Dynamics of motions and deformations of an arbitrary geometry flexural floe in ocean waves

TL;DR

This paper presents a detailed mathematical model for the hydroelastic behavior of arbitrarily shaped sea-ice floes with variable thickness under linear ocean wave forcing, integrating rigid-body motions and flexural deformations.

Contribution

It introduces a unified Green function framework that combines rigid motions and flexural modes for arbitrary floe geometries and thicknesses, including eigenanalysis and resonance analysis.

Findings

Complete orthogonal basis of deformation modes derived

Explicit boundary condition formulations provided

Resonance phenomena linked to wave frequency and natural modes

Abstract

This paper develops a comprehensive mathematical framework for modeling the coupled hydroelastic dynamics of sea-ice floes of arbitrary shape and non-uniform thickness under linear ocean wave forcing. We simultaneously incorporate four dominant rigid-body motions (heave, surge, roll, pitch) and the complete spectrum of flexural deformation modes within a unified Green function formulation. The water flow is modeled using potential theory with Laplace's equation, while the floe obeys a generalized Kirchhoff-Love plate equation with spatially varying flexural rigidity. We formulate the coupled fluid-structure interaction problem through kinematic velocity-matching conditions and dynamic pressure-continuity conditions at the ice-water interface. The elastic eigenproblem with free-edge boundary conditions yields a complete orthogonal basis of deformation modes, accounting for added mass effects through modified natural frequencies. By decomposing the velocity potential into partial potentials associated with incident waves, scattered waves, rigid motions, and elastic modes, we reduce the problem to a system of Fredholm integral equations of the second kind for surface density functions on all boundary segments. The solution methodology employs single-layer potential representations with fundamental Green functions for Laplace's equation. We present explicit formulations for all boundary conditions in compact tensor form, provide asymptotic analysis for the spectrum of non-uniform thickness floes, and discuss resonance phenomena arising from the interaction between incident wave frequency and natural vibration modes.