Flexural gravity wave problems in two-layer fluids

Expansion formulae for flexural gravity wave problems in two-layer fluids are developed in both the cases of water of finite and infinite depths. The developed expansion formulae are applied to (i) derive the line source flexural gravity wave potentials in the presence of floating ice sheet of finite thickness and (ii) investigate the scattering of ice-coupled waves by a narrow crack in an infinite floating ice sheet. Both the problems are analyzed in two dimensions in a two-layer fluid having an interface in case of finite and infinite depths separately. Relations based on Green’s identity are derived for the reflection and transmission coefficients in surface and interface modes. Effect of the density ratio and the position of interface on the reflection and transmission coefficients and surface and interface elevations in the scattering problem is analyzed.