Propagation characteristics of ultra-low-frequency surface-trapped acoustic-gravity waves excited by an underwater point source

Abstract

At ultra-low frequencies, underwater pressure fields may be influenced by dynamic free-surface motion as well as conventional water-column acoustics. This study investigates whether gravity-restored free-surface coupling creates a surface-trapped acoustic–gravity-wave pathway that is absent from a pressure-release model. A pressure-based finite-difference time-domain model is verified against Gaussian pressure-disturbance and Pekeris-waveguide benchmarks and then applied to paired simulations in a penetrable water–sediment waveguide. For a 0.1 Hz point source, both models produce nearly identical early compressional arrivals, whereas only the gravity-restored model generates a delayed, long-lived response concentrated beneath the free surface. Under continuous forcing, this response develops into a coherent, comparatively low-loss, radially propagating wave train. Wavenumber–frequency spectra, phase- and group-velocity estimates, and mechanical energy-flux calculations identify the response as belonging to the finite-depth surface-gravity branch. Singular value decomposition (SVD) further shows that the surface-localized SVD mode weakens as source frequency and source depth increase; deeper sources increase the second-mode fraction and broaden the vertical pressure distribution. These results demonstrate that gravity-restored free-surface coupling enables a distinct pathway for ultra-low-frequency energy redistribution and near-surface transport in underwater waveguides.