Wave set-up on coral reefs. 1. Set-up and wave-generated flow on an idealised two dimensional horizontal reef

Abstract

Wave set-up may be significant in determining water levels on coral reefs particularly in microtidal environments and hence is an important factor for the design of reef-top structures and for the stability of reef-top islands. Laboratory experiments have been made on a two dimensional model of an idealised horizontal reef under two different conditions corresponding to a fringing reef (or closed lagoon) situation and a platform reef (or open lagoon) situation. Both wave set-up on the reef-top and the wave-generated flow across the reef were measured and related to wave and tide level conditions. All other factors being the same, wave set-up is greatest at low tide levels whereas wave-generated flow is greater at higher tide levels. The magnitude of the set-up on a platform reef with a wave-generated flow is less than on a fringing reef without any net flow by an amount equal to the velocity head of the flow across the reef. Dimensionless parameters \\ ̄ gh r T√ η o and q √gH o 3 are found to be functions of relative submergence parameters h r H o or ( η r + h r) H o . For values of ( \\ ̄ gh r + h r ) H o > 1 waves break on the reef-top and radiation stress theory can be used to calculate set-up. For ( \\ ̄ gh r + h r ) H o < 0.7 waves break on the reef-face and set-up is determined by broadcrested weir control at the reef-edge. (The symbols are defined as follows: g is gravitational acceleration; h r is still water depth over horizontal reef-top; H o is offreef wave height (equivalent deep water value); q is discharge per unit length of reef edge; T is wave period and \\ ̄ gh r is maximum wave set-up on reef-top.)