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where ξ is the Iribarren number, is the angle of the seaward slope of a structure, H is the wave height, L 0 is the deep-water wavelength, T is the period and g is the gravitational acceleration. Depending on the application, different definitions of H and T are used, for example: for periodic waves the wave height H 0 at deep water or the ...
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
Waves of the same type are often superposed and encountered simultaneously at a given point in space and time. The properties at that point are the sum of the properties of each component wave at that point. In general, the velocities are not the same, so the wave form will change over time and space.
In fluid dynamics, wave setup is the increase in mean water level due to the presence of breaking waves. Similarly, wave setdown is a wave-induced decrease of the mean water level before the waves break (during the shoaling process). For short, the whole phenomenon is often denoted as wave setup, including both increase and decrease of mean ...
The previous definition of phase velocity has been demonstrated for an isolated wave. However, such a definition can be extended to a beat of waves, or to a signal composed of multiple waves. For this it is necessary to mathematically write the beat or signal as a low frequency envelope multiplying a carrier.
x is the horizontal coordinate and the wave propagation direction (meters), z is the vertical coordinate, with the positive z direction pointing out of the fluid layer (meters), λ is the wave length (meters), T is the wave period . As derived below, the horizontal component ū S (z) of the Stokes drift velocity for deep-water waves is ...
Shallow-water equations can be used to model Rossby and Kelvin waves in the atmosphere, rivers, lakes and oceans as well as gravity waves in a smaller domain (e.g. surface waves in a bath). In order for shallow-water equations to be valid, the wavelength of the phenomenon they are supposed to model has to be much larger than the depth of the ...
After the wave breaks, it becomes a wave of translation and erosion of the ocean bottom intensifies. Cnoidal waves are exact periodic solutions to the Korteweg–de Vries equation in shallow water, that is, when the wavelength of the wave is much greater than the depth of the water.