Translating and pulsating Green function with an ice cover

The translating and pulsating Green function representing the velocity potential due to a time-harmonically pulsating source advancing at a uniform forward speed in water with an ice cover is studied in this paper. The ice cover is modelled as a homogeneous elastic plate. The Green function satisfying the linearized covered-surface condition of elastic plate is derived and represented in two-fold polar and wavenumber integral on the Fourier plane. The integral with respect to the polar angle is first performed by applying the theorem of residue. The resultant wavenumber integral is reformulated and then evaluated numerically by removing the weak singularities. The Green function and its derivatives are calculated and the ice plate deflection is analysed. All the works in this paper lay a foundation for solving the hydrodynamics of sea ice with Boundary Element Method (BEM) and shed some light on the nature of the flexural-gravity wave generated by the translating and pulsating source.