Journal of Waterway, Port, Coastal, and Ocean Engineering

To model internal waves, high-level Green-Naghdi (GN) equations that are strongly nonlinear were developed for a two-layer fluid with a rigid lid over the upper layer. The GN models were applied to two internal-solitary-wave cases: weakly dispersive and strongly dispersive. In the weakly dispersive case, the ratio between the upper and lower layers was 1:4.13. In the strongly dispersive case, the two depth ratios between the upper and lower layers were 1:24 and 10.13:1. For both the weakly and strongly dispersive test cases, the converged GN results for wave speed, wave profile, and velocity distribution agreed well with the experimental data and the solution of Euler equations, even for large-amplitude solitary waves. For the strongly nonlinear and strongly dispersive cases, the converged GN results showed better accuracy than some other strongly nonlinear models.

Scour protection around hydraulic structures in fluvial, estuarine, and coastal waters is an essential component of a meaningful and durable design. The continuous optimization of scour protection systems and design approaches leads to faster and more cost-effective construction processes. Although scour protection now often consists of a two-layer design, approaches that incorporate only one layer depict a major step forward. Therefore, this research focuses on the stability of a wide-graded quarry-stone mixture consisting of crushed granodiorite (Jelsa quarry, Norway) with fractions ranging from 0.063 to 200 mm. The material was exposed to an incrementally increased unidirectional current in a closed-circuit flume. The induced flow field and leading parameters were measured at various positions horizontally and vertically, whereas the erosion rates were determined behind the test bed specimen. With increasing flow velocity the development of a static armor layer was observed at the bed surface. Bed-shear stresses were determined to be strongly variable across the rough test bed. Fractional critical shear stresses indicate highly selective mobility of individual fractions. Least-square fitting of the determined critical shear stresses based on the dimensionless reference grain size $d_i/d_{\sigma }$ (with $d_{\sigma }\hspace{0.17em}$ as the product of the geometric mean size $d_g$ and the geometric standard deviation ${\sigma }_g$) is suitable for describing the stability behavior of the investigated material.

Based on the Crest Level Assessment of Coastal Structures (CLASH) Neural Network Overtopping prediction method, a new 16-parameter overtopping estimator (Q6) was developed for conventional mound breakwaters with crown walls, both with and without toe berms. Q6 was built up using the overtopping estimations given by the CLASH Neural Network and checked using the CLASH database. Q6 was compared to other conventional overtopping formulas, and the Q6 obtained the lowest prediction errors. Q6 provides overtopping predictions similar to the CLASH Neural Network for conventional mound breakwaters but using only six explanatory dimensionless variables ($R_c/H_{m0},Ir,R_c/h,G_c/H_{m0},A_c/R_c$, and a toe berm variable based on $R_c/h$) and two reduction factors (${\gamma }_f$ and ${\gamma }_{\beta }$). Q6 describes explicit relationships between input variables and overtopping discharge, and hence it facilitates use in engineering design to identify cost-effective solutions and to quantify the influence of variations in wave and structural parameters.

Research on the influence of tsunamis on bridges has been based almost exclusively on the results of field surveys and of two-dimensional analysis. Although these analyses can provide estimates of forces and moments on the structure, they do not account for three-dimensional (3D) phenomena, such as channelization, or geometric effects, such as bridge skew. Using a 3D computational fluid dynamics approach, this work analyzes the temporal and spatial dynamics of a bore-type tsunami loading on a model bridge and shows how the skew angle of the bridge relative to the incoming wave can affect the loading history. The analyses found that, unlike a bridge without skew, (1) the bore impact forces on the skewed deck do not all occur at the same time; (2) the skewed bridge is subjected to a force perpendicular to its abutments, which could lead to unseating; and (3) the skewed bridge is subjected to pitching and spinning moments. These effects combine to lead to increased horizontal reactions in the substructure components nearest the incoming wave. The vertical reactions were relatively insensitive to skew angle.

The statistical behavior of wave heights obtained from short-term (i.e., 30-min) wave records during Hurricane Ike was investigated. Spectral data from seven temporary pressure gauges and one National Data Buoy Center (NDBC) buoy moored off the coast of Texas, covering a 12-day period, were used. The wave heights, based on time series reconstructed from the spectra, showed a very good fit to the form of the Rayleigh distribution with$H_{\mathrm{r}\mathrm{m}\mathrm{s}}$ as the parameter of the distribution, whereas the use of the spectrally derived parameter $\sqrt{8m_0}$ led to overprediction of the wave heights. Incorporating the spectral band width ($\alpha$) in the Rayleigh distribution reduced this overprediction. The empirical two-parameter Weibull distribution was also found to represent the wave-height distribution well, but with parameters different from a = 2.126 and b = 8.42. The Tayfun model, used as a representative of Rayleigh-like models, provided the best fit. When converting model-derived significant wave heights to other quantities, such as$H_{1/10}$,$H_{1/100},$and$H_{\mathrm{m}\mathrm{a}\mathrm{x}}$, the standard Rayleigh coefficients are often used in practice. These led to considerable errors in the present analysis, which also shows that the use of correction factor or $\alpha$ can enhance the results. However, direct estimates of these quantities from a time series simulated using the model-derived spectrum may be an even better alternative to using the standard Rayleigh coefficients.

This paper describes an experimental study carried out in a laboratory flume to investigate the interaction of a surface wave with a unidirectional current over a submerged cubic obstacle. The three-dimensional velocity field was measured using an acoustic Doppler velocimeter (ADV). The results highlight the changes induced in the mean velocity profile, turbulent intensity, and Reynolds shear stress in a plane of symmetry from the superposition of surface waves of different frequencies. Modifications in the mean velocities, turbulence intensities, and Reynolds shear stresses with respect to the flat surface case, in the vicinity of the cube, are explored. This study also investigates the dominant turbulent bursting event that contributes to the Reynolds shear stress in the near-bed flow influenced by the cube. The results show that near the boundary, the contributions to the total shear stress from ejection and sweep are dominant. However, away from the boundary, the outward and inward interactions illustrate the prominence of wave−current interacting flow over the cube, which differs greatly from the flow over a flat surface. The mean time intervals of the occurrence of bursting events are obtained from the measurements of the fractional contributions to the total shear stress. The distribution of these time intervals is found to change because of the superposition of waves. As the frequency of the surface waves in a unidirectional current changes, the results show variations in the mean flow and the turbulence statistics that affect the local sediment mobility in the flow region influenced by the submerged cube.

Analysis of velocity and suspended sediment concentration data from field measurements at Pearl Beach in New South Wales, Australia, reveals the existence of onshore currents in the close vicinity of the rippled bed, whereas the velocity is offshore directed farther up in the water column. This might be caused by wave-induced streaming beneath irregular waves over ripples. To test this hypothesis, a simple one-dimensional vertical bottom boundary layer model capable of capturing streaming was applied, yielding a qualitatively fair agreement between the predicted and measured mean velocity and suspended sediment concentration profiles, although the predicted suspended sediment concentration was 1 order of magnitude smaller. Overall, these model results support the hypothesis of the mean near-bed onshore velocity caused by wave-induced streaming over ripples.