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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 ...
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 ...
The Keulegan–Carpenter number is important for the computation of the wave forces on offshore platforms. In fluid dynamics , the Keulegan–Carpenter number , also called the period number , is a dimensionless quantity describing the relative importance of the drag forces over inertia forces for bluff objects in an oscillatory fluid flow .
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.
Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum.
A wave model requires as initial conditions information describing the state of the sea. An analysis of the sea or ocean can be created through data assimilation, where observations such as buoy or satellite altimeter measurements are combined with a background guess from a previous forecast or climatology to create the best estimate of the ongoing conditions.
Stokes's first definition of wave celerity has, for a pure wave motion, the mean value of the horizontal Eulerian flow-velocity Ū E at any location below trough level equal to zero. Due to the irrotationality of potential flow, together with the horizontal sea bed and periodicity the mean horizontal velocity, the mean horizontal velocity is a ...
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 ...