Flow through a rough, shallow reef

This paper presents a simple model of wave-driven flow through a coral reef that is characterized by a shallow, wide reef crest and a deeper, but frictional lagoon. Assuming that the dominant momentum balances are between quadratic drag and barotropic pressure gradients, along-lagoon and cross-reef flows are coupled through continuity and through a setup of the water surface in the lagoon that varies in the along-reef direction. Scaling of the governing equations shows that this flow is governed by a single parameter P that expresses the competing effects of cross-reef and along-lagoon drag. When P < 1, the cross-reef flow is nearly constant, whereas when P > 1, only that portion of the reef closest to the pass through the reef crest through which fluid exists the lagoon supports cross-reef flows.