Waves and shallow water

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When waves travel into areas of shallow water, they begin to be affected by the ocean bottom. The free orbital motion of the water is disrupted, and water particles in orbital motion no longer return to their original position. As the water becomes shallower, the swell becomes higher and steeper, ultimately assuming the familiar sharp-crested wave shape. After the wave breaks, it becomes a wave of translation and erosion of the ocean bottom intensifies.

Ocean A body of water that composes much of a planets hydrosphere

An ocean is a body of water that composes much of a planet's hydrosphere. On Earth, an ocean is one of the major conventional divisions of the World Ocean. These are, in descending order by area, the Pacific, Atlantic, Indian, Southern (Antarctic), and Arctic Oceans. The word "ocean" is often used interchangeably with "sea" in American English. Strictly speaking, a sea is a body of water partly or fully enclosed by land, though "the sea" refers also to the oceans.

Breaking wave A wave that becomes unstable as a consequence of excessive steepness

In fluid dynamics, a breaking wave is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be transformed into turbulent kinetic energy. At this point, simple physical models that describe wave dynamics often become invalid, particularly those that assume linear behaviour.

See also

Ballantine scale A biologically defined scale for measuring the degree of exposure level of wave action on a rocky shore

The Ballantine scale is a biologically defined scale for measuring the degree of exposure level of wave action on a rocky shore. Devised in 1961 by W. J. Ballantine, then at the zoology department of Queen Mary College, London, the scale is based on the observation that where shoreline species are concerned "Different species growing on rocky shores require different degrees of protection from certain aspects of the physical environment, of which wave action is often the most important." The species present in the littoral zone therefore indicate the degree of the shore's exposure.

Boussinesq approximation (water waves) An approximation valid for weakly non-linear and fairly long waves

In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation. The 1872 paper of Boussinesq introduces the equations now known as the Boussinesq equations.

Mild-slope equation The combined effects of diffraction and refraction for water waves propagating over variable depth and with lateral boundaries

In fluid dynamics, the mild-slope equation describes the combined effects of diffraction and refraction for water waves propagating over bathymetry and due to lateral boundaries—like breakwaters and coastlines. It is an approximate model, deriving its name from being originally developed for wave propagation over mild slopes of the sea floor. The mild-slope equation is often used in coastal engineering to compute the wave-field changes near harbours and coasts.


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Gravity wave Wave generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium

In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the ocean, which gives rise to wind waves.

Shoal A natural landform that rises from the bed of a body of water to near the surface and is covered by unconsolidated material

In oceanography, geomorphology, and earth sciences, a shoal is a natural submerged ridge, bank, or bar that consists of, or is covered by, sand or other unconsolidated material, and rises from the bed of a body of water to near the surface. Often it refers to those submerged ridges, banks, or bars that rise near enough to the surface of a body of water as to constitute a danger to navigation. Shoals are also known as sandbanks, sandbars, or gravelbars. Two or more shoals that are either separated by shared troughs or interconnected by past or present sedimentary and hydrographic processes are referred to as a shoal complex.

Physical oceanography The study of physical conditions and physical processes within the ocean

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

Wind wave Surface waves generated by wind that occur on the free surface of bodies of water

In fluid dynamics, wind waves, or wind-generated waves, are surface waves that occur on the free surface of bodies of water. 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.

Upper shoreface The portion of the seafloor that is shallow enough to be agitated by everyday wave action

Upper Shoreface refers to the portion of the seafloor that is shallow enough to be agitated by everyday wave action, the wave base.

Wave base The maximum depth at which a water waves passage causes significant water motion

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.

Internal wave Gravity waves that oscillate within a fluid medium with density variation with depth, rather than on the surface

Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must decrease 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, 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.

A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the phase speed of the wave crests is equal to the group speed of the wave energy for all frequencies. This means that it retains its shape as it moves in the alongshore direction over time.

In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, with gravity and surface tension as the restoring forces. As a result, water with a free surface is generally considered to be a dispersive medium.

Wave tank A laboratory setup for observing the behavior of surface waves

A wave tank is a laboratory setup for observing the behavior of surface waves. The typical wave tank is a box filled with liquid, usually water, leaving open or air-filled space on top. At one end of the tank an actuator generates waves; the other end usually has a wave-absorbing surface. A similar device is the ripple tank, which is flat and shallow and used for observing patterns of surface waves from above.

Geostrophic current An oceanic flow in which the pressure gradient force is balanced by the Coriolis effect

A geostrophic current is an oceanic current in which the pressure gradient force is balanced by the Coriolis effect. The direction of geostrophic flow is parallel to the isobars, with the high pressure to the right of the flow in the Northern Hemisphere, and the high pressure to the left in the Southern Hemisphere. This concept is familiar from weather maps, whose isobars show the direction of geostrophic flow in the atmosphere. Geostrophic flow may be either barotropic or baroclinic. A geostrophic current may also be thought of as a rotating shallow water wave with a frequency of zero. The principle of geostrophy is useful to oceanographers because it allows them to infer ocean currents from measurements of the sea surface height or from vertical profiles of seawater density taken by ships or autonomous buoys. The major currents of the world's oceans, such as the Gulf Stream, the Kuroshio Current, the Agulhas Current, and the Antarctic Circumpolar Current, are all approximately in geostrophic balance and are examples of geostrophic currents.

Shallow water equations A set of partial differential equations that describe the flow below a pressure surface in a fluid

The shallow water equations are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid. The shallow water equations in unidirectional form are also called Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant.

Underwater acoustics The study of the propagation of sound in water and the interaction of sound waves with the water and its boundaries

Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Typical frequencies associated with underwater acoustics are between 10 Hz and 1 MHz. The propagation of sound in the ocean at frequencies lower than 10 Hz is usually not possible without penetrating deep into the seabed, whereas frequencies above 1 MHz are rarely used because they are absorbed very quickly. Underwater acoustics is sometimes known as hydroacoustics.

Wave shoaling The effect by which surface waves entering shallower water change in wave height

In fluid dynamics, wave shoaling is the effect by which surface waves entering shallower water change in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth. Under stationary conditions, a decrease in transport speed must be compensated by an increase in energy density in order to maintain a constant energy flux. Shoaling waves will also exhibit a reduction in wavelength while the frequency remains constant.

Ursell number Dimensionless number indicating the nonlinearity of long surface gravity waves on a fluid layer.

In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953.

In fluid dynamics, Airy wave theory gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational. This theory was first published, in correct form, by George Biddell Airy in the 19th century.

A Sverdrup wave is a wave in the ocean, which is affected by gravity and Earth's rotation.

Greens law The evolution of non-breaking surface gravity waves propagating in shallow water of gradually varying depth and width

In fluid dynamics, Green's law describes the evolution of non-breaking surface gravity waves propagating in shallow water of gradually varying depth and width. The law is named after George Green. In its simplest form, for wavefronts and depth contours parallel to each other, it states: