Airy wave theory
![Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by √(gh) as a function of h/λ. A: phase velocity, B: group velocity, C: phase and group velocity √(gh) valid in shallow water. Drawn lines: based on dispersion relation valid in arbitrary depth. Dashed lines: based on dispersion relation valid in deep water.](/Images/godic/202412/18/Dispersion_gravity_1.svg4803.png")
![](/Images/godic/202412/18/Dispersion_capillary.svg4803.png")
![Wave motion on the interface between two layers of inviscid homogeneous fluids of different density, confined between horizontal rigid boundaries (at the top and bottom). The motion is forced by gravity. The upper layer has mean depth h‘ and density ρ‘, while the lower layer has mean depth h and density ρ. The wave amplitude is a, the wavelength is denoted by λ (related to the wavenumber k by: k = 2π / λ), the gravitational acceleration by g and the phase speed as cp (with cp = Ω(k) / k).](/Images/godic/202412/18/Interfacial_wave_rigid_boundaries.svg4803.png")
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. This theory was first published, in correct form, by George Biddell Airy in the 19th century.