Coastal Engineering Journal

A three-dimensional numerical simulation of time-averaged wave-induced currents was performed, its results were compared with the results of a depth-integrated Boussinesq equation model And the differences were discussed in terms of wave height, instantaneous and mean free surface elevations, mean and time-averaged velocity fields, and turbulence parameters. For the three-dimensional simulation, an internal wave generation and a wave-absorbing sponge layer scheme, which can eliminate the influence of waves reflected from the wave source and wall boundaries toward the domain, were applied to the RANS equation model in a CFD code named FLUENT and the VOF model was utilized for the water surface In this study, two experiments involving wave-induced flows were simulated. First, to examine the wave-induced flows computed by the present model, we performed an existing two-dimensional experiment in which time-averaged mean motions induced by wave breaking were measured on a constant slope. Second, the breaking monochromatic wave case of Vincent and Briggs' experiments [Vincent and Briggs, 1989] was simulated in three dimensions using the present model. The experimental case presented a three-dimensional phenomenon in which a wave-induced jet-like current was generated and influenced the wave transformation over an elliptical submerged shoal. The computations agreed with the measurements and showed vertical distributions of the wave-induced currents over the shoal.

A simple empirical model is proposed for predicting extreme wave run-up on natural beaches during severe wave events (deep water wave heights H₀ ≳8 m or return periods of about 50 years). The new model departs from traditional approaches that use the slope of the beach face β_f and the Iribarren number ξ₀ as parameters for predicting run-up and instead uses the distance offshore x_h to water depth h to estimate a near-shore profile slope as S = h/x_h, where the depth of closure is the proposed choice for h. Extreme run-up R_x is then expressed in terms of S as R_x/H₀ = CS^2/3. Observations from recent severe storm events in South Africa are used to estimate the dimensionless coefficient C≃7.5. The data are also compared with those of Holman [1986] and the results verify his regression equations and confirm they are valid for significant wave heights extending to 8.5 m for beach-face slopes around 0.1. The run-up predictions of Holman [1986], Nielsen and Hanslow [1991] and Stockdon et al. [2006] are compared to those of the proposed new model. The results suggest that the new model reduces the uncertainties in predicting wave run-up on natural beaches compared with previous models, and thus enables improved estimates of extreme wave run-up and the upper limit of beach change for coastal planning and management.

A Monte Carlo simulation study has been carried out on the reliability of the parameter and quantile estimation of the Generalized Extreme-Value (GEV), Generalized Pareto (GPA), and Weibull distributions by means of the L-moment method. The three population distributions are assigned with five to six values of the shape parameter each, and the scale and location parameters are so specified as to yield the ratio of the 50- to 10-year wave heights at the value of 1.1, 1.2, and 1.3. Samples of extreme wave heights are generated from 16 populations at the size varying from 10 to 1000, and 50,000 samples for respective conditions are analyzed for statistical characteristics. The unbiased plotting position recommended by Hosking and Wallis [1997] is confirmed to yield minimal biases on the parameter estimates, but it yields small biases on quantile estimates. A new plotting position estimator is proposed, which yields minimal quantile bias. A set of empirical formulas are derived for estimation of the coefficient of variations of the L-moment ratios and the quantile of the three distributions.

This study investigates wave transformations over an elliptic shoal on a sloping bottom using numerical calculations. The theoretical model is based on the fully nonlinear Boussinesq equation that was applied by Chen et al. [2003]. This equation is expressed by the velocity at any level below the surface. The momentum equation is derived using modified vertical vorticity terms from the equation by Wei et al. [1995]. Bottom friction, wave breaking, and subgrid lateral turbulent mixing proposed by Kennedy et al. [2000] are also included in the equations. Several numerical experiments are conducted for waves with incident angles of 0°, 15°, and 30°. The numerical results demonstrate the phenomena of wave focusing in the rear of the elliptic shoal. The wave focusing not only results in a smaller wave-induced current on top of the shoal than that at the rear of the shoal, but also a strong return flow at the back of the shoal. It is found that the non-dimensional wave height in the wave-focusing zone increases as the relative water depth decreases. Moreover, the orientation of wave height contours in the focusing region is almost identical to that of the incident wave angle. This phenomenon stays true for different incident wave periods.