Airy wave, in fluid dynamics, describes a theory of surface gravity waves of small amplitude in a liquid medium of arbitrary depth; this element of wave theory is also known as linear wave theory. The derivation of the theory, given the assumptions of small wave slope (H/L >> 1) and a depth much greater than the wave height (h/H << 1), gives the expression for the fluid surface elevation:

η(x, t) = (H/2) cos(kx − σt)

where H is the wave height, k the wave number, and σ the wave frequency. This theory is most often applied to ocean bodies and large lakes. An expression for the wave length has also been developed, although it must be solved iteratively. Simpler expressions are available for the limiting cases of deep and shallow water, with deep water being the case where h/L_∞ > 1/4 (where h is the depth and L_∞ the deep water wavelength) and shallow water the case where h/L_∞ < 1/20. The particles move generally in closed elliptical orbits that decrease in diameter with depth, reducing to limiting cases of circles and straight lines in, respectively, deep and shallow water.

Further Reading

• Seas of the world
• Blair Kinsman. Wind Waves: Their Generation and Propagation on the Ocean Surface. Dover, 1984.
• Bernard LeMehaute. An Introduction to Hydrodynamics and Water Waves. Springer-Verlag, 1976.
• Paul D. Komar. Beach Processes and Sedimentation. Prentice-Hall, Inc., 1976.