A note on the turbulence generated by gravity waves

When gravity waves move across the surface of a liquid of small viscosity, an irregular vorticity (turbulence) field is generated which can attain a statistically steady state through the balance of vorticity generation by the straining associated with the waves and of viscous diffusion. The influence of this vorticity field on the wave motion is examined. It is found that in the equations describing the fluctuating properties of the wave motion, the influence is usually of the third order in the wave slope and results in a slow attenuation of the waves of the form a(t) = a(t0) {1 + const, (t - t0)}−½, where a(t) is the wave amplitude at time t.