Wind wave

Did You Know?

• The Pacific Ocean, from Indonesia to Colombia, would contain about 258,824 swells based on an average wavelength of 76.5 m.
• Ripples (capillary waves) are dominated by surface tension and die quickly if the wind stops.
• Wave refraction causes crests to realign at a decreasing angle to depth contours as waves slow in shoaling water.

Formation

Five factors influence the formation of wind waves: wind speed relative to wave speed, the uninterrupted open-water distance (fetch), the width of the fetch area, wind duration, and water depth. All these factors together determine wave size and flow structure. The main wave dimensions are wave height (trough to crest), wavelength (crest to crest), wave period (time between consecutive crests), and wave direction (driven by wind). A fully developed sea reaches the maximum wave size possible for a given wind strength, duration, and fetch; further wind exposure only causes energy dissipation through whitecaps. Waves in an area typically have a range of heights, and the significant wave height—the average height of the highest one-third of waves over a period—is used for reporting and analysis. This value also matches what a trained observer would estimate visually. The largest individual waves are likely to be somewhat less than twice the reported significant wave height. Wave formation on a flat surface begins with random pressure fluctuations from turbulent wind, producing normal and tangential stresses that generate waves. Theoretical analysis usually assumes the water is originally at rest, not viscous, and irrotational, with a random distribution of normal pressure from the wind.

Spectrum

Ocean waves are classified by the disturbing force that creates them, the extent of continued influence after formation, the restoring force that weakens them, and their wavelength or period. Seismic sea waves have a period of about 20 minutes and speeds of 760 km/h, while wind waves (deep-water waves) have periods up to about 20 seconds. The speed of all ocean waves is controlled by gravity, wavelength, and water depth. Wavelength determines the size of water molecule orbits, but water depth determines orbit shape. In deep water (deeper than half the wavelength), molecule paths are circular; in shallow water (shallower than 1/20 the original wavelength), orbits are flattened. Transitional waves travel through depths between 1/20 and half the original wavelength. Longer wavelengths move faster. The speed of a deep-water wave is proportional to the square root of the wavelength, approximated by C = 1.25√L (m/s). The speed of shallow-water waves follows a different equation.

Breaking

A breaking wave happens when the bottom of the wave can no longer hold up the top, so it falls apart. This can occur when the wave moves into shallow water, when two opposing wave systems meet, or if the wave becomes too steep. In deep water, a wave breaks when its height is more than about 0.17 times its length. In shallow water, it breaks when the height exceeds 0.8 times the water depth. Strong wind can also tear the crest off the base. In shallow areas, the seabed slows the wave's base, so the top moves faster, making the front face steeper and sometimes forming a barrel shape. There are three main types. Spilling or rolling waves break gradually and are safest for surfing, common on flat shorelines. Plunging or dumping waves break suddenly, forming a tube, and are favored by skilled surfers; they often occur over reefs or sandbars. Surging waves may not fully break, happening on steep shores, and can knock swimmers over or pull them into deeper water.

Physics of waves

Wind waves are mechanical waves propagating along the water-air interface, with gravity as the restoring force, making them surface gravity waves. Wind transfers energy to the water through pressure and friction. In linear plane waves of one wavelength in deep water, water parcels near the surface move in circular orbits: forward above and backward below relative to wave direction. The surface forms a trochoid with sharper curves upward, so wind waves are a combination of transversal and longitudinal waves. In shallow water, particle trajectories become elliptical. For finite wave amplitudes, particle paths do not close, resulting in Stokes drift. Circular motion radius decreases with depth; at half the wavelength depth, orbital movement is less than 5% of the surface value. The phase speed of a small-amplitude surface gravity wave is approximated by c = √((gλ/2π) tanh(2πd/λ)). In deep water, this simplifies to c ≈ √(gλ/2π), or about 1.25√λ in SI units. Different wavelengths travel at different speeds, so the longest waves arrive first after a storm. For intermediate and shallow water, Boussinesq equations apply; in very shallow water, shallow water equations are used.