Issue link: https://wardsworld.wardsci.com/i/1381964
where θ is the angle of wave propagation relative to the downwind direction. An observer asked to estimate average wave height typically gives a value that is about the average height of the highest one-third of the waves actually present. This statistic, repre- sented as H1/3, is called the significant wave height. In the open sea, Eq. ( 3 ) applies, if a wind blows steadily over a known fetch for a period of time. Because of viscosity, surface waves lose energy as they propa- gate, short-period waves being dampened more rapidly than long-period waves. Waves with long periods (typically 10 s or more) can travel thousands of kilometers with little energy loss. Such waves, generated by distant storms, are called swell. Equations ( 1 ), ( 2 ), and ( 3 ) assume that the waves present were generated by local wind, with no significant swell present. The highest wind waves are produced by large intense storm systems that last for a day or longer. Such systems of very low atmospheric pressure form in the Gulf of Alaska, the region around Iceland and the Weddell Sea. Off the west coast of Canada, there have been several measurements of individual waves with heights around 30 m (100 ft). Northwest of Hawaii, on February 7, 1933, the Navy tanker USS Ramapo encountered the largest open-ocean wind waves ever reliably observed with heights that were reported to be at least 34 m (112 ft). When waves propagate into an opposing current, they grow in height. For example, when swell from a Weddell Sea storm propagates northeastward into the southwestward-flowing Agulhas Current off South Africa, high steep waves are formed. Many large ships in this region have been severely damaged by such waves. Because actual ocean waves consist of many components with different periods, heights, and directions, occasionally a large number of these components can, by chance, come in phase with one another, creating a freak wave with a height several times the significant wave height of the surrounding sea. According to linear theory, waves with different periods propagate with different speeds in deep water and hence the wave components remain in phase only briefly. But nonlinear effects are bound to be significant in a large wave. In such a wave, the effects of nonlinearity can compensate for those of dispersion, allowing a solitary wave to propagate almost unchanged. Consequently, a freak wave can have a lifetime of a minute or two. Linear theory For waves sufficiently small that linear theory applies, Eq. ( 4 ) gives the phase velocity to an accuracy of 1%. Note that wavenumber k = 2π/L. Ocean wave energy E per unit surface area depends only on wave height [Eq. ( 5 )]. This energy propagates at the group velocity [Eq. ( 6 )] and produces a power flux per unit distance along the wave front [Eq. ( 7 )]. For example, waves in the deep sea with 1.8-m (6-ft) height and 10-s period carry a power flux of 30 kW/m (13 hp/ft). Avail- able power fluxes of this magnitude are representative of many coastal regions and represent a substantial renewable energy resource. Various devices with efficiencies of 50% or greater have been developed to convert this wave energy to electrical energy. Surface-gravity waves cause pressure fluctuations and particle motions that are largest near the surface and decrease with depth. In deep water, this dependence on depth d below the still-water level is exponential: e −kd . Stokes drift To first-order (linear theory), particle orbits resulting from wave motion are closed loops. But since a particle moves in the direction of wave propagation in the loop's upper part and in the reverse direction in its lower part, the forward motion is at a shallower level than the reverse motion. Consequently, the forward motion is slightly stronger than the reverse motion and the orbital loops do not quite close. As a result, there is a second-order (nonlinear) net particle motion called Stokes drift. In deep water, the velocity associated with this motion is in the direction of wave propagation [Eq. ( 8 )]. Ocean Waves (continued) + ward ' s science Eq. (3) Eq. (4) Eq. (5) Eq. (6) Eq. (7) Eq. (8)