Three-dimensional Green's function method applied to the steady wave-making problem of submerged bodies sailing under an ice cover

This paper presents an investigation on steady motion of three-dimensional submerged bodies in water beneath an ice sheet. The detailed derivation of the Green's function for steady flow with ice cover is first provided, and its validity is confirmed through computations involving a moving point source and the ice deflection it produces. Then, based on the Green's function, a boundary element method, in conjunction with the corresponding numerical program, is established to evaluate the wave-making resistance and wave propagation on the ice cover. The results show that for the ice thickness tending to zero, the present computations are in close agreement with those obtained from free-surface Green's function method, as reported in the published literature. But as the ice thickness increases, the hydrodynamic performance with ice cover shows a significant difference. There exists a critical speed associated with ice parameters, below which the wave resistance on the submerged body is always equal to zero and the generated waves cannot propagate to infinity. Above the speed, additional waves are found to propagate upstream, along with those traveling downstream, which leads to a larger wave resistance in comparison to the open water. Comprehensive research and analysis are conducted on submerged bodies at various forward speeds, ice thicknesses, and submerged depths. Within the calculated range, it is revealed that the wave resistance and the wave amplitude increase as the submerged depth decreases or the ice sheet gets thicker at speeds exceeding the critical value.