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Dispersion curves - graphs that show relationships between wave velocity, wavelength and frequency in dispersive systems - can be presented in various forms. The form that gives the greatest insight into the underlying physics has ω {\displaystyle \omega } (angular frequency) on the y -axis and k (wave number) on the x -axis.
This means that the velocity of a Rayleigh wave in practice becomes dependent on the wavelength (and therefore frequency), a phenomenon referred to as dispersion. Waves affected by dispersion have a different wave train shape. [1] Rayleigh waves on ideal, homogeneous and flat elastic solids show no dispersion, as stated above.
In physics, the Lamb shift, named after Willis Lamb, is an anomalous difference in energy between two electron orbitals in a hydrogen atom. The difference was not predicted by theory and it cannot be derived from the Dirac equation , which predicts identical energies.
In fluid dynamics, Lamb vector is the cross product of vorticity vector and velocity vector of the flow field, named after the physicist Horace Lamb. [ 1 ] [ 2 ] The Lamb vector is defined as l = u × ω {\displaystyle \mathbf {l} =\mathbf {u} \times {\boldsymbol {\omega }}}
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.
Dispersion of waves on water was studied by Pierre-Simon Laplace in 1776. [ 7 ] The universality of the Kramers–Kronig relations (1926–27) became apparent with subsequent papers on the dispersion relation's connection to causality in the scattering theory of all types of waves and particles.
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In this case the dispersion relation allows for two modes: a barotropic mode where the free surface amplitude is large compared with the amplitude of the interfacial wave, and a baroclinic mode where the opposite is the case – the interfacial wave is higher than and in antiphase with the free surface wave. The dispersion relation for this ...