In fluid dynamics In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications,, wind waves or, more precisely, wind-generated waves are surface waves In physics, a surface wave is a mechanical wave that propagates along the interface between differing media, usually two fluids with different densities. A surface wave can also be an electromagnetic wave guided by a refractive index gradient. In radio transmission, a ground wave is a surface wave that propagates close to the surface of the Earth that occur on the free surface In physics a free surface is the surface of a fluid that is subject to constant perpendicular normal stress and zero parallel shear stress, such as the boundary between two homogenous fluids, for example liquid water and the air in the Earth's atmosphere. Unlike liquids, gases cannot form a free surface on their own of oceans An ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface (~3.61 X 1014 m2) is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas, seas A sea generally refers to a large body of salt water, but the term is used in other contexts as well. Most commonly, the term refers to a large expanse of saline water connected with an ocean, and is commonly used as a synonym for ocean. It is also used sometimes to describe a large saline lake that lacks a natural outlet, such as the Caspian Sea, lakes A lake is a terrain feature , a body of liquid on the surface of a world that is localized to the bottom of basin (another type of landform or terrain feature; that is not global). Another definition is a body of fresh or salt water of considerable size that is surrounded by land. On Earth a body of water is considered a lake when it is inland,, rivers A river is a natural watercourse, usually freshwater, flowing toward an ocean, a lake, a sea, or another river. In a few cases, a river simply flows into the ground or dries up completely before reaching another body of water. Small rivers may also be called by several other names, including stream, creek, brook, rivulet, and rill; there is no, and canals Smaller transportation canals can carry barges or narrowboats, while ship canals allow seagoing ships to travel to an inland port , or from one sea or ocean to another (e.g.: Caledonian Canal, Panama Canal) or even on small puddles A puddle is a small accumulation of liquid, usually water, on a surface. It can form either by pooling in a depression on the surface, or by surface tension upon a flat surface. A puddle is generally considered to be small enough to step over or shallow enough to walk through, and too small to traverse with a boat, raft or submarine and ponds A pond is a body of standing water, either natural or man-made, that is usually smaller than a lake. A wide variety of man-made bodies of water are classified as ponds, including water gardens designed for aesthetic ornamentation, fish ponds designed for commercial fish breeding, and solar ponds designed to store thermal energy. They usually result from the wind Wind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space. Winds are commonly classified by their spatial blowing over a vast enough stretch of fluid surface. Some waves in the oceans can travel thousands of miles before reaching land. Wind waves range in size from small ripples A capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics are dominated by the effects of surface tension to huge rogue waves Rogue waves are relatively large and spontaneous ocean surface waves that are a threat even to large ships and ocean liners. In oceanography, they are more precisely defined as waves whose height is more than twice the significant wave height (SWH), which is itself defined as the mean of the largest third of waves in a wave record. Therefore rogue.[1] When directly being generated and affected by the local winds, a wind wave system is called a wind sea. After the wind ceases to blow, wind waves are called swell A swell, in the context of an ocean, sea or lake, is a formation of long-wavelength surface waves. Swells are far more stable in their directions and frequency than normal wind waves, having often travelled long distances since their formation by tropical storms or other wind systems. Or, more generally, a swell consists of wind generated waves that are not — or hardly — affected by the local wind at the same moment. They have been generated elsewhere, or some time ago.[2] Wind waves in the ocean are called ocean surface waves.

Tsunamis A tsunami (Japanese: 津波 [tsɯnami], lit. 'harbor wave'; English pronunciation: /suːˈnɑːmi/ (t)soo-NAH-mee) or tidal wave is a series of water waves (called a tsunami wave train) caused by the displacement of a large volume of a body of water, usually an ocean, but can occur in large lakes. Tsunamis are a frequent occurrence in Japan; are a specific type of wave not caused by wind but by geological effects. In deep water, tsunamis are not visible because they are small in height and very long in wavelength In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and. They may grow to devastating proportions at the coast due to reduced water depth.

Contents

Wave formation

NOAA The National Oceanic and Atmospheric Administration , pronounced /ˈno(ʊ).ə/, like "noah", is a scientific agency within the United States Department of Commerce focused on the conditions of the oceans and the atmosphere. NOAA warns of dangerous weather, charts seas and skies, guides the use and protection of ocean and coastal ship Delaware II in bad weather on Georges Bank Georges Bank is a large elevated area of the sea floor which separates the Gulf of Maine from the Atlantic Ocean and is situated between Cape Cod, Massachusetts and Cape Sable Island, Nova Scotia (Canada).

The great majority of large breakers one observes on a beach result from distant winds. Four factors influence the formation of wind waves:[3]

All of these factors work together to determine the size of wind waves. The greater each of the variables, the larger the waves. Waves are characterized by:

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 In mathematics, an average, central tendency of a data set is a measure of the "middle" or "expected" value of the data set height of the highest one-third of the waves in a given time period (usually chosen somewhere in the range from 20 minutes to twelve hours), or in a specific wave or storm system. Given the variability of wave height, the largest individual waves are likely to be about twice the reported significant wave height for a particular day or storm.

Types of wind waves

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 Surface tension is a property of the surface of a liquid caused by cohesion of like molecules, which is responsible for many of the behaviours of liquids. Seas are the larger-scale, often irregular motions that form under sustained winds. They tend to last much longer, even after the wind has died, and the restoring force that allows them to persist is gravity. As seas propagate away from their area of origin, they naturally separate according to their direction and wavelength. The regular wave motions formed in this way are known as swells.

Individual "rogue waves Rogue waves are relatively large and spontaneous ocean surface waves that are a threat even to large ships and ocean liners. In oceanography, they are more precisely defined as waves whose height is more than twice the significant wave height (SWH), which is itself defined as the mean of the largest third of waves in a wave record. Therefore rogue" (also called "freak waves", "monster waves", "killer waves", and "king waves") sometimes occur, up to heights near 30 meters, and being much higher than the other waves in the sea state. Such waves are distinct from tides 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. The tides occur with a period of approximately 12 hours and 25 minutes, and with an amplitude that is influenced by the alignment of the sun and moon and the shape of the near-shore, caused by the Moon The Moon is Earth's only natural satellite[nb 4] and is the fifth largest satellite in the Solar System. It is the largest natural satellite in the Solar System relative to the size of its planet, a quarter the diameter of Earth and 1/81 its mass, and is the second densest satellite after Io. It is in synchronous rotation with Earth, always and Sun The Sun is the star at the center of the Solar System. It has a diameter of about 1,392,000 kilometers , about 109 times that of Earth, and its mass (about 2 × 1030 kilograms, 330,000 times that of Earth) accounts for about 99.86% of the total mass of the Solar System. About three quarters of the Sun's mass consists of hydrogen, while the rest is's gravitational pull The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force exerted on one body by a second body is not constant across its diameter. The side nearest to the second body experiences a greater force, while the opposite side experiences a lesser force, tsunamis A tsunami (Japanese: 津波 [tsɯnami], lit. 'harbor wave'; English pronunciation: /suːˈnɑːmi/ (t)soo-NAH-mee) or tidal wave is a series of water waves (called a tsunami wave train) caused by the displacement of a large volume of a body of water, usually an ocean, but can occur in large lakes. Tsunamis are a frequent occurrence in Japan; that are caused by underwater earthquakes An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. Earthquakes are measured with a seismometer; a device which also records is known as a seismograph. The moment magnitude (or the related and mostly obsolete Richter magnitude) of an earthquake is conventionally reported, with magnitude 3 or or landslides A landslide or landslip is a geological phenomenon which includes a wide range of ground movement, such as rock falls, deep failure of slopes and shallow debris flows, which can occur in offshore, coastal and onshore environments. Although the action of gravity is the primary driving force for a landslide to occur, there are other contributing, and waves generated by underwater explosions An underwater explosion, also known as an UNDEX, is an explosion beneath the surface of water. The type of explosion may be chemical or nuclear. They are categorized in accordance with their depth beneath the water's surface, because this has a strong influence on their effects or the fall of meteorites A meteorite is a natural object originating in outer space that survives impact with the Earth's surface. Meteorites can be big or small. Most meteorites derive from small astronomical objects called meteoroids, but they are also sometimes produced by impacts of asteroids. When it enters the atmosphere, impact pressure causes the body to heat up — all having far longer wavelengths In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and than wind waves.

Wave breaking

Big wave breaking Surf in a rocky irregular bottom. Porto Covo, west coast of Portugal See also: surf wave and breaking wave In physics, 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 in turbulent kinetic energy . At this point, simple physical models describing the dynamics of the wave will often become invalid, particularly those which

Some waves undergo a phenomenon A phenomenon , plural phenomena, is any observable occurrence. In popular usage, a phenomenon often refers to an extraordinary event. In scientific usage, a phenomenon is any event that is observable, however commonplace it might be, even if it requires the use of instrumentation to observe it. For example, in physics, a phenomenon may be a called "breaking". A breaking wave In physics, 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 in turbulent kinetic energy . At this point, simple physical models describing the dynamics of the wave will often become invalid, particularly those which 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 is inevitable.

Individual waves in deep water break when the wave steepness — the ratio In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Example: For every Spoon of sugar, you need 2 spoons of flour of the wave height H to the wavelength In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and 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.[4] Waves can also break if the wind grows strong enough to blow the crest off the base of the wave.

Three main types of breaking waves are identified by surfers Two major subdivisions within stand-up surfing are longboarding and shortboarding, reflecting differences in surfboard design including surfboard length, and riding style or surf lifesavers Surf lifesaving is a multifaceted movement that comprises key aspects of voluntary lifeguard services and competitive surf sport. Originating in early 20th century Australia, the movement has expanded globally to other countries including New Zealand, Ireland, South Africa, and the United States. Their varying characteristics make them more or less suitable for surfing, and present different dangers.

Science of waves

Shallow water wave (Animation) Deep water wave (Animation) Motion of a particle in a wind wave. A = At deep water. The orbital In physics, an orbit is the gravitationally curved path of one object around a point or another body, for example the gravitational orbit of a planet around a star motion of fluid particles decreases rapidly with increasing depth below the surface. B = At shallow water (sea floor is now at B). The elliptical movement of a fluid particle flattens with decreasing depth. 1 = Propagation direction. 2 = Wave crest. 3 = Wave trough. See also: Airy wave theory

Wind waves are mechanical waves In mathematics and science, a wave is a disturbance that travels through space and time, usually by transference of energy. Waves are described by a wave function that can take on many forms depending on the type of wave. A mechanical wave is a wave that propagates through a medium due to restoring forces produced upon its deformation. For example, that propagate along the interface between water Water is a chemical substance with the chemical formula H2O. Its molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state, water vapor or steam 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 forces perturb the equilibrium of the water surface. These forces transfer energy from the air to the water, forming waves. In the case of monochromatic linear plane waves in deep water, particles near the surface move in circular paths, making wind waves a combination of longitudinal (back and forth) and transverse (up and down) wave motions. When waves propagate in shallow water, (where the depth is less than half the wavelength) the particle trajectories are compressed into ellipses.[5][6]

As the wave amplitude (height) increases, the particle paths no longer form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as Stokes drift.[7][8]

For intermediate and shallow water, the Boussinesq equations are applicable, combining frequency dispersion and nonlinear effects. And in very shallow water, the shallow water equations can be used.

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 the surface. The phase speed of the surface wave (also called the celerity) is well approximated by

where

c = phase speed;
λ = wavelength;
d = water depth;
g = acceleration due to gravity at the Earth's surface.

In deep water, where , so and the hyperbolic tangent approaches 1, the speed c, in m/s, approximates , when λ is measured in meters. 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.

When several wave trains are present, as is always the case in nature, the waves form groups. In deep water the groups travel at a group velocity which is half of the phase speed.[9] Following a single wave in a group one can see the wave appearing at the back of the group, growing and finally disappearing at the front of the group.

As the water depth d decreases towards the coast, this will have an effect: wave height changes due to wave shoaling and refraction. As the wave height increases, the wave may become unstable when the crest of the wave moves faster than the trough. This causes surf, a breaking of the waves.

The movement of wind waves can be captured by wave energy devices. The energy density (per unit area) of regular sinusoidal waves depends on the water density ρ, gravity acceleration g and the wave height H (which is equal to twice the amplitude, a):

The velocity of propagation of this energy is the group velocity.

Wind wave models

Main article: Wind wave model

Surfers are very interested in the wave forecasts. There are many websites that provide predictions of the surf quality for the upcoming days and weeks. Wind wave models are driven by more general weather models that predict the winds and pressures over the oceans, seas and lakes.

Wind wave models are also an important part of examining the impact of shore protection and beach nourishment proposals. For many beach areas there is only patchy information about the wave climate, therefore estimating the effect of wind waves is important for managing littoral environments.

See also

Notes

  1. ^ Tolman, H.L. (2008), "Practical wind wave modeling", in Mahmood, M.F., CBMS Conference Proceedings on Water Waves: Theory and Experiment, Howard University, USA, 13–18 May 2008: World Scientific Publ., (in press), ISBN 978-981-4304-23-8, http://polar.ncep.noaa.gov/mmab/papers/tn270/Howard_08.pdf
  2. ^ Holthuijsen (2007), page 5.
  3. ^ Young, I. R. (1999). Wind generated ocean waves. Elsevier. ISBN 0080433170. p. 83.
  4. ^ R.J. Dean and R.A. Dalrymple (2002). Coastal processes with engineering applications. Cambridge University Press. ISBN 0-521-60275-0. p. 96–97.
  5. ^ For the particle trajectories within the framework of linear wave theory, see for instance: Phillips (1977), page 44. Lamb, H. (1994). Hydrodynamics (6th edition ed.). Cambridge University Press. ISBN 9780521458689. Originally published in 1879, the 6th extended edition appeared first in 1932. See §229, page 367. L. D. Landau and E. M. Lifshitz (1986). Fluid mechanics. Course of Theoretical Physics. 6 (Second revised edition ed.). Pergamon Press. ISBN 0 08 033932 8. See page 33.
  6. ^ A good illustration of the wave motion according to linear theory is given by Prof. Robert Dalrymple Java applet.
  7. ^ For nonlinear waves, the particle paths are not closed, as found by George Gabriel Stokes in 1847, see the original paper by Stokes. Or in Phillips (1977), page 44: "To this order, it is evident that the particle paths are not exactly closed … pointed out by Stokes (1847) in his classical investigation".
  8. ^ Solutions of the particle trajectories in fully nonlinear periodic waves and the Lagrangian wave period they experience can for instance be found in: J.M. Williams (1981). "Limiting gravity waves in water of finite depth". Philosophical Transactions of the Royal Society of London, Series A 302 (1466): 139–188. doi:10.1098/rsta.1981.0159. J.M. Williams (1985). Tables of progressive gravity waves. Pitman. ISBN 978-0273087335.
  9. ^ In deep water, the group velocity is half the phase velocity, as is shown here. Another reference is [1].

References

External links

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