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 planewaves on the surface. In the process, a new set of the second-order perturbation equations is derived and power-correlation coefficients between random planewaves 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. The wind- pressure model and the first-order perturbation analysis are generalized versions of those in the previous paper [1].