Skip to main content

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  • Callaghan DP, Nielsen P, Cartwright N, Gourlay MR, Baldock TE (2006) Atoll lagoon flushing forced by waves. Coastal Eng 53:691–704

    Google Scholar 

  • Craig P, Birkeland C, Belliveau S (2001) High temperatures tolerated by a diverse assemblage of shallow-water corals in American Samoa. Coral Reefs 20:185–189

    Article  Google Scholar 

  • Hench JL, Leichter JL, Monismith SG (2008) Episodic circulation and exchange in a wave driven coral reef lagoon system. Limnol Ocean 53:2681–2694

    Article  Google Scholar 

  • Kench PS, Brander RW (2006) Wave processes on coral reef flats: Implications for reef geomorphology using Australian case studies. J Coastal Res 22:209–223

    Google Scholar 

  • Longuet-Higgins M, Stewart R (1962) Radiation stress and mass transport in gravity waves, with application to ‘surf beats’. J Fluid Mech 13:481–504

    Google Scholar 

  • Lowe RJ, Falter JL, Monismith SG, Atkinson MJ (2009) Wave-driven circulation of a coastal reef lagoon system. J Phys Oceangr 39:873–893

    Article  Google Scholar 

  • Lowe RJ, Hart C, Pattiaratchi CB (2010) Morphological constraints to wave-driven circulation in coastal reef-lagoon systems: a numerical study. J Geophys Res 115:C09021

    Google Scholar 

  • Monismith SG, Herdman LM, Ahmerkamp S, Hench JL (2013) Wave transformation and wave-driven flow across a steep coral reef. J Phys Oceangr 43:1356–1379

    Article  Google Scholar 

  • Oliver TA, Palumbi SR (2009) Distributions of stress-resistant coral symbionts match environmental patterns at local but not regional scales. Mar Ecol Prog Ser 378:93–103

    CAS  Article  Google Scholar 

  • Reidenbach MA, Monismith SG, Koseff JR, Yahel G, Genin A (2006) Boundary layer turbulence and flow structure over a fringing coral reef. Limnol Oceanogr 51:1956–1968

    Google Scholar 

  • Roelvink JA, Reniers A, van Dongeren A, Van Thiel de Vries J, McCall R, Lescinski J (2009) Modeling storm impacts on beaches, dunes and barrier islands. Coastal Eng 56:1133–1152

    Google Scholar 

  • Rosman JH, Hench JL (2011) A framework for understanding drag parameterizations for coral reefs. J Geophys Res 116:C08025

    Google Scholar 

  • Symonds G, Black KP, Young IR (1995) Wave-driven flow over shallow reefs. J Geophys Res 100:2639–2648

    Article  Google Scholar 

  • Taebi S, Lowe RJ, Pattiaratchi CB, Ivey GN, Symonds G, Brinkman R (2011) Nearshore circulation in a tropical fringing reef system. J Geophys Res 116:C02016

    Google Scholar 

  • Tait RJ (1972) Wave set-up on coral reefs. J Geophys Res 77:2207–2211

    Article  Google Scholar 

  • Vetter O, Becker JM, Merrifield MA, Pequignet AC, Aucan J, Boc SJ, Pollock CE (2010) Wave setup over a Pacific Island fringing reef. J Geophys Res 115:C12066

    Google Scholar 

Download references


The author is grateful for numerous discussions with Ryan Lowe, Jim Hench, Jim Falter, the late Marlin Atkinson, and other colleagues including Graham Symonds about the physics of flows over coral reefs. This work was partially supported by the Environmental Ventures Program of the Woods Institute for the Environment at Stanford University.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Stephen G. Monismith.

Additional information

Communicated by Biology Editor Dr. Anastazia Banaszak

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Monismith, S.G. Flow through a rough, shallow reef. Coral Reefs 33, 99–104 (2014).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Hydrodynamics
  • Circulation
  • Drag
  • Flow