In his famous paper of 1847 (Stokes GG. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455), Stokes introduced the drift effect of particles in a fluid that is undergoing wave motion. This effect, now known as Stokes drift, is the result of differences between the Lagrangian and Eulerian velocities of the fluid element and has been well-studied, both in the laboratory and as a mechanism of mass transport in the oceans. On a smaller scale, it is of vital importance to the hydrodynamics of coral reefs to understand drift effects arising from waves on the ocean surface, transporting nutrients and oxygen to the complex ecosystems within. A new model is proposed for a class of coral reefs in shallow seas, which have a permeable layer of depth-varying permeability. We then note that the behaviour of the waves above the reef is only affected by the permeability at the top of the porous layer, and not its properties within, which only affect flow inside the porous layer. This model is then used to describe two situations found in coral reefs; namely, algal layers overlying the reef itself and reef layers whose permeability decreases with depth. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

中文翻译：

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斯托克斯在珊瑚礁中随深度变化的渗透率漂移

在他 1847 年的著名论文（Stokes GG. 1847 On theory of Ocouncey wave. Trans. Camb. Phil. Soc. 8, 441–455）中，Stokes 介绍了粒子在经历波动的流体中的漂移效应。这种效应，现在称为斯托克斯漂移，是流体元素的拉格朗日速度和欧拉速度之间差异的结果，并且已经在实验室中和作为海洋中的质量传输机制进行了充分研究。在较小的范围内，了解海洋表面波浪引起的漂移效应，将营养物质和氧气输送到内部复杂的生态系统，对珊瑚礁的流体动力学至关重要。为浅海中的一类珊瑚礁提出了一种新模型，这些珊瑚礁具有随深度变化的渗透率的渗透层。然后我们注意到，珊瑚礁上方的波浪行为仅受多孔层顶部渗透率的影响，而不受其内部特性的影响，后者仅影响多孔层内部的流动。然后使用该模型来描述在珊瑚礁中发现的两种情况；即覆盖在礁体上的藻层和渗透率随深度降低的礁体层。本文是主题问题“斯托克斯 200（第 2 部分）”的一部分。