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In fluid dynamics, Airy wave theory (often referred to as linear wave theory) gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational.
The conditions for being in the far field and exhibiting an Airy pattern are: the incoming light illuminating the aperture is a plane wave (no phase variation across the aperture), the intensity is constant over the area of the aperture, and the distance from the aperture where the diffracted light is observed (the screen distance) is large ...
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.
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 ...
Shoaling coefficient as a function of relative water depth /, describing the effect of wave shoaling on the wave height – based on conservation of energy and results from Airy wave theory. The local wave height at a certain mean water depth is equal to =, with the wave height in deep water (i.e. when the water depth is greater than about half ...
The term "Airy beam" derives from the Airy integral, developed in the 1830s by Sir George Biddell Airy to explain optical caustics such as those appearing in a rainbow. [1] The Airy waveform was first theorized in 1979 by M. V. Berry and Nándor L. Balázs. They demonstrated a nonspreading Airy wave packet solution to the Schrödinger equation. [2]
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.
The Airy wave train is the only dispersionless wave in one dimensional free space. [20] In higher dimensions, other dispersionless waves are possible. [21] The Airy wave train in phase space. Its shape is a series of parabolas with the same axis, but oscillating according to the Airy function.