Wave interaction with a large number of ice floes of arbitrary shapes

Water wave interaction with a large number of floes is investigated, based on the linearized velocity potential theory for fluid flow, and elastic thin plate theory for ice floes. The solution procedure starts from a domain decomposition approach, and equations for velocity potentials are constructed via the boundary integral method in the free-surface and ice-covered subdomains, separately. The velocity potentials and normal velocities at the interface of different domains are expressed in terms of eigenfunction expansions in the vertical direction. This allows the three-dimensional equation to be reduced to a set of two-dimensional ones. Continuity of velocity and pressure are then imposed at the interface. A formula for evaluating hydrodynamic forces is derived, which requires only the results on the floe edge. When the number of ice floes becomes large, an efficient scheme is introduced to reduce computational effort, while the desired accuracy is maintained. The procedure is applicable to ice floes of arbitrary shapes and arrangements. Case studies are conducted for single and double arrays of circular and elliptical ice floes. Extensive results are provided for the hydrodynamic forces and far-field scattered wave energy. Their features and corresponding physics are discussed.