Design formulas of transmission coefficients for permeable breakwaters

New empirical formulas of the transmission coefficient for permeable breakwaters were suggested based on available experimental data regarding the low-crest structure （LCS）, including the permeable rubble mound breakwater and pile-type breakwater. The rationality of the present formulas was verified by their comparison with existing empirical and analytical formulas. Numerical flume results were obtained by solving the modified Boussinessq-type wave equations （MBEs）, and a new expression relating the friction coefficient of to the relative submerged depth Rt/H8 was also derived. Comparative analysis shows that the results of the present formulas agree with the numerical flume results as well as available experimental data, and the present formulas are superior to the existing empirical and analytical expressions in estimating the transmission coefficient. The present formulas can provide references for estimation of the transmission coefficient in engineering practice.

Fully Coupled Simulation of Interactions Among Waves, Permeable Breakwaters and Seabeds Based on N−S Equations

Interstitial flows in breakwater cores and seabeds are a key consideration in coastal and marine engineering designs and have a direct impact on their structural safety.In this paper,a unified fully coupled model for wave−permeable breakwater−porous seabed interactions is built based on an improved N−S equation.A numerical wave flume is constructed,and numerical studies are carried out by applying the finite difference method.In combination with a physical model test,the accuracy of the numerical simulation results is verified by comparing the calculated and measured values of wave height at measurement points and the seepage pressure within the breakwater and seabed.On this basis,the characteristics of the surrounding wave field and the internal flow field of the pore structure,as well as the evolution process of the fluctuating pore water pressure inside the breakwater and seabed,are further analyzed.The spatial distribution of the maximum fluctuating pore water pressure in the breakwater is compared between two cases by considering whether the seabed is permeable,and then the effect of seabed permeability on the dynamic pore water pressure in the breakwater is clarified.This study attempts to provide a reference for breakwater design and the protection of nearby seabeds.

Wave Height Transformation and Set-up Between A Submerged Permeable Breakwater and A Seawall

In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.

Hydrodynamic Coefficient Investigation on a Partial Permeable Stepped Breakwater Under Regular Waves

Traditional breakwater takes the advantage of high protection performance and has been widely used.However,it contributes to high wave reflection in the seaside direction and poor water exchange capacity between open seawater and an inside harbor.Consequently,a partially permeable stepped breakwater(PPSB)is proposed to ensure safety and good water exchange capacity for an inside harbor,and a 3-D computational fluid dynamics(CFD)mathematical model was used to investigate the hydrodynamic coefficients using Reynolds-Averaged Navier-Stokes equations,Re-Normalization Group(RNG)k-εequations,and the VOF technique.A series of experiments are conducted to measure the wave heights for validating the mathematical model,and a series of dimensionless parameters considering wave and PPSB effects were presented to assess their relationships with hydrodynamic coefficients,respectively.With the increase in the reciprocal value of PPSB slope,incident wave steepness and permeable ratio below still water level(SWL),the wave reflection coefficient decreases.The wave transmission coefficient decreases with an increase in the reciprocal value of the PPSB slope and incident wave steepness;however,it increases with the increase in the permeable ratio below SWL.With increases in the reciprocal value of the PPSB slope,permeable ratio below SWL and incident wave steepness for relatively high wave period scenarios,the wave energy dissipation coefficient increases;however,it decreases slightly with increases in the incident wave steepness for the smallest wave period scenarios.Furthermore,simple prediction formulas are conducted for predicting the hydrodynamic coefficients and they are well validated with the related data.

NUMERICAL SIMULATIONS OF NONLINEAR WAVE TRANSFORMATION AROUND WAVE-PERMEABLE STRUCTURE

The problem of wave partial/full reflection and transmission by wave-permeable structure is approached by solving the shape-related function with focus on the understanding of wave attenuation. 2D depth averaged Boussinesq type wave equations are given with new damping item in simulating the nonlinear wave transmission through wave-permeable structure. 1D wave equation is examined to give the analytical expression of the absorbing coefficient, and is compared with laboratory data in flume to calibrate the coefficients, and the expression is applied directly in modified Boussinesq type equations. Compared with wave basin data for various incident wave conditions, the accurate predictions of combined diffraction refraction effects in simulating nonlinear wave going through wave-permeable breakwater in the engineering application can be obtained. It shows that wave-permeable breakwaters with proper absorbing effects can be used as an effective alternative to massive gravity breakwaters in reduction of wave transmission in shallow water.