North Pacific storm waves as seen from the NOAA M/V Noble Star, Winter 1989. The Pacific Ocean is the largest of the Earth 's Oceanic divisions The National Oceanic and Atmospheric Administration ( NOAA) is a scientific agency within the United States Department of Commerce focused on the conditions of the A ship prefix is a combination of letters usually abbreviations used in front of the name of a civilian or naval Ship.
Ocean waves

Ocean surface waves are surface waves that occur in the upper layer of the ocean. In Physics, surface wave can refer to a Mechanical wave that propagates along the interface between differing media usually two fluids with different densities An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. They usually result from wind, and are also referred to as wind waves. These waves may travel thousands of miles before striking land. They range in size from small ripples to huge rogue waves. A capillary wave is a Wave travelling along the interface between two fluids whose dynamics are dominated by the effects of Surface tension. Rogue waves, also known as freak waves, monster waves or extreme waves, are relatively large and spontaneous Ocean surface waves that are a threat There is little actual forward motion of individual water particles in a wave, despite the large amount of energy it may carry forward.

Tsunamis are a specific type of surface wave not caused by wind but by geological effects. A tsunami ((tsuːˈnɑːmi is a series of waves created when A tsunami ((tsuːˈnɑːmi is a series of waves created when In deep water, tsunamis are not visible because they are small in height and very long in wavelength. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. They may grow to devastating proportions at the coast due to reduced water depth.

## Wave formation

NOAA ship Delaware II in bad weather on Georges Bank. The National Oceanic and Atmospheric Administration ( NOAA) is a scientific agency within the United States Department of Commerce focused on the conditions of the 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,

The great majority of large breakers one sees on an ocean beach result from distant winds. Three factors influence the formation of wind waves:

• wind speed,
• distance of open water that the wind has blown over; called fetch, and
• time duration the wind has blown over a given area. Wind is the flow of Air or other Gases that compose an Atmosphere (including but not limited to the Earth's) Fetch, often called the fetch length, is a term for the length of water over which a given Wind has blown A tone may be sustained for varying lengths of time. duration is a property of tone that becomes one of the bases rhythem or an amount of Time or a particular time

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

• Height (from trough to crest),
• Wavelength (from crest to crest),
• Period (time interval between arrival of consecutive crests at a stationary point),
• Wave propagation direction (with respect to north). A crest is the point on a Wave with the greatest positive value or upward displacement in a Cycle. A crest is the point on a Wave with the greatest positive value or upward displacement in a Cycle. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. Periodicity is the quality of occurring at regular intervals or periods (in Time or Space) and can occur in different contexts A Clock marks Wave propagation is any of the ways in which waves travel through a Waveguide. This is about the direction for other uses see North (disambiguation.

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. In Physical oceanography, significant wave height, also known as SWH, or H s, is the average Wave height ( trough This figure represents the average height of the highest one-third of the waves in a given time period (usually chosen somewhere in the range from 20 minutes till twelve hours), or in a specific wave or storm system. In Mathematics, an average, or central tendency of a Data set refers to a measure of the "middle" or " expected " value of 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 if the wind stops. A capillary wave is a Wave travelling along the interface between two fluids whose dynamics are dominated by the effects of Surface tension. A capillary wave is a Wave travelling along the interface between two fluids whose dynamics are dominated by the effects of Surface tension. A swell, in the context of an Ocean, is a formation of long Wavelength Ocean surface waves on the sea The restoring force that allows them to propagate is surface tension. For the work of fiction see Surface Tension (short story. Surface tension is a property of the surface of a Liquid that causes it to 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.

Some waves undergo a phenomenon called "breaking". A phenomenon (from Greek φαινόμενoν, pl φαινόμενα - phenomena) is any observable occurrence A breaking wave is one whose base can no longer support its top, causing it to collapse. 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 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. A 1:24 slope may be a long, shallow swell found in deep waters. A 1:14 and higher slope is a wave that is too steep to remain coherent. Waves can also break if the wind grows strong enough to blow the crest off the base of the wave.

Spilling type of surf

Three main types of breaking waves are identified by surfers or surf lifesavers. Surfing is a surface water sport in which the participant is carried along the face of a breaking wave, most commonly using a Surfboard, although wave-riders Surf lifesaving is a multifaceted movement that comprises key aspects of voluntary Lifeguard services and competitive surf sport Their varying characteristics make them more or less suitable for surfing, and present different dangers.

• Spilling, or rolling: these are the safest on which to surf; they can be found in relatively sheltered areas.
• Plunging, or dumping: these break suddenly and can "dump" swimmers—pushing them to the bottom with great force. Strong winds can cause dumpers; they can also be found where there is a sudden rise in the sea floor.
• Surging: these may never actually break as they approach the water's edge, as the water below them is very deep. These waves can knock swimmers over and drag them back into deeper water.

## Science of waves

Motion of a particle in an ocean wave.
A = At deep water. The orbital motion of fluid particles decreases rapidly with increasing depth below the surface. 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
B = At shallow water (ocean 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.

Ocean surface waves are mechanical waves that propagate along the interface between water and air; the restoring force is provided by gravity, and so they are often referred to as surface gravity waves. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Water is a common Chemical substance that is essential for the survival of all known forms of Life. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five In Fluid dynamics, gravity waves are waves generated in a Fluid medium or at the interface between two media (e As the wind blows, pressure and friction forces perturb the equilibrium of the ocean surface. Wind is the flow of Air or other Gases that compose an Atmosphere (including but not limited to the Earth's) 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 ocean surface waves a combination of longitudinal (back and forth) and transverse (up and down) wave motions. Longitudinal waves are waves that have vibrations along or parallel to their direction of travel that is waves in which the motion of the medium is in the same direction as the motion A transverse wave is a moving Wave that consists of oscillations occurring perpendicular to the direction of energy transfer When waves propagate in shallow water, (where the depth is less than half the wavelength) the particle trajectories are compressed into ellipses. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a [1][2]

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. For a pure Wave motion in Fluid dynamics, the Stokes drift velocity is the Average Velocity when following a specific Fluid [3][4]

For intermediate and shallow water, the Boussinesq equations are applicable, combining frequency dispersion and nonlinear effects. In Fluid dynamics, the Boussinesq approximation for Water waves is an Approximation valid for weakly Non-linear and fairly long waves In Fluid dynamics, dispersion of water waves generally refers to Frequency dispersion And in very shallow water, the shallow water equations can be used. The shallow water equations (also called Saint Venant equations after Adhémar Jean Claude Barré de Saint-Venant) are a set of Hyperbolic partial differential

As the depth into the ocean 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. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. The phase speed of the surface wave (also called the celerity) is well approximated by

$c=\sqrt{\frac{g \lambda}{2\pi} \tanh \left(\frac{2\pi d}{\lambda}\right)}$

where

c = phase speed;
λ = wavelength;
d = water depth;
g = acceleration due to gravity at the Earth's surface. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. Standard gravity, usually denoted by g 0 or g n is the nominal acceleration due to gravity at the Earth's surface at sea level

In deep water, where $d \ge \frac{1}{2}\lambda$, so $\frac{2\pi d}{\lambda} \ge \pi$ and the hyperbolic tangent approaches 1, c, in m/s, approximates $1.25\sqrt\lambda$, 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, when after a storm waves arrive on the coast, the first ones to arrive are the long–wavelength swells.

When several wave trains are present, as is always the case in the ocean, the waves form groups. In deep water the groups travel at a group velocity which is half of the phase speed. The group velocity of a Wave is the Velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space [5] 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 on the speed of the crest and the trough of the wave; the crest moves faster than the trough. The coast is defined as the part of the land adjoining or near the Ocean. A crest is the point on a Wave with the greatest positive value or upward displacement in a Cycle. A crest is the point on a Wave with the greatest positive value or upward displacement in a Cycle. This causes surf, a breaking of the waves. SURF (Speeded Up Robust Features is a robust image descriptor that can be used in computer vision tasks

Individual "freak waves" (also "rogue waves", "monster waves", "killer waves", and "king waves") sometimes occur in the ocean, often as high as 30 meters. Rogue waves, also known as freak waves, monster waves or extreme waves, are relatively large and spontaneous Ocean surface waves that are a threat Rogue waves, also known as freak waves, monster waves or extreme waves, are relatively large and spontaneous Ocean surface waves that are a threat Rogue waves, also known as freak waves, monster waves or extreme waves, are relatively large and spontaneous Ocean surface waves that are a threat Rogue waves, also known as freak waves, monster waves or extreme waves, are relatively large and spontaneous Ocean surface waves that are a threat Rogue waves, also known as freak waves, monster waves or extreme waves, are relatively large and spontaneous Ocean surface waves that are a threat Such waves are distinct from tides, caused by the moon and sun's pull, tsunamis that are caused by underwater earthquakes or landslides, and waves generated by underwater explosions or the fall of meteorites. Characteristics A tide is a repeated cycle of sea level changes in the following stages Over several hours the water rises or advances up a beach in the flood The Sun (Sol is the Star at the center of the Solar System. A tsunami ((tsuːˈnɑːmi is a series of waves created when An earthquake is the result of a sudden release of energy in the Earth 's crust that creates Seismic waves Earthquakes are recorded with a Seismometer A landslide 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 An underwater explosion, also known as an UNDEX, is an Explosion beneath the surface of water A meteorite is a natural object originating in Outer space that survives an impact with the Earth 's surface

The movement of ocean waves can be captured by wave energy devices. Wave power refers to the Energy of Ocean surface waves and the capture of that energy to do useful work — including Electricity generation, 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):

$E=\frac{1}{8}\rho g {H}^2=\frac{1}{2}\rho g a^2.$

The velocity of propagation of this energy is the group velocity. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system The group velocity of a Wave is the Velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope

## Ocean wave measurement

Ship board observations of waves has been recorded for over 130 years. This long record of the wave climate is complemented by indirect measurements of wave activity found in the Earth's "hum" recorded by seismometers. More accurate quantitative measurements can be made using a wave pole on a fixed structure. An observer stands on the shore in a designated spot and sights the wave alongside a pole positioned between them and the waves. Such poles are often part of weather monitoring stations located along coastlines, particularly those associated with lighthouses. A lighthouse is a Tower, building or framework designed to emit light from a system of lamps and lenses or in older times from a fire and used as an 'Electronic poles' known as wave staffs are often used for precise engineering applications, and are operated on some research platforms such as the Aqua Alta tower in the Adriatic Sea, offshore of Venice. Wave staffs are usually replaced by radar (widely used in the Netherlands) or laser altimeters (such as found on some U. S. NDBC stations) for routine measurements.

A more common and robust way of measuring waves is using a buoy that records the motion of the water surface, which does not require a fixed platform. The buoy motion provides a time history of the water elevation for that location and statistics can be calculated including the significant and maximum wave heights and periods. Modern waverider buoys usually measure their movement along three dimensions and give information about wave direction. For the south east Queensland coastline there are waverider bouys about every 100 km along the coast. Queensland is a state of Australia, occupying the north-eastern corner of the mainland continent The waverider buoys are typically positioned off the entrances of major ports or major recreational surfing or swimming beaches. ||-||-|-||-||-||-||-||-||-|} A port is a facility for receiving Ships and transferring cargo Surfing is a surface water sport in which the participant is carried along the face of a breaking wave, most commonly using a Surfboard, although wave-riders A network of waverider buoys properly positioned can allow the interpolation of the wave climate for that region. In the mathematical subfield of Numerical analysis, interpolation is a method of constructing new data points within the range of a Discrete set of Waverider buoy data is a typical input for coastal modelling, the waverider wave train is typically the deep water wave climate that is refracted across the seabed contours into the wave breaking zone. The coast is defined as the part of the land adjoining or near the Ocean. Refraction is the change in direction of a Wave due to a change in its Speed. 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

In coastal areas, the wave-induced velocities and pressure fluctuations can also be recorded using pressure gauges (sometimes of the same kind that measure tides) and current meters.

Wave heights can also be measured from space, at least in a statistical sense, using the change in the form of radar pulses reflected off the sea surface by altimeter radars as found on the French/U. S. Topex/Poseidon and Jason satellites. Other radar techniques, either ground-based wave radar or airborne systems such as real or synthetic aperture radars, can also provide measurements of wave statistics. Ocean surface waves can be measured by several Radar Remote sensing techniques Such radar systems are best suited for long period waves (swells), allowing the tracking of swells over very long distances.

## Ocean wave models

Surfers are very interested in the predicted wave climate. There are many websites that provide predictions of the surf quality for the upcoming days and weeks. The Ocean Wave models are driven by more general climate models that predict the winds and pressures over the oceans. This article is about the theories and mathematics of climate modeling

Ocean 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 ocean waves is important for managing littoral environments. Littoral refers to the coast of an ocean or sea or to the banks of a river lake or estuary

## References

• "Anatomy of a Wave" Holben, Jay boatsafe.com captured 5/23/06
• Carr, Michael "Understanding Waves" Sail Oct 1998: 38-45. A rainbow is an optical and meteorological phenomenon that causes a spectrum of Light to appear in the Sky when the Sun A rainbow is an optical and meteorological phenomenon that causes a spectrum of Light to appear in the Sky when the Sun
• Rousmaniere, John. The Annapolis Book of Seamanship, New York: Simon & Schuster 1989
• National Weather Service
• G. G. Stokes (1847). "On the theory of oscillatory waves". Transactions of the Cambridge Philosophical Society 8: 441–455.
Reprinted in: G. G. Stokes (1880). Mathematical and Physical Papers, Volume I. Cambridge University Press, 197–229.
• Phillips, O. M. (1977). The dynamics of the upper ocean, 2nd edition, Cambridge University Press. ISBN 0 521 29801 6.

## Notes

1. ^ For the particle trajectories within the framework of linear wave theory, see for instance:
Phillips (1977), page 44.
Lamb, H. (1994). Sir Horace Lamb FRS ( 29 November 1849 – 4 December 1934) was a British Applied mathematician and author of several influential Hydrodynamics, 6th edition, 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, Second revised edition, Course of Theoretical Physics 6, Pergamon Press. ISBN 0 08 033932 8.   See page 33.
2. ^ A good illustration of the wave motion according to linear theory is given by Prof. Robert Dalrymple Java applet.
3. ^ For nonlinear waves, the particle paths are not closed, as found by George Gabriel Stokes in 1847, see the original paper by Stokes. Sir George Gabriel Stokes 1st Baronet FRS ( 13 August 1819 &ndash 1 February 1903) was a mathematician and physicist 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".
4. ^ 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.
J. M. Williams (1985). Tables of progressive gravity waves. Pitman. ISBN 978-0273087335.
5. ^ In deep water, the group velocity is half the phase velocity, as is shown here. The group velocity of a Wave is the Velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space In Fluid dynamics, gravity waves are waves generated in a Fluid medium or at the interface between two media (e Another reference is [1].