Santu Das

Wave propagation in a two-layer compressible ocean covered by a thin, elastic, compressed sea ice is examined by combining the linearized compressible water-wave theory with elastic thin-plate theory. In the gravity- and inertia-dominated regimes demarcated by the ice-thickness-related dimensionless parameter Ka, while the acoustic–gravity wave modes remain strictly monotonic with positive group velocity, the flexural-gravity wave mode undergoes wave blocking (no energy propagation) under high compressive force. We analytically prove and numerically demonstrate that water compressibility shifts the plate buckling threshold away from its incompressible counterpart. The variations of primary and secondary blocking points with applied compression, density ratio, interface depth, and plate thickness are shown along with a comparison with the incompressible counterpart. The system's constituent kinetic, gravitational, compressibility, and plate-associated elastic and inertial components are derived, with the kinetic component being dominant. Time-domain simulations demonstrate forward propagation, stagnation of a portion, and splitting of the wave pulse within the regular, blocking, and instability regimes, respectively, under both interface and surface forcing. These results provide new insight into how stratification, compressibility, and ice-cover mechanics govern wave propagation and energy transfer in realistic oceans.

Acoustic‐gravity wave (AGW) and ocean surface wave profiles produced by the simultaneous movement of two adjacent rectangular seafloor blocks of unequal size in opposite directions, imitating a two‐fault submarine earthquake, have been analytically studied using linearized water wave theory. Utilizing the Fourier transformation method coupled with the stationary phase approximation, the far‐field solutions of the generating surface wave and AGW profiles are deduced. The model is validated with the existing literature. Different expressions of far‐field profiles induced by asymmetry of the moving blocks are emphasized. The surface amplitudes and pressure impressions of our two‐fault system are found to be higher than those of an equivalent single rectangular moving block. The spectral energy densities (gravitational potential, kinetic, and elastic) are derived and computed. While gravitational potential energy density typically dominates for pure gravity waves, it remains negligible for AGWs, where the kinetic and elastic energies are nearly equally partitioned, reflecting a fundamental energy balance inherent to compressible fluid dynamics. The derived solutions for the potential function generalize the earlier model of a single moving block and provide insight into the wave dynamics generated by more complex multifault seafloor displacements, where the present solution would be crucial for applying the superposition of wave profiles.

The surface-gravity wave evolution, imitating tsunamis triggered by the ocean floor’s arbitrary temporal motion over a generic seafloor topography, is investigated using the linearised water-wave theory of a compressible ocean. The pressure wave bounce between the water surface and ocean floor, followed by the generation of acoustic-gravity wave (AGW) propagation away from the initial disturbance, is shown with unprecedented details. The computational novelty covers accurate pressure-wave-field computation using high-frequency AGW modes, unlike the dominant first AGW in surface waves. The mathematical problem is solved using the Fourier transformation and eigenfunction expansion techniques, following a multistep approximation of the arbitrarily deep sea. Test cases of two idealistic subsurface geometries (continental shelf and mountain range) using the ocean floor’s linear and parabolic temporal growth show elongation and shortening of the surface wavelength and changes in the propagation speed due to the variable seafloor topography through simulations. The mutual interaction of the pressure waves within the water column unravels depth-change-induced scattering. While high-frequency pressure at a shallower depth is dominant for the continental shelf, a significantly reduced amplitude across a mountain ridge is visualised with a corresponding lower impact of the acoustic-gravity wave on the surface wave. Substantial contrast in the pressure wave field triggered by a slight change in the rupture’s properties suggests its careful consideration when building tsunami prediction models. Since these AGWs are precursors to tsunamis, we believe their detection through an accurate pressure measurement will give very important information about the associated tsunami wave.

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.

The surface gravity wave evolution, imitating tsunamis triggered by the ocean floor's arbitrary temporal motion over a generic seafloor topography, is investigated using the linearised water wave theory of a compressible ocean. The unprecedented details of pressure wave bounce between the water surface and ocean floor, followed by the generation of acoustic-gravity wave (AGW) propagation away from the initial disturbance, are shown for the first time. The computational novelty covers accurate pressure-wave-field computation using high-frequency AGW modes, unlike the dominant first AGW in surface waves. The mathematical problem is solved using the Fourier transformation and eigenfunction expansion techniques, following a multistep approximation of the arbitrarily deep sea. Test cases of two idealistic subsurface geometries (continental shelf and mountain range) using the ocean floor's linear and parabolic temporal growth show elongation and shortening of the surface wavelength and changes in the propagation speed due to the variable seafloor topography through simulations. The mutual interaction of the pressure waves within the water column unravels depth-change-induced scattering. While high-frequency pressure at a shallower depth is dominant for the continental shelf, a significantly reduced amplitude across a mountain ridge is visualised with a corresponding lower impact of the acoustic-gravity wave on the surface wave. Substantial contrast in the pressure wavefield triggered by a slight change in the rupture's properties suggests its careful consideration when building tsunami prediction models. Since these AGWs are precursors to tsunamis, we believe their detection through an accurate pressure measurement will give very important information about the associated tsunami wave.