Bottom pressures in a shallow compressible ocean due to nonlinear wave–non-uniform elastic-seafloor interactions

The generation and propagation of acoustic-gravity–Scholte wave fields produced by different types of nonlinear interactions between ocean surface waves and shallow, non-uniform depth contours of an elastic seafloor are investigated. Specifically, nonlinear interactions between surface waves and the seafloor, surfacewaves themselves and the seafloor, and acoustic-gravity-waves and the seafloor are shown to produce resonantly strong bottom pressures. Whereas the interaction between shoreward-propagating surface waves and seafloor depth contours (and the resulting seafloor waves and microseisms) has been discussed in the literature, not much is known about the compression wave–seafloor wave groups forming an important component of the overall energy transfer process in shallow water. Forcing due to the different wave interactions involving the seafloor depth contours and the dispersion relations for the coupled ocean–seafloor system are derived, providing estimates of the energy transfer that results at resonance when the interaction produces a wavenumber–frequency combination that lies on one of the dispersion surfaces for the two-media system. Wavenumber spectra and their temporal evolution are found analytically for stationary random surface-wave fields, and the acoustic-gravity wave potentials, seafloor pressure amplitudes, seafloor power densities and Scholte wave amplitudes are computed, and their sensitivity to critical parameters is estimated. The nonlinear interactions derived here may account for some of the 200 % increase of low-frequency ( $0.01\leqslant f\leqslant 0.03$ Hz) spectral densities of bottom pressure observed between 25 and 8 m water depths in the Atlantic Ocean at a site off Duck, NC. Further, subject to experimental validation, the power densities estimated here could contribute energy for sensing operations.