Wave structure interaction problems for two-layer fluids in three dimensions

Abstract

The effect of compressive force on flexural gravity waves in two-layer fluids is analysed. Wave characteristics for surface and interfacial modes in the cases of deep and shallow water are studied and the effect of compression on these modes is analysed in special cases from the general problem. Generalized expansion formulae and associated orthogonal mode-coupling relations are derived for the velocity potentials to deal with wave structure interaction problems in three dimensions in both the cases of finite and infinite water depths in channels of finite and semi-infinite widths. Several characteristics of the eigenfunctions are derived in specific cases. As an application of the expansion formulae, wave scattering due to partially frozen cracks in floating ice sheet is analysed in a channel of finite width and depth in the presence of compressive force in two-layer fluids.