Site Navigation
Categories:
Water waves
Wave mechanics
Fluid dynamics
Physical oceanography

Summary Of: Dispersion (water waves)

Encyclodia Page On: Dispersion (water waves)

These Are Links To Other Documents
dispersion | fluid dynamics | water waves | frequency | waves | wavelengths | phase speeds | water | surface | gravity | surface tension | water | free surface | dispersive medium | wavelength | phase speed | shallower water | capillary waves | nonlinear | amplitude | Sinusoidal wave. | | propagating wave | sine wave | elevation | SI | metre | amplitude | radians | seconds | wavelength | period | wavenumber | angular frequency | crest | trough | integer | physics | functional relationship | acceleration by gravity | Phase velocity | Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by shallow-water phase velocity √(gh) as a function of relative depth h / λ.Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity √(gh) valid in shallow water.Drawn lines: dispersion relation valid in arbitrary depth.Dashed lines (blue and red): deep water limits. | | Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by deep-water phase velocity √(½ gλ / π) as a function of relative depth h / λ.Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity √(gh) valid in shallow water.Drawn lines: dispersion relation valid in arbitrary depth.Dashed lines (blue and red): deep water limits. | | sinusoidal | amplitude | wavelength | phase velocity | shallow water | acceleration by gravity | period | reciprocal | frequency | Group velocity | Frequency dispersion in bichromatic groups of gravity waves on the surface of deep water. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. More … In this deep-water case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure.New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front.For gravity surface-waves, the water particle velocities are much smaller than the phase velocity, in most cases. | | bichromatic | gravity waves | phase velocity | Interference | amplitude | beat pattern | narrow-band | The number of waves per group as observed in space at a certain moment (upper blue line), is different from the number of waves per group seen in time at a fixed position (lower orange line), due to frequency dispersion. More … For the shown case, a bichromatic group of gravity waves on the surface of deep water, the group velocity is half the phase velocity. In this example, there are 5.75 waves between two wave group nodes in space, while there are 11.5 waves between two wave group nodes in time. | | North Pacific storm waves as seen from the NOAA M/V Noble Star, Winter 1989. | | North Pacific | NOAA | M/V | bichromatic | modulation | mathematically | amplitude | wave number | angular frequency | trigonometric identities | Frequency dispersion of surface gravity waves on deep water. The superposition (dark blue line) of three sinusoidal wave components (light blue lines) is shown. More … For the three components respectively 22 (bottom), 25 (middle) and 29 (top) wavelengths fit in a horizontal domain of 2,000 meter length. The component with the shortest wavelength (top) propagates slowest. The wave amplitudes of the components are respectively 1, 2 and 1 meter. The differences in wavelength and phase speed of the components results in a changing pattern of wave groups, due to amplification where the components are in phase, and reduction where they are in anti-phase. | surface gravity waves | superposition | wavelengths | amplitudes | phase speed | wave groups | wavelength | envelope | sea state | statistics | power spectrum | rad | phase velocity | group velocity | wavelength | phase velocity | shallow water | Pierre-Simon Laplace | George Biddell Airy | Philip Kelland | Joseph Louis Lagrange | Capillary wave | Dispersion of gravity-capillary waves on the surface of deep water. Phase and group velocity divided by as a function of relative wavelength .Blue lines (A): phase velocity, Red lines (B): group velocity.Drawn lines: dispersion relation for gravity-capillary waves.Dashed lines: dispersion relation for deep-water gravity waves.Dash-dot lines: dispersion relation valid for deep-water capillary waves. | | surface tension | solitary wave | soliton | Korteweg–de Vries equation | perturbation theory | amplitude | Doppler shift | velocity | vector | inner product | Dispersive partial differential equation | Dispersion relation | Dispersion (optics) | Phase velocity | Group velocity | Capillary wave | Benjamin–Bona–Mahony equation | Boussinesq approximation (water waves) | Davey–Stewartson equations | Kadomtsev–Petviashvili equation | KP equation | Korteweg–de Vries equation | KdV equation | Luke's variational principle | Nonlinear Schrödinger equation | Shallow water equations | doi | ISBN 978 981 02 0420 4 | ISBN 981 02 0427 2 | Lamb, H. | ISBN 978 0 521 45868 9 | Landau, L.D. | Lifshitz, E.M. | ISBN 0 008 339932 | Lighthill, M.J. | ISBN 0 521 29233 6 | ISBN 0 521 29801 6 | ISBN 0 471 94090 9 | homogeneous | medium | Reynolds, O. | Lord Rayleigh (J. W. Strutt) | doi | Categories | Water waves | Wave mechanics | Fluid dynamics | Physical oceanography |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Dispersion (water waves)".