Capillary wave
From Free net encyclopedia
A capillary wave is a wave travelling along the interface between two fluids, whose dynamics are dominated by the effects of surface tension. Capillary waves are common in nature and the home and are often referred to as ripples. The wavelength of capillary waves is typically less than about a centimeter.
The dispersion relation for capillary waves is
- <math>
\omega^2=\frac{\sigma}{\rho+\rho'}k^3</math> where ω is the 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 <math> \lambda=\frac{2 \pi}{k}</math>
The waves with large wavelengths are generally also affected by gravity and are then called gravity-capillary waves. Their dispersion relation reads, for infinite depth of the two fluids,
- <math>
\omega^2=\frac{g(\rho-\rho')}{\rho+\rho'}k+\frac{\sigma}{\rho+\rho'}k^3</math> where ω is the frequency, g the acceleration due to gravity, σ the surface tension, ρ the density and k the wavenumber. This class of waves involves ocean surface waves.