Issue link: https://wardsworld.wardsci.com/i/1381964
Ocean Waves (continued) A simple sinusoidal wave train (Fig. 2) is characterized by three attributes: wave height (H), the vertical distance from trough to crest; wavelength (L), the horizontal crest-to-crest distance; and wave period (T), the time between passage of successive crests past a fixed point. The phase velocity (C = L/T) is the speed of propagation of a crest. For a given ocean depth (h), wavelength increases with increasing period. The restoring force for these surface waves is predominantly gravitational. Therefore, they are known as surface gravity waves, unless their wavelength is shorter than 1.8 cm, in which case surface ten- sion provides the dominant restoring force. Classification Surface gravity waves may be classified according to the nature of the forces producing them. Tides are ocean waves induced by the varying gravitational influence of the Moon and Sun. They have long periods, usually 12.42 h for the strongest constituent. Storm surges are individual waves produced by the wind and dropping barometric pressure associated with storms; they characteristically last several hours. Earthquakes or other large, sudden movements of the Earth's crust can cause waves, called tsunamis, which typically have periods of less than an hour. Wakes are waves resulting from relative motion of the water and a solid body, such as the motion of a ship through the sea or the rapid flow of water around a rock. Wind- generated waves, having periods from a fraction of a second to tens of seconds, are called wind waves. Like tides, they are ubiquitous in the ocean and continue to travel well beyond their area of generation. The ocean is never completely calm. Wind waves The growth of wind waves (Fig. 3) by the transfer of energy from the wind is not fully understood. At wind speeds less than 1.1 m/s (2.5 mi/h), a flat water surface remains unruffled by waves. For waves traveling slower than the wind, secondary, wave-induced airflows shift the wave-induced pressure distur- bance downwind so the lowest pressure is ahead of the crests. This results in energy transfer from the wind to the wave and hence growth of the wave. If a constant wind blows over a sufficient length of ocean, called the fetch, for a sufficient length of time, a wave field develops whose statistical characteristics depend only on wind velocity. In particular, the spectrum of sea-surface elevation for such a fully developed sea has the form of Eq. (1), where f is frequency ( = 1/T ), g = 9.8 m/s2 (32 ft/s2) is gravita- tional acceleration, f m = 0.13 g/U is the frequency of the spectral peak (U = wind speed at 10 m or 32.8 ft elevation) and A = 5.2 × 10-6 is a constant. The fetch is limited near a coast with the wind blowing off- shore and the waves grow as they propagate toward the open ocean. In such a limited-fetch situation, Eq. ( 1 ) is modified: A and fm become dependent on the fetch length and the peak in the spectrum is enhanced. Even when the mean wind blows from a single direction, the surface waves that it generates are seen to travel in a variety of directions centered on the downwind direction. The directional spectrum of such a wave field can be approximately represent- ed by a formula, such as Eq. ( 2 ), + ward ' s science Fig. 2 Sinusoidal wave attributes. (Credit: NOAA) Fig. 3 Once generated, waves gain energy from the wind by wave-coupling of pressure fluctuations in the air just above the waves. (Credit: NOAA) Eq. (1) Eq. (2)