Studies On The Numerical Model For Wave Propagation,Breaking And Setup On Coral Reefs

With the development of the protection and construction of coral reefs,the prediction of wave propagation and setup on coral reefs has become an urgent problem of primary focus.The bathymetry of coral reefs varies from that of ordinary normal coastal beaches,the main differences lie on two aspects: the steep slopes and the permeable and rough bottoms.As waves propagate from the deep sea to reef flats,wave shoaling,reflection,refraction,nonlinear wave breaking,infragravity waves motions and the affect of permeable bottoms should be considered,which brings enormous challenges to numerical simulations.There are still many problems when applying the existing numerical models on coral reefs directly.For example,the wave setup and wave height are underestimated when designing the artificial islands on the reef tops in Nanhai,China.Therefore,it is very important to seek or establish reliable numerical wave models for coral reefs.Based on the analysis,a research on numerical models of wave propagation,breaking and setup is carried out in this study,the research focuses on the wave transformation on steep slopes,wave setup and the affect of large bottom friction.The main contents of this paper include:(1)A comparative study of three numerical wave models for coral reefs(FUNWAVE-TVD,Coulwave and NHWAVE)is carried out.The models are compared theoretically,and the main connections and differences of different models are concluded.The applicability and prediction precision of four numerical wave models in complex coral reef environments are tested and compared by using four representative laboratory experiments.The distributed source wave generation method is introduced into NHWAVE to overcome the insufficiency of line source wave generation method.The numerical results show that all the models can simulate the wave height reasonably through the calibration of the breaking parameters;NHWAVE can predict wave setup reasonably for different breaker types;Coulware and FUNWAVE-TVD can predict wave setup reasonably by spilling breaker and surging breaker,but tend to underestimate wave setup by plunging breaker.Boussinesq wave models with eddy viscosity model can simulate wave propagation on steep coral reefs more accurately than those using hybrid wave breaking model.(2)Each of the above models has some disadvantage,to better simulate wave propagation over coral reefs,a Boussinesq-type wave model for steep coral reefs is established.A governing equation and a numerical scheme more suitable for steep terrains are chosen.An eddy viscosity method,modified to better suit steep terrains,is employed to simulate energy dissipation due to wave breaking.The nested model is established in accordance with the topographic characteristics of reefs as well as the requirements imposed by the hybrid limiter on meshing.The simulation of the present model is tested by comparing with the previous three wave models.The compare results show that the present model can simulate wave reflection more accurately and can predict wave setup for different wave types,making it more reliable and more accurate than FUNWAVE-TVD and Coulwave on steep bathymetry.To representative cases,the nested model can save about 40% of the compute time without losing simulation accuracy.(3)Two improved methods for hybrid wave breaking model are proposed: “directly improved method” and “optimally improved method”.Both methods take the terrain-dependent criterion as wave breaking threshold.An extra loop iteration is introduced in “directly improved method” to judge wave breaking by using the ratio of wave height to water depth directly,which is more accurate than using the ratio of surface elevation to depth roughly.The “optimally improved method” further considered the geometrical shape of breaking wave,which can make the criterion from wave height to surface elevation.Both methods have very strong practicability because they don't need parameter calibration,nevertheless “optimally improved method” is more convenient to use.Two improve methods are applied on FUNWAVE-TVD,and their simulation efficiency is tested by laboratory data of wave propagation on different terrains.The results show that both improved methods can simulate wave breaking on steep slopes accurately without need finer grids,the improvement efforts of the two methods are close to each other.For three typical laboratory experiments of wave propagation over steep slopes,the simulation precision of “directly improved method” improves by 12.6%~42.5%,the simulation precision of “optimally improved method” improves by 10.1%~40.3%.(4)To simulate permeable reef beds,a Boussinesq wave model was coupled with Dancy equation to establish a two-layer model.The upper layer is pure water and the lower layer considers the effect of permeable reef beds.The equation is discretized using a finite difference method to establish a wave model,a slot technique is employed to treat the moving shoreline,the modified eddy viscosity method is employed to treat wave breaking.The model is vilified by laboratory experiments of wave propagation on permeable submerged breakwater.The model is also applied on a preliminary study of the influence of the decay of the coral reefs to wave propagation over them.In summary,a numerical wave model for steep coral reefs is built in this paper,and the hybrid wave breaking model is modified for steep terrains,the model and the methods are verified by experimental data.The results show that the established model is more efficiency and can be used on the protection and construction of coral reefs.The model suitable for permeable reef beds is established,and the model is of significant for further study on waves propagation on permeable reef beds.