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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 ...
Here ψ is the angle between the path of the wave source and the direction of wave propagation (the wave vector k), and the circles represent wavefronts. Consider one of the phase circles of Fig.12.3 for a particular k , corresponding to the time t in the past, Fig.12.2.
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").
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]
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 ...
In 1884, Lord Kelvin led a master class on "Molecular Dynamics and the Wave Theory of Light" at Johns Hopkins University. [90] Kelvin referred to the acoustic wave equation describing sound as waves of pressure in air and attempted to describe also an electromagnetic wave equation , presuming a luminiferous aether susceptible to vibration.
The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward). The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.