# Bound and free gravity-capillary waves

## Bound and Freely Propagating Gravity-Capillary Waves

## New Insights into Radar Backscattering and Wave Damping

## Measurements of the surface elevation and slope and of the backscattered radar power at X and Ka band were carried out with mechanically generated gravity waves as well as with wind waves on slick-free and slick-covered water surfaces. The measured radar Doppler shifts show that on a slick-free water surface, bound gravity-capillary (X and Ka band Bragg) waves are generated at the crests of steep gravity waves with frequencies between 3 and 5 Hz. However, steep gravity waves with a frequency of 2 Hz do not generate bound Ka band Bragg waves, and the Ka band backscattering from these waves is associated with wave breaking. In the wind speed range from 1.5 to 10 m/s, bound gravitycapillary waves contribute to the X and Ka band backscatter from slick-free water surfaces. The fraction of bound to freely propagating Bragg waves depends on, among other things, radar frequency, wind speed, wave amplitude of the dominant water wave, and slick coverage. In particular, the strong damping of the gravity waves by the slick at wind speeds of approximately 8 m/s leads to the disappearance of the bound Bragg waves and therefore to a reduction of the X and Ka band Doppler shifts to values corresponding to freely propagating Bragg waves. It is concluded that the study is pertinent to the understanding of former results of radar backscattering measurements in the presence of oceanic surface films.

References:

Gade, M., W. Alpers, S.A. Ermakov, H. Hühnerfuss, and P.A. Lange, 1998: Wind-wave tank measurements of bound and freely propagating short gravity-capillary waves,

J. Geophys. Res., 103,21697-21710.

### Bound (Parasitic) Capillary Waves

Steep gravity waves on the water surface with wavelengths less than 0.5 m can generate short gravity-capillary waves near their crests, which then propagate along the steep forward wave slopes. Since they do not propagate with their own phase velocity but with the (higher) phase velocity of the generating (parent) wave, they are called bound or parasitic waves. Their generation is linked to the fact that large-amplitude gravity waves have non-sinusoidal profiles and thus contain higher order harmonics. These harmonics are bound waves which, in general, do not obey the dispersion relation for free gravity-capillary waves. They propagate with the phase velocity of the 0th-order (parent) wave and since the phase velocity of these parent gravity waves is higher than the minimum phase velocity of water waves, some high-order harmonics may satisfy the dispersion relation for gravitycapillary waves. The higher order harmonics are identical to free surface waves traveling at their intrinsic phase and group velocity, and they form a wave packet moving along the steep gravity wave profile.