Dynamics of Wave Setup over a Steeply Sloping Fringing Reef

Mark L. Buckley School of Earth and Environment, and The Oceans Institute, and ARC Centre of Excellence for Coral Reef Studies, University of Western Australia, Crawley, Western Australia, Australia

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Ryan J. Lowe School of Earth and Environment, and The Oceans Institute, and ARC Centre of Excellence for Coral Reef Studies, University of Western Australia, Crawley, Western Australia, Australia

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Jeff E. Hansen School of Earth and Environment, and The Oceans Institute, University of Western Australia, Crawley, Western Australia, Australia

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Ap R. Van Dongeren Unit ZKS, Department AMO, Deltares, Delft, Netherlands

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Abstract

High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.

Corresponding author address: Mark L. Buckley, School of Earth and Environment, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia. E-mail: mark.buckley@uwa.edu.au

Abstract

High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.

Corresponding author address: Mark L. Buckley, School of Earth and Environment, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia. E-mail: mark.buckley@uwa.edu.au
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  • Apotsos, A., B. Raubenheimer, S. Elgar, R. T. Guza, and J. A. Smith, 2007: Effects of wave rollers and bottom stress on wave setup. J. Geophys. Res., 112, C02003, doi:10.1029/2006JC003549.

    • Search Google Scholar
    • Export Citation
  • Baldock, T. E., A. Golshani, D. P. Callaghan, M. I. Saunders, and P. J. Mumby, 2014: Impact of sea-level rise and coral mortality on the wave dynamics and wave forces on barrier reefs. Mar. Pollut. Bull., 83, 155–164, doi:10.1016/j.marpolbul.2014.03.058.

    • Search Google Scholar
    • Export Citation
  • Battjes, J. A., 1972: Radiation stresses in short-crested waves. J. Mar. Res., 30, 56–64.

  • Battjes, J. A., 1974: Surf similarity. Proc. 14th Conf. on Coastal Engineering, Copenhagen, Denmark, ASCE, 466–480.

  • Battjes, J. A., 1988: Surf-zone dynamics. Annu. Rev. Fluid Mech., 20, 257–293, doi:10.1146/annurev.fl.20.010188.001353.

  • Battjes, J. A., and M. J. F. Stive, 1985: Calibration and verification of a dissipation model for random breaking waves. J. Geophys. Res., 90, 9159–9167, doi:10.1029/JC090iC05p09159.

    • Search Google Scholar
    • Export Citation
  • Becker, J. M., M. A. Merrifield, and M. Ford, 2014: Water level effects on breaking wave setup for Pacific Island fringing reefs. J. Geophys. Res. Oceans, 119, 914–932, doi:10.1002/2013JC009373.

    • Search Google Scholar
    • Export Citation
  • Bonmarin, P., 1989: Geometric-properties of deep-water breaking waves. J. Fluid Mech., 209, 405–433, doi:10.1017/S0022112089003162.

    • Search Google Scholar
    • Export Citation
  • Booij, N., R. C. Ris, and L. H. Holthuijsen, 1999: A third-generation wave model for coastal regions: 1. Model description and validation. J. Geophys. Res., 104, 7649–7666, doi:10.1029/98JC02622.

    • Search Google Scholar
    • Export Citation
  • Bouws, E., H. Gunther, W. Rosenthal, and C. L. Vincent, 1985: Similarity of the wind wave spectrum in finite depth water: 1. Spectral form. J. Geophys. Res., 90, 975–986, doi:10.1029/JC090iC01p00975.

    • Search Google Scholar
    • Export Citation
  • Bowen, A. J., D. L. Inman, and V. P. Simmons, 1968: Wave set-down and set-up. J. Geophys. Res., 73, 2569–2577, doi:10.1029/JB073i008p02569.

    • Search Google Scholar
    • Export Citation
  • Buckley, M., R. Lowe, and J. Hansen, 2014: Evaluation of nearshore wave models in steep reef environments. Ocean Dyn., 64, 847–862, doi:10.1007/s10236-014-0713-x.

    • Search Google Scholar
    • Export Citation
  • Dally, W. R., and C. A. Brown, 1995: A modeling investigation of the breaking wave roller with application to cross-shore currents. J. Geophys. Res., 100, 24 873–24 883, doi:10.1029/95JC02868.

    • Search Google Scholar
    • Export Citation
  • Dean, R. G., and R. A. Dalrymple, 1991: Water Wave Mechanics for Engineers and Scientist. Advanced Series on Ocean Engineering, Vol. 2, World Scientific, 368 pp.

  • Dean, R. G., and C. J. Bender, 2006: Static wave setup with emphasis on damping effects by vegetation and bottom friction. Coastal Eng., 53, 149–156, doi:10.1016/j.coastaleng.2005.10.005.

    • Search Google Scholar
    • Export Citation
  • Duncan, J. H., 1981: An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. Roy. Soc. London, A377, 331–348, doi:10.1098/rspa.1981.0127.

    • Search Google Scholar
    • Export Citation
  • Eslami Arab, S., A. van Dongeren, and P. Wellens, 2012: Studying the effect of linear refraction on low-frequency wave propagation (physical and numerical study). Proc. 33rd Conf. on Coastal Engineering, Santander, Spain, Coastal Engineering Research Council, waves.9, doi:10.9753/icce.v33.waves.9.

  • Falter, J. L., R. J. Lowe, Z. L. Zhang, and M. McCulloch, 2013: Physical and biological controls on the carbonate chemistry of coral reef waters: Effects of metabolism, wave forcing, sea level, and geomorphology. PLoS One, 8, e53303, doi:10.1371/journal.pone.0053303.

    • Search Google Scholar
    • Export Citation
  • Feddersen, F., 2004: Effect of wave directional spread on the radiation stress: Comparing theory and observations. Coastal Eng., 51, 473–481, doi:10.1016/j.coastaleng.2004.05.008.

    • Search Google Scholar
    • Export Citation
  • Feddersen, F., R. T. Guza, S. Elgar, and T. H. C. Herbers, 2000: Velocity moments in alongshore bottom stress parameterizations. J. Geophys. Res., 105, 8673–8686, doi:10.1029/2000JC900022.

    • Search Google Scholar
    • Export Citation
  • Feddersen, F., E. L. Gallagher, R. T. Guza, and S. Elgar, 2003: The drag coefficient, bottom roughness, and wave-breaking in the nearshore. Coastal Eng., 48, 189–195, doi:10.1016/S0378-3839(03)00026-7.

    • Search Google Scholar
    • Export Citation
  • Gourlay, M. R., 1996: Wave set-up on coral reefs. 2. Set-up on reefs with various profiles. Coastal Eng., 28, 17–55, doi:10.1016/0378-3839(96)00009-9.

    • Search Google Scholar
    • Export Citation
  • Govender, K., G. P. Mocke, and M. J. Alport, 2002: Video-imaged surf zone wave and roller structures and flow fields. J. Geophys. Res., 107, doi:10.1029/2000JC000755.

    • Search Google Scholar
    • Export Citation
  • Govender, K., H. Michallet, M. J. Alport, U. Pillay, G. P. Mocke, and M. Mory, 2009: Video DCIV measurements of mass and momentum fluxes and kinetic energies in laboratory waves breaking over a bar. Coastal Eng., 56, 876–885, doi:10.1016/j.coastaleng.2009.04.002.

    • Search Google Scholar
    • Export Citation
  • Grant, W. D., and O. S. Madsen, 1979: Combined wave and current interaction with a rough bottom. J. Geophys. Res., 84, 1797–1808, doi:10.1029/JC084iC04p01797.

    • Search Google Scholar
    • Export Citation
  • Grilli, S. T., I. A. Svendsen, and R. Subramanya, 1997: Breaking criterion and characteristics for solitary waves on slopes. J. Waterw. Port Coastal Ocean Eng., 123, 102–112, doi:10.1061/(ASCE)0733-950X(1997)123:3(102).

    • Search Google Scholar
    • Export Citation
  • Iwata, K., and T. Tomita, 1992: Variation of potential and kinetic wave energy in surf zone. Proc. 23rd Int. Conf. Coastal Engineering, Venice, Italy, ASCE, 336–349.

  • Lentz, S., and B. Raubenheimer, 1999: Field observations of wave setup. J. Geophys. Res., 104, 25 867–25 875, doi:10.1029/1999JC900239.

    • Search Google Scholar
    • Export Citation
  • Lentz, S., M. Fewings, P. Howd, J. Fredericks, and K. Hathaway, 2008: Observations and a model of undertow over the inner continental shelf. J. Phys. Oceanogr., 38, 2341–2357, doi:10.1175/2008JPO3986.1.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., 1970: Longshore currents generated by obliquely incident sea waves: 1. J. Geophys. Res., 75, 6778, doi:10.1029/JC075i033p06778.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., and R. W. Stewart, 1962: Radiation stress and mass transport in gravity waves, with application to ‘surf beats.’ J. Fluid Mech., 13, 481–504, doi:10.1017/S0022112062000877.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., and R. W. Stewart, 1964: Radiation stresses in water waves; A physical discussion, with applications. Deep-Sea Res. Oceanogr. Abstr., 11, 529–562, doi:10.1016/0011-7471(64)90001-4.

    • Search Google Scholar
    • Export Citation
  • Lowe, R. J., and J. L. Falter, 2015: Oceanic forcing of coral reefs. Annu. Rev. Mar. Sci., 7, 43–66, doi:10.1146/annurev-marine-010814-015834.

    • Search Google Scholar
    • Export Citation
  • Lowe, R. J., J. L. Falter, S. G. Monismith, and M. J. Atkinson, 2009: A numerical study of circulation in a coastal reef-lagoon system. J. Geophys. Res., 114, C06022, doi:10.1029/2008JC005081.

    • Search Google Scholar
    • Export Citation
  • Lowe, R. J., C. Hart, and C. B. Pattiaratchi, 2010: Morphological constraints to wave-driven circulation in coastal reef-lagoon systems: A numerical study. J. Geophys. Res., 115, C09021, doi:10.1029/2009JC005753.

    • Search Google Scholar
    • Export Citation
  • Massel, S. R., and M. R. Gourlay, 2000: On the modelling of wave breaking and set-up on coral reefs. Coastal Eng., 39, 1–27, doi:10.1016/S0378-3839(99)00052-6.

    • Search Google Scholar
    • Export Citation
  • Mei, C. C., 2005: Theory and Applications of Ocean Surface Waves. Advanced Series on Ocean Engineering, Vol. 23, World Science, 1136 pp.

  • Monismith, S. G., 2007: Hydrodynamics of coral reefs. Annu. Rev. Fluid Mech., 39, 37–55, doi:10.1146/annurev.fluid.38.050304.092125.

  • Okayasu, A., T. Shibayama, and N. Mimura, 1986: Velocity field under plunging waves. Proc. 20th Conf. on Coastal Engineering, Taipei, Taiwan, ASCE, 660–674.

  • Phillips, O. M., 1977: The Dynamics of the Upper Ocean. Cambridge Monogr. Mech. Appl. Math., Vol. 2, Cambridge University Press, 344 pp.

  • Raubenheimer, B., R. T. Guza, and S. Elgar, 2001: Field observations of wave-driven setdown and setup. J. Geophys. Res., 106, 4629–4638, doi:10.1029/2000JC000572.

    • Search Google Scholar
    • Export Citation
  • Reniers, A. J. H. M., and J. A. Battjes, 1997: A laboratory study of longshore currents over barred and non-barred beaches. Coastal Eng., 30, 1–21, doi:10.1016/S0378-3839(96)00033-6.

    • Search Google Scholar
    • Export Citation
  • Ruessink, B. G., G. Rarnaekers, and L. C. van Rijn, 2012: On the parameterization of the free-stream non-linear wave orbital motion in nearshore morphodynamic models. Coastal Eng., 65, 56–63, doi:10.1016/j.coastaleng.2012.03.006.

    • Search Google Scholar
    • Export Citation
  • Sheppard, C., D. J. Dixon, M. Gourlay, A. Sheppard, and R. Payet, 2005: Coral mortality increases wave energy reaching shores protected by reef flats: Examples from the Seychelles. Estuarine Coastal Shelf Sci., 64, 223–234, doi:10.1016/j.ecss.2005.02.016.

    • Search Google Scholar
    • Export Citation
  • Skotner, C., and C. J. Apelt, 1999: Application of a Boussinesq model for the computation of breaking waves: Part 2: Wave-induced setdown and setup on a submerged coral reef. Ocean Eng., 26, 927–947, doi:10.1016/S0029-8018(98)00062-6.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., 2006: Wave–current interactions in finite depth. J. Phys. Oceanogr., 36, 1403–1419, doi:10.1175/JPO2911.1.

  • Stansby, P. K., and T. Feng, 2004: Surf zone wave overtopping a trapezoidal structure: 1-D modelling and PIV comparison. Coastal Eng., 51, 483–500, doi:10.1016/j.coastaleng.2004.06.001.

    • Search Google Scholar
    • Export Citation
  • Stephens, S. A., and D. L. Ramsay, 2014: Extreme cyclone wave climate in the southwest Pacific Ocean: Influence of the El Niño Southern Oscillation and projected climate change. Global Planet. Change, 123, 13–26, doi:10.1016/j.gloplacha.2014.10.002.

    • Search Google Scholar
    • Export Citation
  • Stive, M. J. F., and H. G. Wind, 1982: A study of radiation stress and set-up in the nearshore region. Coastal Eng., 6, 1–25, doi:10.1016/0378-3839(82)90012-6.

    • Search Google Scholar
    • Export Citation
  • Stive, M. J. F., and H. J. De Vriend, 1994: Shear stresses and mean flow in shoaling and breaking waves. Proc. 24th Conf. on Coastal Engineering, Kobe, Japan, ASCE, 594–608.

  • Storlazzi, C. D., E. Elias, M. E. Field, and M. K. Presto, 2011: Numerical modeling of the impact of sea-level rise on fringing coral reef hydrodynamics and sediment transport. Coral Reefs, 30, 83–96, doi:10.1007/s00338-011-0723-9.

    • Search Google Scholar
    • Export Citation
  • Svendsen, I. A., 1984a: Wave heights and set-up in a surf zone. Coastal Eng., 8, 303–329, doi:10.1016/0378-3839(84)90028-0.

  • Svendsen, I. A., 1984b: Mass flux and undertow in a surf zone. Coastal Eng., 8, 347–365, doi:10.1016/0378-3839(84)90030-9.

  • Svendsen, I. A., 2006: Introduction to Nearshore Hydrodynamics. Advanced Series on Ocean Engineering, Vol. 24, World Science, 744 pp.

  • Svendsen, I. A., and U. Putrevu, 1993: Surf zone wave parameters from experimental data. Coastal Eng., 19, 283–310, doi:10.1016/0378-3839(93)90033-5.

    • Search Google Scholar
    • Export Citation
  • Torres-Freyermuth, A., I. J. Losada, and J. L. Lara, 2007: Modeling of surf zone processes on a natural beach using Reynolds-averaged Navier-Stokes equations. J. Geophys. Res., 112, C09014, doi:10.1029/2006JC004050.

    • Search Google Scholar
    • Export Citation
  • van Dongeren, A., G. Klopman, A. Reniers, and H. Petit, 2002: High-quality laboratory wave generation for flumes and basins. Ocean Wave Measurement and Analysis (2001), B. L. Edge and J. M. Hemsley, Eds., American Society of Civil Engineers, 1190–1199, doi:10.1061/40604(273)120.

  • Vetter, O., J. M. Becker, M. A. Merrifield, A. C. Pequignet, J. Aucan, S. J. Boc, and C. E. Pollock, 2010: Wave setup over a Pacific Island fringing reef. J. Geophys. Res., 115, C12066, doi:10.1029/2010JC006455.

    • Search Google Scholar
    • Export Citation
  • Yao, Y., Z. H. Huang, S. G. Monismith, and E. Y. M. Lo, 2012: 1DH Boussinesq modeling of wave transformation over fringing reefs. Ocean Eng., 47, 30–42, doi:10.1016/j.oceaneng.2012.03.010.

    • Search Google Scholar
    • Export Citation
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