Floe Size Effect on Gravity Wave Propagation Through Ice Covers

When modeling gravity wave propagation through an array of discrete ice floes, considered as a homogenous elastic continuum, the equivalent elasticity is less than the intrinsic material elasticity of ice. The array behaves increasingly like a collection of rigid floating masses when the floe sizes decrease. Extending a former wave flume experiment with polyethylene plates (Sakai & Hanai, 2002, https://web2.clarkson.edu/projects/iahrice/IAHR%202002/Volume%202/189.pdf), we conducted an experiment with saline ice floes at the Hamburg Ship Model Basin (HSVA). Using the measured wave number and the dispersion relation from a continuous elastic plate theory, we determine the equivalent elasticity. Parallel theoretical solutions are obtained using the matched eigenfunction expansion method (Kohout et al., 2007, https://doi.org/10.1016/j.jfluidstructs.2006.10.012), assuming ice floes as an array of thin elastic plates floating over inviscid water. Despite data scatter in laboratory tests, the celerity (phase speed) from the laboratory and theoretical results both show a decreasing trend when the floe size reduces. The corresponding equivalent elastic modulus decreases from the intrinsic modulus to zero. The matched eigenfunction expansion method is then applied to investigate cases under field conditions. Using all the theoretical results, an empirical relation is proposed for the equivalent elasticity in terms of wavelength, floe size, and length scale from the intrinsic elasticity of the floes. In addition to celerity, wave amplitude along the ice cover is compared with the theoretical results. Large discrepancies of wave attenuation from laboratory and theoretical solutions are found, indicating that attenuation mechanisms other than wave scattering need to be considered.