Effect of In-Plane Compression on Wave Dispersion in a Viscoelastic Medium over an Inviscid Fluid Layer

Wave propagation in a viscoelastic medium over an inviscid fluid layer has been extensively studied due to its applications in environmental and ocean modelling, particularly in the context of ice-covered seas. The present work examines wave dispersion in a thick viscoelastic medium overlying an inviscid fluid, with additional in-plane compression applied at both the free surface and the interface. The dispersion relation governing this configuration is derived and the dispersion characteristics along with the group velocity are analysed for both elastic and viscoelastic cases. Shallow- and deep-water approximations are also obtained from the derived dispersion relation and their behaviour is examined. A critical buckling load is identified, and a relation connecting the governing parameters with this critical load is obtained under the shallow-water approximation, which distinguishes the stable and unstable regions of wave propagation. The analysis is further extended to the viscoelastic case, where the effect of viscosity on the dispersion characteristics is investigated. A critical viscosity is identified, beyond which the behaviour of the compression-induced mode changes significantly. These findings enhance our understanding of wave dispersion in a two-layer system consisting of a viscoelastic medium over an inviscid fluid, which serves as an idealised model for ice-covered domains and surface layers such as oil spills in the ocean.