s, they are a nature reserve and popular underwater diving spot, with boat tours typically departing from Tutukaka. The Poor Knights Islands Marine Reserve surrounds the island. Beaglehole (1955) comments that the origin of the island name is not clear, and speculates that the name could be related to the Poor Knights of Windsor, or, that the islands were named for their resemblance to Poor Knight's Pudding, a bread-based dish topped with egg and fried, popular at the time of discovery by Europeans.


A seiche ( SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbours and seas. The key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave.

The term was promoted by the Swiss hydrologist François-Alphonse Forel in 1890, who was the first to make scientific observations of the effect in Lake Geneva, Switzerland. The word originates in a Swiss French dialect word that means "to sway back and forth", which had apparently long been used in the region to describe oscillations in alpine lakes.

Seiches in harbours can be caused by long period or infragravity waves, which are due to subharmonic nonlinear wave interaction with the wind waves, having periods longer than the accompanying wind-generated waves.

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".

Walter Munk

Walter Heinrich Munk (October 19, 1917 – February 8, 2019) was an American physical oceanographer. He was a professor of geophysics at the Scripps Institution of Oceanography at the University of California, San Diego in La Jolla. Born to a prominent Austrian family, in 1932 Munk was sent to school in the United States at age 14. Abandoning a New York banking career, Munk obtained a scientific education at the California Institute of Technology and his doctorate from Scripps. During World War II, Munk and his doctoral advisor Harald Sverdrup developed methods for predicting surf conditions on beaches, saving countless lives during allied landings in North Africa, the Pacific, and Northern Europe. After the war, Scripps grew from a small biological station to a major research institution. Munk and his wife Judy were active in developing the Scripps campus and integrating it with the new University of California, San Diego.

One of the first to bring statistical methods to the analysis of oceanographic data, Munk's work is noted for creating fruitful areas of research that continue to be explored. These areas include surface waves, geophysical implications of variations in the Earth's rotation, tides, internal waves, deep-ocean drilling into the sea floor, acoustical measurements of ocean properties, sea level rise, and climate change. In a 1991 experiment, Munk and his collaborators tested the ability of underwater sound to propagate from the Southern Indian Ocean across all ocean basins. The aim was to use the acoustic signals to measure changes in broad-scale ocean temperatures. The experiment was criticized by environmental groups, who expected that the loud acoustic signals would adversely affect marine life. Munk was a member of the JASON think tank, and he held a Secretary of the Navy/Chief of Naval Operations Oceanography Chair. Munk died at age 101 in La Jolla, California.


In physics, mathematics, and related fields, a wave is a disturbance (change from equilibrium) of one or more fields such that the field values oscillate repeatedly about a stable equilibrium (resting) value. If the relative amplitude of oscillation at different points in the field remains constant, the wave is said to be a standing wave. If the relative amplitude at different points in the field changes, the wave is said to be a traveling wave. Waves can only exist in fields when there is a force that tends to restore the field to equilibrium.

The types of waves most commonly studied in physics are mechanical and electromagnetic. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A traveling mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves in air are variations of the local pressure that propagate by collisions between gas molecules. Other examples of mechanical waves are seismic waves, gravity waves, vortices, and shock waves. In an electromagnetic wave the electric and magnetic fields oscillate. A traveling electromagnetic wave (light) consists of a combination of variable electric and magnetic fields, that propagates through space according to Maxwell's equations. Electromagnetic waves can travel through transparent dielectric media or through a vacuum; examples include radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.

Other types of waves include gravitational waves, which are disturbances in a gravitational field that propagate according to general relativity; heat diffusion waves; plasma waves, that combine mechanical deformations and electromagnetic fields; reaction-diffusion waves, such as in the Belousov–Zhabotinsky reaction; and many more.

Mechanical and electromagnetic waves transfer energy,, momentum, and information, but they do not transfer particles in the medium. In mathematics and electronics waves are studied as signals. On the other hand, some waves do not appear to move at all, like standing waves (which are fundamental to music) and hydraulic jumps. Some, like the probability waves of quantum mechanics, may be completely static.

A physical wave is almost always confined to some finite region of space, called its domain. For example, the seismic waves generated by earthquakes are significant only in the interior and surface of the planet, so they can be ignored outside it. However, waves with infinite domain, that extend over the whole space, are commonly studied in mathematics, and are very valuable tools for understanding physical waves in finite domains.

A plane wave seems to travel in a definite direction, and has constant value over any plane perpendicular to that direction. Mathematically, the simplest waves are the sinusoidal ones in which each point in the field experiences simple harmonic motion. Complicated waves can often be described as the sum of many sinusoidal plane waves. A plane wave can be a transverse, if its effect at each point is described by a vector that is perpendicular to the direction of propagation or energy transfer; or longitudinal, if the describing vectors are parallel to the direction of energy propagation. While mechanical waves can be both transverse and longitudinal, electromagnetic waves are transverse in free space.

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.

Wind wave

In fluid dynamics, wind waves, or wind-generated waves, are water surface waves that occur on the free surface of the oceans and other bodies (like lakes, rivers, canals, puddles or ponds). They result from the wind blowing over an area of fluid surface. Waves in the oceans can travel thousands of miles before reaching land. Wind waves on Earth range in size from small ripples, to waves over 100 ft (30 m) high.When directly generated and affected by local waters, a wind wave system is called a wind sea. After the wind ceases to blow, wind waves are called swells. More generally, a swell consists of wind-generated waves that are not significantly affected by the local wind at that time. They have been generated elsewhere or some time ago. Wind waves in the ocean are called ocean surface waves.

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 the water seas of Earth, the hydrocarbon seas of Titan may also have wind-driven waves.

Ocean zones
Sea level


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