The Stokes phenomenon is a class of asymptotic behaviour that was first discovered by Stokes in his study of the Airy function. It has since been shown that the Stokes phenomenon plays a significant role in the behaviour of surface waves on flows past submerged obstacles. A detailed review of recent research in this area is presented, which outlines the role that the Stokes phenomenon plays in a wide range of free surface flow geometries. The problem of inviscid, irrotational, incompressible flow past a submerged step under a thin elastic sheet is then considered. It is shown that the method for computing this wave behaviour is extremely similar to previous work on computing the behaviour of capillary waves. Exponential asymptotics are used to show that free-surface waves appear on the surface of the flow, caused by singular fluid behaviour in the neighbourhood of the base and top of the step. The amplitude of these waves is computed and compared to numerical simulations, showing excellent agreements between the asymptotic theory and computational solutions. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

中文翻译：

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关于弹性片下流动的斯托克斯现象的注记

斯托克斯现象是斯托克斯在研究艾里函数时首次发现的一类渐近行为。此后已经表明，斯托克斯现象在表面波对穿过水下障碍物的流动的行为中起着重要作用。对这一领域的最新研究进行了详细回顾，其中概述了斯托克斯现象在广泛的自由表面流动几何形状中所起的作用。然后考虑无粘性、无旋转、不可压缩流过薄弹性片下的浸没台阶的问题。结果表明，计算这种波行为的方法与之前计算毛细波行为的工作极为相似。指数渐近线用于表明自由表面波出现在流动表面，由台阶底部和顶部附近的奇异流体行为引起。计算这些波的振幅并与数值模拟进行比较，显示渐近理论和计算解决方案之间的极好一致性。本文是主题问题“斯托克斯 200（第 2 部分）”的一部分。