| The hydrodynamic characteristics of waves propagating over mangrove forest is very complicated to investigate.The study of this topic has important theoretical significance and application value for offshore,coastal engineering and coastal ecological restoration.At present,there still exists the following problems in the numerical model for the study of characteristics on wave propagation and wave attenuation in the mangrove forest: In the numerical model,the turbulence behavior for wave breaking is rarely considered in the mangrove forest,the porous effect which can "squeeze" the flow is ignored.Regarding the wave-reducing properties of mangroves,the characteristics of the mangrove forest on wave breaking,the effects of nonlinear waves,and porous effects in mangrove forest should be further investigated.In this paper,we have investigated the wave propagation and wave breaking over fringing reefs based on the Navier-Stokes equation and the two-phase k-? k-?SST turbulence model.Furthermore,we established a numerical model for wave propagation over mangrove forest based on porous media and by introducing drag force and inertia force.Comparisons between full-water wave model and porous-media wave model demonstrate the model accuracy by means of experimental results.The main research work and results are as follows.(1)we have investigated the wave propagation and wave breaking over fringing reefs based on the Navier-Stokes equation and the two-phase k-? k-?SST turbulence model.The numerical model includes the turbulence effects by adopting two-phase k-? k-?SST turbulence model,and accounts for density variations around the surface between air and water,which can avoid overestimating the generation of turbulence energy.The volume of fluid method(VOF)is used to capture the free surface of the wave,the velocity boundary condition is used at the inflow boundary with active wave absorption system to absorb the reflected wave,and the velocity at the outflow boundary is adjusted by adding correction velocity.The numerical results show that the turbulent energy is mainly located at the wave crest in the surf zone and mainly at the water surface when waves propagate over fringing reefs.The wave energy that is transferred between the harmonics induced by the nonlinearity and wave breaking can be well reproduced.The accuracy of numerical model to predict the wave height and wave setup/setdown is also improve.(2)A numerical model for wave propagation over mangrove forest is established where the control equation is based on porous media and by introducing drag force and inertia force.The numerical model describes the distribution of mangrove porous media by introducing porosity,and replacing the actual flow velocity with Darcy velocity to deal with the discontinuity of mass and momentum at the interface;the hydrodynamics induced by mangrove forest is modeled by the drag force and inertial force.The two-phase k-? k-?SST turbulence model is adopted in order to account for turbulence effects of mangroves and wave breaking.The numerical model has been validated with variant wave conditions,bathymetry and the distribution of mangrove forest,which shows good simulation results on wave propagation and attenuation over mangrove forest.When the water depth becomes smaller and the wave height becomes larger,the wave breaking occurs inside the mangrove area,and the turbulence behavior is significant.The model including the turbulence effects has better applicability.When the broken waves propagate through the mangrove forest,the nonlinearity of the wave increases,and the inertial force also becomes as an important factor that affects the simulation results of the wave height.The degree of inertia effects increases as the density of the mangrove forest increases.(3)The accuracy of full-water wave model and porous-media wave model is analyzed by comparing with experimental data.The comparison shows that the porous-media wave model is capable of considering the flow "squeeze" phenomenon of mangrove forest and the reflection effects of mangrove branches,and better predicts the increase of the height of in front of mangrove forest and the reflected wave,the wave attenuation inside the mangrove forest,and the reduction of the wave runup at the end of mangrove forest.When the density of mangroves increases,the accuracy of porous-media wave model is significantly better than that of the full-water wave model.(4)Wave attenuation over mangrove forest is further investigated by aspects of wave breaking,the nonlinearity of wave and the porous effects of mangrove forest.The mangrove forest can change the wave breaking behavior,and the degree of influence is affected by the incident wave conditions and the distribution of mangrove.After wave breaking,wave energy is greatly transmitted to the higher-order harmonics,and the mangrove forest has a stronger attenuation ability to reduce the higher-order harmonics.With the porous effects of mangrove forest,the reflection of the waves at the front end of the mangrove area is strengthened,and the attenuation is greater when passing through the mangrove area.Although wave reduction rates for breaking waves in smaller in the mangrove forest,it can greatly reduce the average velocity distribution of undertow and reduce scour in the surf zone.(5)In this paper,with the open source toolbox Open FOAM as the development platform,mathematical program for the numerical model of wave propagation over mangrove forest based on the porous-media Navier-Stokes equation and the two-phase k-? k-?SST turbulence model is developed.The comparison with the experimental data that include more than ten cases shows good agreement between numerical results and experimental data.In this paper,The two-phase turbulent wave numerical model for wave propagation and breaking over fringing reef and the numerical model of wave propagation over the mangrove area based porous media have improved the accuracy of the numerical model.Discussion on wave breaking,the wave nonlinearities and the effects of porous media has improved the understanding of wave attenuation over mangrove forest.The research results can be applied to the theoretical study of the hydrodynamic characteristics of mangrove forest and the application of wave prevention and mitigation in coastal areas. |
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