Ripple factor derivation

Jump to navigation Jump to search This article is about ripples on fluid interfaces. Ripple factor derivation waves produced by droplet impacts on the interface between water and air. 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 on water is typically less than a few centimeters, with a phase speed in excess of 0. Ordinary gravity waves have a still longer 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. Dashed lines: dispersion relation for deep-water gravity waves.

Dash-dotted lines: dispersion relation valid for deep-water capillary waves. Phase velocity is two thirds of group velocity in this limit. Between these two limits is a point at which the dispersion caused by gravity cancels out the dispersion due to the capillary effect. At a certain wavelength, the group velocity equals the phase velocity, and there is no dispersion. The derivation of the general dispersion relation is therefore quite involved. Therefore, first the assumptions involved are pointed out.