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Furthermore, this phenomenon has nothing to do with turbulence. Everything discussed here is based on the linear theory of an ideal fluid, cf. Airy wave theory. Parts of the pattern may be obscured by the effects of propeller wash, and tail eddies behind the boat's stern, and by the boat being a large object and not a point source.
A Kelvin wave is a wave in the ocean, a large lake or the atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive , i.e., the phase speed of the wave crests is equal to the group speed of the wave energy ...
In practice the wave pattern between the V-shaped wavefronts is usually mixed with the effects of propeller backwash and eddying behind the boat's (usually square-ended) stern. The Kelvin angle is also derived for the case of deep water in which the fluid is not flowing in different speed or directions as a function of depth ("shear").
Wave trapping is the result of the Earth's rotation and its spherical shape which combine to cause the magnitude of the Coriolis force to increase rapidly away from the equator. Equatorial waves are present in both the tropical atmosphere and ocean and play an important role in the evolution of many climate phenomena such as El Niño .
If the density and velocity vary continuously in space (with the lighter layers uppermost, so that the fluid is RT-stable), the dynamics of the Kelvin-Helmholtz instability is described by the Taylor–Goldstein equation: (~ ~) + [()] ~ =, where = / denotes the Brunt–Väisälä frequency, U is the horizontal parallel velocity, k is the wave ...
The first tide predicting machine (TPM) was built in 1872 by the Légé Engineering Company. [11] A model of it was exhibited at the British Association meeting in 1873 [12] (for computing 8 tidal components), followed in 1875-76 by a machine on a slightly larger scale (for computing 10 tidal components), was designed by Sir William Thomson (who later became Lord Kelvin). [13]
William Thomson, 1st Baron Kelvin (26 June 1824 – 17 December 1907 [7]), was a British mathematician, mathematical physicist and engineer. [8] [9] Born in Belfast, he was the professor of Natural Philosophy at the University of Glasgow for 53 years, where he undertook significant research and mathematical analysis of electricity, was instrumental in the formulation of the first and second ...
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.