A generalised inner product-based wave scattering from an underwater source in a compressible ocean

Motivated by applications to underwater explosions and volcanic eruptions, this paper considers the evolution of an initial pressure disturbance in the ocean, including effects due to the dynamic and static compression of water and the free surface. In order to solve the equations of motion of a linear compressible ocean, a special inner product is introduced, which allows us to apply self-adjoint operator theory. What results is a Hilbert space in which the acoustic–gravity modes are orthogonal in the generalised sense. This allows the time-domain evolution of the free surface and subsurface pressure field resulting from an initial disturbance to be calculated. Our simulations show initial radial propagation of the pressure pulse and subsequent reflection from the water's surface and the rigid ocean floor, eventually leading to horizontal propagation away from the source point. The solutions with and without the inclusion of the static compression are compared, and the effect of static compression is shown to be small but not negligible.