Study on Flow Field Around Vertical Breakwater Under Different Overtopping Conditions Based on Numerical Simulation

A numerical wave flume is constructed based on the Reynolds Averaged Navier-Stokes （RANS） equations with turbulence closure by a modified k - ε model to study the viscous interactiorrs of waves with vertical breakwaters for different overtopping cases. The goveruing equations, the turbulence model, boundary conditions, and solution method for the nu- merical wave flume are introduced briefly. The reliability of the numerical wave flume is examined by comparing the nu- merical results with the experimental measurements, and good agreements between them indicate the validity of the pre- sent model. The developments of mean velocity fields, the contours of vorticity, and the influences of wave nonlinearity on turbulence field as wave passing through vertical breakwaters are discussed in detail based on the numerical results. It is noted that the vortices at the rear of the lower submerged breakwater are close to the bottum and maytbe induce the scouring to the leeside toe of marine structure in practice. Over all, a conclusion can be obtained from this study that the turbulence in wave field around structure is induced directly by the development of boundary layer on the solid boundary, the nonlinear interaction of free surface with obstaele, and the plunging of overtopping waves.

Oblique and Multi-Directional Random Wave Loads on Vertical Breakwaters

Extensive 3-D model tests have been performed to study the effects of wave obliquity and multi-directionality on the wave loads acting on vertical breakwaters. The variation of horizontal and uplift forces acting on an unit length of a breakwater with wave direction, the longitudinal distribution of wave forces, as well as the longitudinal load reduction are analyzed. Some empirical formulae of the longitudinal distribution coefficient and the longitudinal load reduction factor are presented for practical use.

Interaction of Irregular Waves with Vertical Breakwater and Characteristics of Secondary Wave Generated by Overtopping

This study investigated the interaction between irregular waves and vertical breakwater.The main goal was to determine the wave force on the breakwater for different depths,along with the evolution of the secondary wave generated by overtopping.The open source code DualSPHysics was used in the simulation.Wavelet transform was employed to remove the acoustic components from the weakly compressible smoothed particle hydrodynamics pressure solution.The results of the experiments and simulations showed that although the wave height at the low water level(case 2 was smaller than that at the high water level(case 1,the horizontal and uplifting force of case 2 was higher than that of case 1.In case 2,a large impact pressure occurred because of the plunging wave and wave breaking effects.As the water level was close to the breakwater top in case 1,the secondary wave generated by overtopping was studied.Results indicated that wave and breakwater interactions transfer wave energy from the leading wave component to higher harmonics.Two main harmonics were identified in the secondary wave.The first harmonic was the incident peak frequency,which was still the dominant component.During the wave propagation behind the breakwater,the frequencies of harmonics remained unchanged,but the amplitude of the first harmonic showed an obvious change.Under the same wave condition,the first and second harmonics did not change with depth.

Study of Vertical Breakwater Reliability Based on Copulas

The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.

Simplified Method for Calculating Standing Wave Pressure on Vertical Breakwater

Through numerical modeling, a kind of simplified calculating method for standing wave pressure on vertical face breakwater have been put forward. Not only the formulas proposed in this paper are simple in form and very easy in use, but also they possess continuity on the full range of standing wave. And more, the precision requiremennts of calculation can be satisfied to a certain extent in engineering practice.

Vertical membrane floating breakwater

The basic purpose of any breakwater is to protect a harbor, moored vessels or an offshore structure from excessive incident wave attack. Breakwater can be classified as either fixed structures or floating ones. The vertical membrane floating breakwater which will be introduced in this paper belongs to the latter.

Modeling Loads Caused by Breaking Waves Striking Vertical Walls

Breaking waves can have tremendous destructive impact on vertical walls, yet they are poorly understood. By using particle imaging velocimetry （PIV） technology and high-precision pressure transducers, actual breaking wave loads on vertical walls were studied. By simultaneously comparing the flow field structure and wave pressure, the mechanisms of breaking wave pressure could be analyzed. The probability distribution of the peak value of the first impact of a breaking wave was investigated. The results showed that the impact pressure p is mainly distributed in the range of 0.25-2.75 pv2, with the greatest possible probability at p/pv2 = 0.75.

RESEARCH ON WAVE FORCES ACTING ON THE UNIT LENGTH OF A VERITICAL BREAKWATER BY TESTS AND A NUMERICAL MODEL

Comprehensive 3D model tests and numerical simulation were performed to study the effects of wave obliquity and multidirectionality on the wave forces acting on vertical breakwaters. The variation of wave forces acting on the unit length of a breakwater was analyzed, and the results were compared with Goda＇s formula. A numerical model based on a short-crest wave system was used to model regular wave forces for practical use, which showed good results for those waves with small incident angles.