waterwave

Waterwave is a term used to describe waves on the surface of a body of water. They occur when energy is transferred to the water surface by wind, tectonic activity, or other disturbances, and are restored by gravity, and for small waves also by surface tension. These waves can occur in oceans, seas, lakes, and reservoirs, and vary in wavelength, period, and amplitude.

Two broad classes are capillary waves and gravity waves. Capillary waves have short wavelengths (roughly less than 2 cm to a few centimeters) and are primarily governed by surface tension. Gravity waves have longer wavelengths and are governed by gravity as the restoring force; they include wind waves and tsunamis.

In deep water, the dispersion relation is ω^2 = gk, where ω is angular frequency and k is wavenumber. The phase velocity is c_p = ω/k = √(g/k), and the group velocity is c_g = dω/dk = (1/2)√(g/k) = c_p/2. In shallow water, the speed is approximately c ≈ √(gh), and waves become nearly non-dispersive to first order.

Common phenomena include wind-generated waves (the sea state), swell that travels from distant wind systems, and breaking waves near shore, as well as ship waves. Capillary ripples can appear on calm days, while tsunamis are long-wavelength gravity waves that propagate across oceans with speeds that depend on depth and can shorten dramatically near coastlines.

Measurement and study involve buoys, radar, and satellites to observe wave properties, along with spectral analysis. Applications cover navigation safety, coastal engineering, and climate-related research.