![]() ![]() ![]() In the absence of the other effects, wave shoaling is the change of wave height that occurs solely due to changes in mean water depth – without changes in wave propagation direction and dissipation. Some of the important wave processes are refraction, diffraction, reflection, wave breaking, wave–current interaction, friction, wave growth due to the wind, and wave shoaling. ![]() Waves nearing the coast change wave height through different effects. This is particularly evident for tsunamis as they wax in height when approaching a coastline, with devastating results. In shallow water and parallel depth contours, non-breaking waves will increase in wave height as the wave packet enters shallower water. In other words, as the waves approach the shore and the water gets shallower, the waves get taller, slow down, and get closer together. Shoaling waves will also exhibit a reduction in wavelength while the frequency remains constant. Under stationary conditions, a decrease in transport speed must be compensated by an increase in energy density in order to maintain a constant energy flux. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth. In fluid dynamics, wave shoaling is the effect by which surface waves, entering shallower water, change in wave height. However, the group velocity first increases by 20% with respect to its deep-water value (of c g = 1 / 2 c 0 = gT/(4π)) before decreasing in shallower depths. The phase speed – and thus also the wavelength L = c p T – decreases monotonically with decreasing depth. The grey line corresponds with the shallow-water limit c p = c g = √( gh). Quantities have been made dimensionless using the gravitational acceleration g and period T, with the deep-water wavelength given by L 0 = gT 2/(2π) and the deep-water phase speed c 0 = L 0/ T. The phase velocity c p (blue) and group velocity c g (red) as a function of water depth h for surface gravity waves of constant frequency, according to Airy wave theory. ![]()
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