The scattering of gravity waves by turbulence

A theory is developed to describe the properties of waves on the free surface of a liquid in turbulent motion. The distinction between the interacting wave and turbulent motions is achieved by separating the velocity field uniquely into a surface-induced contribution characteristic of the wave motion and a vorticity-induced contribution associated with the turbulence. The theory is applied to the scattering of gravity waves passing over the surface of deep water which has a turbulent motion of sufficiently low mean square vorticity. Expressions are derived for the directional distribution of the scattered wave (equation 4.19) and for the logarithmic decrement resulting from the scattering (4.20). It is shown that, under typical conditions in open sea, the attenuation from scattering will be greater than that from direct viscous dissipation for wavelengths greater than about 3 m.