WAVE

on a body of water, a ridge or swell on the surface, normally having a forward motion distinct from the oscillatory motion of the particles that successively compose it. The undulations and oscillations may be chaotic and random, or they may be regular, with an identifiable wavelength between adjacent crests and with a definite frequency of oscillation. In the latter case, the waves may be progressive, in which the crests and troughs appear to travel at a steady speed in a direction at right angles to themselves. Alternatively, they may be standing waves, in which there is no progression. In this case, there is no rise and fall at all in some places, the nodes, while elsewhere the surface rises to a crest and then falls to a trough at a regular frequency. There are two physical mechanisms that control and maintain wave motion. For most waves, gravity is the restoring force that causes any displacements of the surface to be accelerated back toward the mean surface level. The kinetic energy gained by the fluid returning to its rest position causes it to overshoot, resulting in the oscillating wave motion. In the case of very short wavelength disturbances of the surface, i.e., ripples, the restoring force is surface tension, wherin the surface acts like a stretched membrane. If the wavelength is less than a few millimetres, surface tension dominates the motion, which is described as a capillary wave. Surface gravity waves in which gravity is the dominant force have wavelengths greater than approximately 10 cm (4 in.). In the intermediate length range, both restoring mechanisms are important. The mathematical theory of water wave propagation shows that for waves whose amplitude is small compared to their length, the wave profile can be sinusoidal, and there is a definite relationship between the wavelength and the wave period, which also controls the speed of wave propagation. Longer waves travel faster than shorter ones, a phenomenon known as dispersion. If the water depth is less than one-twentieth of the wavelength, the waves are known as long gravity waves, and their wavelength is directly proportional to their period. The deeper the water, the faster they travel. For capillary waves, shorter wavelengths travel faster than longer ones. The energy of the waves is proportional to the square of the amplitude, i.e., the maximum displacement of the surface above or below its rest position. Mathematical analysis shows that a distinction must be made between the speed of the troughs and crests, called the phase speed, and the speed and direction of the transport of energy or information associated with the wave, termed the group velocity. For non-dispersive long waves the two are equal, whereas for surface gravity waves in deep water the group velocity is only half the phase speed. Thus, in a train of waves spreading out over a pond after a sudden disturbance at a point, the wave front travels at only half the speed of the crests, which appear to run through the packet of waves and disappear at the front. For capillary waves, the group velocity is one and one-half times the phase speed. Waves whose amplitude is large compared to their length cannot be so readily described by mathematical theory, and their form is distorted from a sinusoidal shape. The troughs tend to flatten and the crests sharpen toward a point, a shape known as a conoidal wave. In deeper water the limiting height of a wave is one-seventh of its length. As it approaches this height the pointed crests break to form whitecaps. In shallow water the long-amplitude waves distort, because crests travel faster than troughs to form a profile with a steep rise and slow fall. As such waves travel into shallower water on a beach, they steepen until breaking occurs. Waves on the sea surface are generated by the action of the wind. During generation the disturbed sea surface is not regular and contains many different oscillatory motions at different frequencies. Wave spectra are used by oceanographers to describe the distribution of energy at different frequencies. The form of the spectrum can be related to wind speed and direction and the duration of the storm and the fetch (or distance upwind) over which it has blown, and this information is used for wave prediction. After the storm has passed, the waves disperse, the longer-period waves (about 8 to 20 seconds) propagating long distances as well, while the shorter-period waves are damped out by internal friction.