A Semi-Analytical Model on Wave-Induced Setup over Fringing Reefs with a Shallow Reef Crest
Yu Yao*,**,†, Zhengjiang Tang*, Ruichao Du*, and Changbo Jiang*,**
*School of Hydraulic Engineering, Changsha University of Science and Technology
Changsha 410114, P.R. China
**Key Laboratory of Water-Sediment Sciences and
Water Disaster Prevention of Hunan Province, Changsha 410114, P.R. China
The vulnerability of low-lying reef-fringed atolls to coastal inundation in extreme wave events is of increasing concern in the context of global sea level rise. Wave-induced setup is an important component of wave runup along reef shorelines. We improved a semi-analytical model to investigate wave-induced setup over fringing reefs crested by a shallow reef. Using mass balance and hydraulics, we developed the model based on flow around reef crest kinematics. We proposed a scaling factor to account for flow unsteadiness and reef-crest shape effects. Our solution showed that wave setup on the reef flat is a function of both offshore wave steepness and the wave refection coefficient. Validation of the model by laboratory data shows that the model reproduces the maximum wave-induced setup on the reef flat in the presence of a reef crest with diffident crest widths. Applying the model to experimental data under various reef configurations and wave conditions were also successful. We found that the scaling factor in the model increased with increasing fore-reef slope but was insensitive to variations in reef-crest width. A key requirement for the model to do is that the reef-crest submergence must be small enough or nearly emergent so that an approximate critical flow condition exists.
-  W. H. Munk and M. C. Sargent, “Adjustment of Bikini atoll to ocean waves,” Trans. Am. Geophys. Union Vol.29, pp. 855-860, 1948.
-  R. J. Lowe, J. L. Falter, S. G. Monismith, and M. J. Atkinson, “Wave-driven circulation of a coastal reef-lagoon system,” J. Phys. Oceanog. Vol.39, pp. 873-893, 2009.
-  M. A. Merrifield, J. M. Becker, M. Ford, and Y Yao, “Observations and estimates of wave-driven water level extremes at the marshall islands,” Geophys. Res. Lett., Vol.41, pp. 7245-7253, 2014.
-  A.-C. Péquignet, J. M. Becker, M. A. Merrifield, and J. Aucan, “Forcing of resonant modes on a fringing reef during tropical storm Man-Yi,” Geophys. Res. Lett., Vol.36, L03607, 2009, doi:10.1029/2008GL036259.
-  W. N. Seelig, “Laboratory study of reef-lagoon system hydraulics,” J. Wtrwy. Port, Coast. and Ocean Eng., ASCE, Vol.109, pp. 380-391, 1983.
-  P. S. Kench and R. W. Brander, “Wave processes on coral reef flats: Implications for reef geomorphology using Australian case studies,” J. Coast. Res., Vol.22, pp. 209-223, 2006.
-  J. L. Hench, J. J. Leichter, and S. G. Monismith, “Episodic circulation and exchange in a wave-driven coral reef and lagoon system,” Limnol. Oceanogr., Vol.53, pp. 2681-2694, 2008.
-  A.-C. Péquignet, J. M. Becker, M. A. Merrifield, and S. J. Boc, “The dissipation of wind wave energy across a fringing reef at Ipan, Guam,” Coral Reefs, Vol.30, pp. 71-82, 2011.
-  M. R. Gourlay, “Wave set-up on coral reefs. 1. Set-up and wave-generated flow on an idealised two dimensional reef,” Coast. Eng., Vol.27, pp. 161-193, 1996.
-  Z. Demirbilek, O. G. Nwogu, and D. L. Ward, “Laboratory Study of Wind Effect on Runup over Fringing Reefs,” Report 1: Data report, Coastal and Hydraulics Laboratory Technical Report ERDC/CHL-TR-07-4, U.S. Army Engineer Research and Development Center, Vicksburg, MS, 2007.
-  Y. Yao, Z. H. Huang, S. G. Monismith, and E. Y. M. Lo, “Characteristics of monochromatic waves breaking over fringing reefs,” J. Coastal Res., Vol.29, pp. 94-104, 2013.
-  Y. Yao, E. Y. M. Lo, Z. H. Huang, and S. G. Monismith, “An Experimental Study of wave-induced set-up over a horizontal reef with an idealized ridge,” Proc. 28th Int. Conf. Offshore Mech. and Artic Eng., ASME, Honolulu, Hawaii, USA., Vol.6, pp. 383-389, 2009.
-  Y. Yao, “Dynamics of Water Waves over Fringing Coral Reefs,” Phd Thesis, Nanyang Technological University, Singapore, 2012.
-  M. S. Longuet-Higgins and R. W. Stewart, “Radiation stresses in water waves; a physical discussion, with applications,” Deep-Sea Res., Vol.11, pp. 529-562, 1964.
-  R. J. Tait, “Wave set-up on coral reefs,” J. Geophys. Res., Vol.77, pp. 2207-2211, 1972.
-  G. Symonds, K. P. Black, and I. R. Young , “Wave-driven flow over shallow reefs,” J. Geophys. Res.,Vol.100, pp. 2639-2648, 1995.
-  C. J. Hearn, “Wave-breaking hydrodynamics within coral reef systems and the effect of changing sea level,” J. Geophys. Res., Vol.104, pp. 30007-30019, 1999.
-  M. R. Gourlay and G. Colleter, “Wave-generated flow on coral reefs: an analysis for two-dimensional horizontal reef-flats with steep faces,” Coast. Eng., Vol.52, pp. 353-387, 2005.
-  O. Vetter, J. M. Becker, M. A. Merrifield, A.-C. Péquignet, J. Aucan, S. J. Boc, and C. E. Pollock, “Wave setup over a Pacific Island fringing reef,” J. Geophys. Res., Vol.115, C12066, 2010, doi:10.1029/2010JC006455.
-  J. M. Becker, M. A. Merrifield, and M. Ford, “Water level effects on breaking wave setup for Pacific Island fringing reefs,” J. Geophys. Res. Oceans, Vol.119, 2014, doi:10.1002/2013JC009373.
-  S. G. Monismith, “Flow through a rough, shallow reef,” Coral Reefs, Vol.33, pp. 99-104, 2014.
-  V. Roeber, K. F. Cheung, and M. H. Kobayashi, “Shock-capturing Boussinesq-type model for nearshore wave processes,” Coast. Eng., Vol.57, pp. 407-423, 2010.
-  R. J. Lowe , A. S. Leon, G. Symonds, J. L.Falter, and R. Gruber, “The intertidal hydraulics of tide-dominated reef platforms,” J. Geophys. Res. Oceans, Vol.120, 2015, doi:10.1002/2015JC010701.
-  B. R. Munson, D. F. Young, and T. H. Okiishi, “Fundamentals of Fluid Mechanics,” John Wiley and Sons. Inc., USA., 2002, 840 pp.
-  M. Calabrese, D. Vicinanza, and M. Buccino, “2D wave setup behind submerged breakwaters,” Ocean Eng., Vol.35, pp. 1015-1028, 2008.
-  I. A. Svendsen, “Mass flux and undertow in the surf zone,” Coastal Engineering, Vol.8, pp. 347-365, 1984.
-  M. W. Owen, “Design of Seawalls Allowing for Wave Overtopping,” Technical Report EX-924, HR-Wallingford, UK., 1980.
-  J. W. Van der Meer and J. P. F. M. Janssen, “Wave run-up and wave overtopping at dikes,” In: N. Kobayashi, Z. Demirbilek (Eds.), “Wave Forces on Inclined and Vertical Structures,” Ch.1, pp. 1-27, 1995.
-  T. Pullen, N. W. H. Allsop, T. Bruce, A. Kortenhaus, H. Schuttrumpf, and J. W. van der Meer, “EurOtop: Wave Overtopping of Sea Defenses and Related Structures: Assessment Manual,” Science Report: SC050059, Environment Agency, UK, 2007.
-  Y. Goda, “Derivation of unified wave overtopping formulas for seawalls with smooth, impermeable surfaces based on selected CLASH datasets,” Coast. Eng., Vol.56, No.4, pp. 385-399, 2009.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.