Coastal Engineering Journal

The breaking-limited (or depth-limited) approach is a traditional method to determine the maximum possible wave height for the design of coastal structures in the surf zone. It is well recognized that the maximum wave height in the surf zone is limited by wave breaking. The maximum possible wave height is usually determined from a breaker height formula. The present study was undertaken to examine the applicability of 14 existing breaker height formulas for computing the maximum possible wave heights. The existing breaker height formulas were examined against measured regular and irregular wave heights. A total of 17 863 data points from 30 sources of published experimental data were used to examine the formulas. The experiments cover a wide range of wave and bottom topography conditions including small-scale, large-scale, and field experiments. It was found that the errors of existing formulas for regular and irregular waves have the same tendency. The existing formulas give considerable underestimation of the maximum possible wave heights in shallow water. The top three formulas were modified by including a new form of relative depth into each formula. Overall, the modified formulas give a considerable better estimation than those of existing formulas.

This paper examines the applicability of a stochastic model for the propagation of random waves in shallow water including triad near-resonance interactions. The model is derived from evolution equations for complex Fourier amplitudes of fully dispersive multi-directional waves. The closure used in the stochastic equations is adopted from the theory of weak turbulence based on the assumption of quasi-normal sea state. In the model formulation, the second- and third-order wave statistics are formulated by evolution equations for the wave energy spectrum and bispectrum. These equations are implemented numerically, for the case of unidirectional waves, to compute the evolution of the wave energy spectrum and the bispectrum. Experimental measurements for random wave transformation over a shoal (submerged bar) are compared against the numerical-model results. The stochastic model accurately predicted the wave spectra and third-order statistics, in regions where the Ursell number is smaller than 1.5. For larger Ursell-number values, the stochastic model tends to over-estimate the content of high-frequency energy, and the skewness and asymmetry, compared to its deterministic counterpart.

A set of fully nonlinear Boussinessq-type equations with improved linear and nonlinear properties is considered for wave–current interaction analysis. These phase-resolving equations are so that the highest order of the derivatives is three. We implement a new source function for the wave–current generation within the domain, which allows to generate a wide range of wave–current conditions. The set of equations is solved using a fourth order explicit numerical scheme which semi-discretizes the equations in space and then integrates in time using an explicit Runge–Kutta scheme. A novel treatment of the boundaries, which uses radiative boundary conditions for the current and damps the waves, is used to avoid boundary reflections. Several validation tests are presented to demonstrate the capabilities of the new model equations for wave–current interaction.

A monitoring system, called the optic sediment sensor (OSS), for study of the detailed processes of bathymetric changes in the surf zone has been developed. The OSS system consists of an array of fiber gap sensors (FGSs), a support structure (steel pipes), an electronics unit that transmits and receives light through fiber-optic cables, and a data acquisition system. The FGSs are mounted in a 2-m long vertical steel pipe; the sensor spacing is 10 cm. Steel pipes containing FGSs were embedded in the seafloor at two places at water depths of 4–5 m beneath a pier at the Hazaki Oceanographical Research Station (HORS) (Port and Airport Research Institute) on the Sudahama Coast, facing the Pacific Ocean, Japan. The electronics unit and the data acquisition system were installed in an observation room on the pier. The OSS systems successfully recorded well-defined and consecutive bathymetric changes caused by storm waves (maximum significant wave-height = 3 m); e.g. reversal of seabed erosion and deposition within a day could be recognized. If the OSS system could be installed in many more locations along the pier, the consecutive process of the formation, migration, and deformation of the whole of the longshore bar may be clarified.

Manning's n values for open channel (river) flow have been studied by hydraulic engineers since the late 19th century, and a rich literature exists on the topic including large-scale laboratory experiments and actual field measurements. Both river flood models and shallow water equation tsunami inundation models incorporate the importance of varying equivalent roughness values with the large-scale roughness elements present for different land use types. However, many tsunami models (especially in Japan) use n values based on a very limited set of small-scale model laboratory experiments with inappropriate Reynolds and Weber numbers, instead of using Manning's n values from the open channel flow literature. Due to this, equivalent Manning's n values for vegetated and urban areas in these tsunami inundation models are too small, causing the mitigating effect of forests and urban regions to be underestimated. This paper presents a review of Manning's n research applied to both river flood and tsunami inundation models, and suggests values to improve the reliability of the latter.

An ultrasonic velocity profiler (UVP) acquires instantaneous distributions of axial velocity along the ultrasonic beam emitted from the transducer. In this paper, organizations of the transverse flows over a span of a laboratory wave flume in the surf zone were identified experimentally on the basis of UVP measurements. Ensemble mean divergent and convergent flows were observed over the span of the flume in the surf zone regardless of breaker conditions. By analogy with the flow evolution in a previous computation, by Watanabe and Saeki [1999], we identified that the organization of the wave-breaking-induced counter-rotating vortices determined the spatial and temporal variations in the transverse flows at the early stages of the breaking process regardless of the widths of wave flumes and friction on the sidewalls and bottom. The observed transverse flows were driven by pairs of counter-rotating vortices produced under the breaking waves and the change in the orientation during the passage of breaking waves. The fundamental features of the transverse flows evolving in the breaking process, depending on the breaker type, are discussed statistically to parameterize velocity, time, and length scales of the variations of the transverse velocity. The dimensionless length and time scales had negative linear correlations with the Froude number (defined by relative transverse convection with respect to gravity) as well as a surf similarity parameter, which indicates that the gravity effect associated with the projections of the breaking wave crests defines the primary roller vorticity and shear intensity at the plunging location, resulting in destabilization of the flows in the transverse direction to form organized transverse flow structures.

This paper presents an experimental investigation of the evolution of induced vortices as a solitary wave propagating past a submerged trench. The trajectories of moving fluid particles and transport of trench contents are also analyzed. Using the planar laser induced fluorescence (PLIF) visualization technique, the captured images of the motion of fluorescent dyed fluid particles indicate that, during the process of wave crest passing a trench, a clockwise vortex near the leading edge of the trench is formed and shown to grow vertically while the downstream-transporting front is expanded with more particles carried away from the trench. The incident wave-height has a strong influence on the displacement of moving fluid particles. The numerically determined maximum transporting distances downstream of the experimentally defined trenches were compared with a close match to the values estimated from the extracted images. The removal percentages of trench particles are heavily affected by the incident wave-height. For a square trench with an opening size of 50% of the water depth outside of the trench, numerically, it is found an α = 0.4 solitary wave can entrain nearly 60% of the particles that are initially settled in the trench.