The response of ice floes to ocean waves

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Abstract
A precise linear mathematical theory is reported to model the response of a solitary ice floe in ocean waves, allowing the floe to bend with the passing wave. Both infinite and finite water depths are considered, and the model is also extended to include a pair of separated floes of different length, the case of n‐floes then being a natural and straightforward development. For a single ice floe, perfect transmission is achieved whenever the wavelength beneath the ice couples perfectly to the length of the ice floe. Then the strains induced in the bending ice floe reach a maximum, and because multiple‐cycle tuning can occur in floes which are long compared to the wavelength, strain response amplitude operators (RAOs) are complicated. By considering the case of infinite stiffness, heave and roll RAOs are also found for typical ocean wave periods, and these agree well with two‐dimensional rigid‐body models. Finally, ice floes of different diameters but constant 1‐m thickness are subjected to spectral forcing, and the strain spectral density for each is found. Spectral density envelopes increase gradually with floe diameter, achieving a maximum value for a floe of about 102m. Thereafter strains never decrease below those for the 80‐m curve owing to multiple‐cycle tuning. This may explain the presence of zones within an ice field where floe size never exceeds some prescribed value. Results obtained from the complete theory for two adjacent floes do not differ significantly from those found by applying the single‐floe model serially except when the separation is very small.

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