Gravity-wave-induced pressure fluctuations in the deep ocean

We establish a mathematically consistent theory of the pseudo-sound pressure fluctuation in the deep ocean induced by nonlinearly interacting random plane waves on the surface. In the process, a new set of the second-order perturbation equations is derived and power-correlation coefficients between random plane waves are introduced. A phenomenological model is adopted for wind pressure which excites the surface waves consisting of wind-driven sea and swell. By solving the first-order- and the second-order-perturbation equations with this wind pressure as the excitation, we obtain an expression for the pressure fluctuation and its power spectral density in the gravity-wave regime. It is concluded that only the swell part of the surface waves generates the pressure fluctuation and the spectral density is modified by the power correlation coefficient.