A variational principle is proposed to derive the governing equations for the problem of ocean wave interactions with a floating ice shelf, where the ice shelf is modelled by the full linear equations of elasticity and has an Archimedean draught. The variational principle is used to form a thin-plate approximation for the ice shelf, which includes water–ice coupling at the shelf front and extensional waves in the shelf, in contrast to the benchmark thin-plate approximation for ocean wave interactions with an ice shelf. The thin-plate approximation is combined with a single-mode approximation in the water, where the vertical motion is constrained to the eigenfunction that supports propagating waves. The new terms in the approximation are shown to have a major impact on predictions of ice shelf strains for wave periods in the swell regime.

中文翻译：

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海浪与冰架相互作用的薄板近似

提出了变分原理来推导海浪与浮动冰架相互作用问题的控制方程，其中冰架由完全线性弹性方程建模并具有阿基米德吃水深度。变分原理用于形成冰架的薄板近似，其中包括陆架前部的水-冰耦合和陆架中的延伸波，这与海浪与冰相互作用的基准薄板近似形成对比架子。薄板近似与水中的单模近似相结合，其中垂直运动被限制为支持传播波的本征函数。近似中的新项被证明对涌浪区域中波浪周期的冰架应变的预测有重大影响。