Wind wave

North Pacific storm waves as seen from the NOAA M/V *Noble Star*, Winter 1989.

Ocean surface waves are surface waves that occur on the free surface of the ocean. They usually result from wind, and are also referred to as wind waves. Some waves can travel thousands of miles before reaching land. They range in size from small ripples to huge rogue waves. 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 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. 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 great majority of large breakers one observes on an ocean beach result from distant winds. Four factors influence the formation of wind waves:^[1]

wind speed,
distance of open water that the wind has blown over — called fetch,
time duration the wind has blown over a given area,
water depth.

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:

Wave 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).

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 a 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. 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:

Capillary waves, or ripples
Seas
Swells

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. 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" (also called "freak waves", "monster waves", "killer waves", and "king waves") sometimes occur in the ocean, up to heights near 30 meters, and being much higher than the other waves in the sea state. Such waves are distinct from tides, caused by the Moon and Sun's gravitational pull, tsunamis that are caused by underwater earthquakes or landslides, and waves generated by underwater explosions or the fall of meteorites — all having far longer wavelengths than ocean surface waves (including rogue waves).

Wave breaking

Some waves undergo a phenomenon called "breaking". A breaking wave 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 of the wave height H to the wavelength 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.^[2] 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 or surf lifesavers. Their varying characteristics make them more or less suitable for surfing, and present different dangers.

Spilling, or rolling: these are the safest waves on which to surf. They can be found in most areas with relatively flat shorelines. They are the most common type of shorebreak
Plunging, or dumping: these break suddenly and can "dump" swimmers—pushing them to the bottom with great force. These are the preferred waves for experienced surfers. Strong offshore winds and long wave periods can cause dumpers. They are often found where there is a sudden rise in the sea floor, such as a reef or sandbar.
Surging: these may never actually break as they approach the water's edge, as the water below them is very deep. They tend to form on steep shorelines. These waves can knock swimmers over and drag them back into deeper water.

Science of waves

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. As the wind blows, pressure and friction forces perturb the equilibrium of the ocean 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 ocean surface 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.^[3]^[4]

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.^[5]^[6]

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 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. 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.

In deep water, where $d\geq {\frac {1}{2}}\lambda$ , so ${\frac {2\pi d}{\lambda }}\geq \pi$ and the hyperbolic tangent approaches $1$ , $c$ , in m/s, approximates $1.25{\sqrt {\lambda }}$ , when $\lambda$ 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.^[7] 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 ocean waves can be captured by wave energy devices. The energy density (per unit area) of regular sinusoidal waves depends on the water density $\rho$ , 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 ga^{2}.

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

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. '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 buoys about every 100 km along the coast. The waverider buoys are typically positioned off the entrances of major ports or major recreational surfing or swimming beaches. A network of waverider buoys properly positioned can allow the interpolation of the wave climate for that region. 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.

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. 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.

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.

Notes

^ Young, I. R. (1999). Wind generated ocean waves. Elsevier. ISBN 0080433170. p. 83.
^ R.J. Dean and R.A. Dalrymple (2002). Coastal processes with engineering applications. Cambridge University Press. ISBN 0-521-60275-0. p. 96–97.
^ For the particle trajectories within the framework of linear wave theory, see for instance:
Phillips (1977), page 44.
Lamb, H. (1994). Hydrodynamics (6^th edition ed.). Cambridge University Press. ISBN 9780521458689. {{cite book}}: |edition= has extra text (help) Originally published in 1879, the 6^th extended edition appeared first in 1932. See §229, page 367.
L. D. Landau and E. M. Lifshitz (1986). Fluid mechanics. Course of Theoretical Physics. Vol. 6 (Second revised edition ed.). Pergamon Press. ISBN 0 08 033932 8. {{cite book}}: |edition= has extra text (help) See page 33.
^ A good illustration of the wave motion according to linear theory is given by Prof. Robert Dalrymple Java applet.
^ 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".
^ 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.
^ In deep water, the group velocity is half the phase velocity, as is shown here. Another reference is [1].

References

"Anatomy of a Wave" Holben, Jay boatsafe.com captured 5/23/06
Carr, Michael "Understanding Waves" Sail Oct 1998: 38-45.
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. pp. 197–229.
Phillips, O.M. (1977). The dynamics of the upper ocean (2^nd edition ed.). Cambridge University Press. ISBN 0 521 29801 6. {{cite book}}: |edition= has extra text (help)

External links

[1] Young, I. R. (1999). Wind generated ocean waves. Elsevier. ISBN 0080433170. p. 83.

[2] R.J. Dean and R.A. Dalrymple (2002). Coastal processes with engineering applications. Cambridge University Press. ISBN 0-521-60275-0. p. 96–97.

[3] For the particle trajectories within the framework of linear wave theory, see for instance:
Phillips (1977), page 44.
Lamb, H. (1994). Hydrodynamics (6^th edition ed.). Cambridge University Press. ISBN 9780521458689. {{cite book}}: |edition= has extra text (help) Originally published in 1879, the 6^th extended edition appeared first in 1932. See §229, page 367.
L. D. Landau and E. M. Lifshitz (1986). Fluid mechanics. Course of Theoretical Physics. Vol. 6 (Second revised edition ed.). Pergamon Press. ISBN 0 08 033932 8. {{cite book}}: |edition= has extra text (help) See page 33.

[4] A good illustration of the wave motion according to linear theory is given by Prof. Robert Dalrymple Java applet.

[5] 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".

[6] 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.

[7] In deep water, the group velocity is half the phase velocity, as is shown here. Another reference is [1].

[1]

[2]

[3]

[4]

[5]

[6]

[7]