Numerical simulation of wave transformation over platform reef using SPH method

Abstract

Different from the fringing reef along the coastal beach, the reef face of the deep-sea platform reef is very steep and the water depth varies rapidly from a few thousand meters at the reef toe to a few meters at the reef edge. The special geomorphology of the deep-sea platform reef makes its hydrodynamics much different from that of the fringing reef with a gentle reef-face. Besides, the wave-generated flow induced by wave breaking has a great influence on sediment movement, nutrient transport and habitats for marine organisms on the reef flat. Therefore, the knowledge of the hydrodynamics of the deep-sea platform reef is of great importance to guide the subsequent development and protection of the deep-sea platform reefs. An improved smoothed particle hydrodynamic (SPH) model using the periodic boundary conditions and a water circulation technology as well as a non-reflected momentum source wave maker is developed to study wave transformation over the deep-sea platform reef. The Favre average N-S equations along with the sub-particle scale (SPS) turbulence closure model are employed as the governing equations to describe the wave motion. The idealized model of the platform reef is composed of a reef face with a slope of 1:1 and a horizontal reef flat. To verify the SPH model, the corresponding physical model tests are also carried out in the nonlinear wave flume of the state key laboratory of coastal and offshore engineering, Dalian university of technology. A good agreement is obtained between the numerical and experimental results, which indicates the present SPH model can accurately simulate wave transformation over the deep-sea platform reef and that it also can reasonably capture the spatial distributions of wave height and wave set-up on the reef flat. In addition, the unphysical rise and fall of the water level in the lagoon and the ocean due to the overtopping on the reef-flat, which usually occur for the long-time simulation using the vertical 2D numerical model, can be overcome by using the periodic boundary condition and a water flow circuit instead of the solid boundary condition to simulate the left and right boundaries of the flume. The wave height decay tempestuously due to wave energy dissipation by wave breaking. As observed both in the physical and numerical tests, wave breaking occurs on the reef-face or the reef-rim at the low water levels and emerges over the reef-rim or the reef-flat at the high water levels. For the coral reef with a gentle reef-face, the previous studies pointed that the basic type of wave breaking at the reef-rim is collapsing for a small relative wave height ( H / h r) and is plunging for a large relative wave height. While for the coral reef with a very steep reef-face focused in the present study, collapsing wave is the main type of wave breaking at the reef-rim as observed both in the physical and numerical tests.The wave height after breaking decreases dramatically and the broken wave propagates along the reef-flat as a bore-like wave, and the amplitude of wave setup is almost constant along the reef-flat.