An analytical approach was used to model the wave-induced set-up and flow through simple shoal geometry when water depth is a linear function of the distance. Two different approaches were applied to parameterize the energy dissipation due to wave breaking. The resulting set-up height and flow velocity were determined and their dependence on the geometry of the shoal and offshore forcing was demonstrated. The extension of the solution to a more complicated bathymetry and verification against the experimental data will be given in the second part of the paper.
Dally W.R., Dean R.G., Dalrymple R.A., 1985, Wave height variation across beaches of arbitrary profile, J. Geophys. Res., 90, 11917–11927.
Gourlay M.R., 1994, Wave transformation on a coral reef, Coast. Eng., 23, 17–42.
Gourlay M.R., 1996, Wave set-up on coral reefs: 1. Set-up and wave-generated flow on an idealized two dimensional horizontal reef, Coast. Eng., 27, 161–193.
Hardy T.A., Young I.R., 1996, Field study of wave attenuation on an offshore coral reef, J. Geophys. Res., 101, 14311–14326.
Hearn C. J., Parker I.N., 1988, Hydrodynamic processes on the Ningaloo Reef, Western Australia, Proc. 6th Int. Symp. Coral Reefs, 2, 497–502.
Kraines S.B., Yanagi T., Isobe M., Komiyama H., 1998, Wind-wave driven circulation on the coral reef at Bora Bay, Miyako Island, Coral Reefs, 17, 133–143.
Lie V., Torum A., 1991, Ocean waves over shoals, Coast. Eng., 15, 545–562.
Longuet-HigginsM. S., 1970, Longshore currents generated by obliquely incident sea waves, J. Geophys. Res., 75, 6790–6801.
Longuet-Higgins M. S., Stewart R.W., 1964, Radiation stresses in water waves; a physical discussion with applications, Deep-Sea Res., 11, 529–562.
Massel S.R., 1989, Hydrodynamics of coastal zones, Elsevier, Amsterdam, 336 pp.
Massel S.R., 1996a, Ocean surface waves: their physics and prediction, World Sci. Publ., Singapore–London–Hong Kong, 491 pp.
Massel S.R., 1996b, On the largest wave height in water of constant depth, Ocean Eng., 23, 553–573.
Massel S.R., 1999, Fluid mechanics for marine ecologists, Springer Verlag, Heidelberg–Berlin, 566 pp.
Massel S.R., Gourlay M.R., 2000, On the modelling of wave breaking and set-up on coral reefs, Coast. Eng., 39, 1–27.
Nelson R.C., 1994, Depth limited design wave heights in very flat regions, Coast. Eng., 23, 43–59.
Nelson R.C., 1996, Hydraulic roughness of coral reef platforms, Appl. Ocean Res., 18, 265–274.
Singamsetti S.R., Wind E.G., 1980, Breaking waves: characteristics of shoaling and breaking periodic waves normally incident to plane beaches of constant slope, Delft Hydr. Lab., Rep. M1371, 80 pp.
Symonds G., Black K.P., Young I.R., 1995, Wave-driven flow over shallow reefs, J. Geophys. Res., 100, 2639–2648.
Veron J.E.N., 1986, Corals of Australia and the Indo-Pacific, Univ. Hawaii Press, Honolulu, 644 pp.
Wolanski E., Delesalle B., Dufour V., Aubanel A., 1993, Modeling the fate of pollutants in the Tiahura Lagoon, Moorea, French Polynesia, Proc. 11th Austr. Coast. Ocean Eng. Conf., Townsville, 1, 583–589.