Linear wave forcing of an array of axisymmetric ice floes

• Published in: IMA Journal of Applied Mathematics
• Main Authors: Bennetts, L., Squire, V.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Oxford Univ Press 2010
• Subjects: Green's function; periodic array; sea ice; flexural-gravity waves; scattering; Luke; Sea ice
• Online Access: http://hdl.handle.net/2440/75458; https://doi.org/10.1093/imamat/hxp038

Under linear and time-harmonic conditions, a set of periodic Green's functions is derived to combine the interactions of an infinite number of identical equispaced floating bodies. The bodies themselves are compliant thin elastic plates that can represent ice floes, and unlike previous studies, they are permitted to vary axisymmetrically in thickness through both their upper and their lower surfaces, with a realistic draught also admitted. Initially, the governing equations are simplified by means of an expansion of the vertical dependence of the unknown velocity potential combined with a variational principle, which reduces calculations to the horizontal plane alone. The unknowns of the resulting equations are written as an integral representation in the free-surface domain and as a Fourier expansion in the domain of the ice-covered fluid, and these are matched at their common boundary to complete the solution process. Our method is validated using numerical results for example problems. The effects of varying the distance between the floes, as well as the introduction of thickness variations and submergence, are also demonstrated. Luke G. Bennetts and Vernon A. Squire