The effect of compressed ice-shelf on acoustic-gravity wave propagation in a compressible ocean having elastic bottom

Abstract

Acoustic-gravity wave propagation under a compressed ice-shelf is mathematically modelled under the assumption of small ice-shelf deflection, linearised compressible water wave theory, and ocean floor elasticity. The dispersion relation associated with the acoustic-gravity modes is derived. Special cases of the free surface gravity wave motion with a rigid and elastic bottom, and flexural-gravity wave motion with rigid ocean bottom are approximated by utilising the dispersion relation. The effect of ice-shelf thickness and compressive stress on the propagation speed is investigated for different acoustic-gravity modes. The pressure distribution along the water column and the ice-shelf due to different acoustic-gravity modes are illustrated. While ice thickness significantly alters the phase speed and pressure distribution, the compressive force generally has a negligible effect on the phase speed of acoustic-gravity modes. However, the compression has significant effect on the pressure distribution. A separate treatment for relatively low frequencies shows a significant impact of the compressive force on the spatial pressure distribution. The dominance of the leading acoustic-gravity modes on different physical characteristics is evident from their graphical representations. An orthogonality property for the depth-dependent functions of the velocity potential in the water region is established along with a few approximate forms. This mathematical model can be treated as a more general one that can unify several well-established models of acoustic-gravity wave propagation.