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 …