A noteworthy example of this is waves generated south of Tasmania during heavy winds that will travel across the Pacific to southern California, producing desirable surfing conditions.
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.
[3][4][5] Waves in bodies of water may also be generated by other causes, both at the surface and underwater (such as watercraft, animals, waterfalls, landslides, earthquakes, bubbles, and impact events).
Further exposure to that specific wind could only cause a dissipation of energy due to the breaking of wave tops and formation of "whitecaps".
This pressure fluctuation produces normal and tangential stresses in the surface water, which generates waves.
It is usually assumed for the purpose of theoretical analysis that:[8] The second mechanism involves wind shear forces on the water surface.
John W. Miles suggested a surface wave generation mechanism that is initiated by turbulent wind shear flows based on the inviscid Orr–Sommerfeld equation in 1957.
Since the wind speed profile is logarithmic to the water surface, the curvature has a negative sign at this point.
This relation shows the wind flow transferring its kinetic energy to the water surface at their interface.
These waves tend to last much longer, even after the wind has died, and the restoring force that allows them to propagate is gravity.
As waves propagate away from their area of origin, they naturally separate into groups of common direction and wavelength.
The Pacific Ocean is 19,800 km (12,300 mi) from Indonesia to the coast of Colombia and, based on an average wavelength of 76.5 m (251 ft), would have ~258,824 swells over that width.
The speed of all ocean waves is controlled by gravity, wavelength, and water depth.
Most characteristics of ocean waves depend on the relationship between their wavelength and water depth.
In general, the longer the wavelength, the faster the wave energy will move through the water.
The speed of a deep-water wave may also be approximated by: where g is the acceleration due to gravity, 9.8 meters (32 feet) per second squared.
As deep-water waves enter the shallows and feel the bottom, however, their speed is reduced, and their crests "bunch up", so their wavelength shortens.
As the waves slow down in shoaling water, the crests tend to realign at a decreasing angle to the depth contours.
This process continues while the depth decreases, and reverses if it increases again, but the wave leaving the shoal area may have changed direction considerably.
Rays—lines normal to wave crests between which a fixed amount of energy flux is contained—converge on local shallows and shoals.
Because these effects are related to a spatial variation in the phase speed, and because the phase speed also changes with the ambient current—due to the Doppler shift—the same effects of refraction and altering wave height also occur due to current variations.
This may be exaggerated to the extent that the leading face forms a barrel profile, with the crest falling forward and down as it extends over the air ahead of the wave.
When waves propagate in shallow water, (where the depth is less than half the wavelength) the particle trajectories are compressed into ellipses.
[29][30] In reality, for finite values of the wave amplitude (height), the particle paths do not form closed orbits; rather, after the passage of each crest, particles are displaced slightly from their previous positions, a phenomenon known as Stokes drift.
At a depth equal to half the wavelength λ, the orbital movement has decayed to less than 5% of its value at the surface.
For intermediate and shallow water, the Boussinesq equations are applicable, combining frequency dispersion and nonlinear effects.
If the wavelength is very long compared to the water depth, the phase speed (by taking the limit of c when the wavelength approaches infinity) can be approximated by On the other hand, for very short wavelengths, surface tension plays an important role and the phase speed of these gravity-capillary waves can (in deep water) be approximated by where When several wave trains are present, as is always the case in nature, the waves form groups.
Wind wave models are also an important part of examining the impact of shore protection and beach nourishment proposals.
[37] The strongest of these is the secondary microseism which is created by ocean floor pressures generated by interfering ocean waves and has a spectrum that is generally between approximately 6–12 s periods, or at approximately half of the period of the responsible interfering waves.
Microseisms were first reported in about 1900, and seismic records provide long-term proxy measurements of seasonal and climate-related large-scale wave intensity in Earth's oceans [40] including those associated with anthropogenic global warming.