Capillary waves
A capillary wave is a wave traveling along the phase boundary of a fluid, whose dynamics and phase velocity are dominated by the effects of surface tension.
Capillary waves are common in nature, and are often referred to as ripples. The wavelength of capillary waves in water is typically less than a few centimeters, with a phase speed in excess of 0.2 meter/second.
A higher wavelength on a fluid interface will result in gravity–capillary waves which are influenced by both the effects of surface tension and gravity, as well as by fluid inertia. Ordinary gravity waves have a still higher wavelength.
When generated by light wind in open water, a nautical name for them is cat's paw waves, since they may resemble paw prints. Light breezes which stir up such small ripples are also sometimes referred to as cat's paws. On the open ocean, much larger ocean surface waves (seas and swells) may result from coalescence of smaller wind-caused ripple-waves.
The dispersion relation for capillary waves is
where ω is the angular frequency, σ the surface tension, ρ the density of the heavier fluid, ρ' the density of the lighter fluid and k the wavenumber. The wavelength is For the boundary between fluid and vacuum (free surface), the dispersion relation reduces to
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