Journal of Waterway, Port, Coastal, and Ocean Engineering

Low-frequency waves induced by the shoaling of random gravity waves (the primary waves) on sloping beaches were studied experimentally. Incident primary waves with a Pierson-Moskowitz (PM) spectrum were mechanically generated at a water depth of 0.7 m and propagated toward beaches with three different slopes (1/20, 1/30, and 1/40) in separate experiments. Four wave conditions with significant wave heights ranging from 0.078 to 0.125 m were used. The time series of surface elevations were simultaneously recorded at various water depths along the beach. Low-frequency waves were obtained from the data with a low-pass filter. Our results show that the spectra of low-frequency waves on beaches are dramatically changed by the beach slope and the wave height of incident primary waves. The cross-correlation of low-frequency waves with the surface-elevation envelope of the primary waves shows that the incident bound long waves are dominant. Free low-frequency waves propagate in the offshore direction with very low amplitudes due to high energy dissipation on the beach. The energy ratio between the low-frequency and the primary waves in the shoaling region outside the surf zone strongly correlates to the local surface skewness. For a given water depth, the low-frequency wave energy is proportional to $m_0^{3/2}$ , where $m_0$ is the primary wave energy, in agreement with the field observations.

An approach to estimating sediment transport along the Delaware–Maryland coast is described. Wave information study (second generation model, WISWAVE 2.0) hindcast frequency-direction spectra from 1980 to 1999 are used to generate a radiation stress-conserving angle for bringing offshore waves to breaking to estimate alongshore sediment transport. Using standard values for the coefficients in the United States Army Corps of Engineers’ Coastal Engineering Research Center (CERC) equation yields 20-year mean alongshore sediment transport rates between 470,942 and $-\mathrm{517,088}{\text{m}}^3/\text{year}$ depending on alongshore location after shoaling waves to shore. Interannual variability is large with SDs between 95,078 and $\mathrm{241,313}{\text{m}}^3/\text{year}$ again depending on alongshore location. Alongshore sediment transport rate estimates are commensurate with past studies using WIS data but overpredict the typically cited value of $\sim \mathrm{100,000}{\text{m}}^3/\text{year}$ near Indian River Inlet, Delaware based on sediment budget data by a factor of 3–4. This overestimation could be compensated for by altering the constant $K$ in the CERC transport equation or slight variations in the shoreline normal. The yearly estimates of the nodal point location where the sediment transport rate reverses direction were just south of the Delaware–Maryland border. The nodal point experienced interannual variability on the order of several thousand meters and is mainly attributed to the interannual variability in wave forcing. It is found that estimating alongshore sediment transport rates from offshore wave data are dependent on proper preservation of the radiation stress (using a radiation stress-conserving wave angle) and accurate determination of the shoreline normal.

Subaerial landslide generated impulse waves were investigated in a prismatic wave channel based on Froude similitude and granular slide material. The tests included the following seven governing parameters: still water depth, slide impact velocity, slide thickness, bulk slide volume, bulk slide density, slide impact angle, and grain diameter. All governing parameters, except for the grain diameter with a negligible effect, are included in the impulse product parameter $\mathsf{P}$ allowing for a simple application. Empirical equations based on 211 experiments for all relevant wave features in practice including the maximum wave height, the maximum wave amplitude with its location and period in the slide impact zone, and both the wave height and amplitude decay and the period increase in the wave propagation zone are a simple function of $\mathsf{P}$ . The presented equations were validated with 223 runs resulting in improved goodness of fit. The limitations of the herein derived empirical equations are also highlighted. The wave height and amplitude equations based on a wave channel (2D) agree well with the 1958 Lituya Bay case.

A numerical model that combines a random wave transformation and a wave-induced current model was developed in order to predict the wave and current fields around a detached breakwater. The wave field was determined using the EBED model, as reported by Mase in 2001, with a modified energy dissipation term. The surface roller associated with wave breaking was modeled based on a modification of the equations in works by Dally and Brown, and Larson and Kraus, in which the term for the roller energy flux in the alongshore direction was added to the energy balance equation. The nearshore currents and water elevation were determined from the continuity equation together with the depth-averaged momentum equations. The model was validated by three unique high-quality data sets obtained during experiments on detached breakwaters in the large-scale sediment transport facility basin at the Coastal and Hydraulics Laboratory in Vicksburg, Miss. The calculated significant wave height and longshore current were in good agreement with these measurements, whereas the cross-shore current was underestimated because undertow processes were not included in the modeling (depth-averaged equations employed). The calculated wave setup was somewhat overestimated; however, the absolute differences between the calculations and measurements were overall relatively small.

This case study on the Mississippi River Gulf Outlet earthen berm/spoil bank (EBSB) illustrates a method to quantitatively analyze wave-induced lateral erosion and breaching through the flood side of coastal flood protection levees with grass armor prior to overtopping. Lateral wave-induced erosion was evaluated based on a three-step process: (1) velocity profiles were generated using a general purpose transient dynamic finite element program; (2) resistance to wave-induced erosion as a result of grass cover (turf) on the flood face of the EBSB was estimated and no wave-induced erosion was applied until the grass cover protection failed; and (3) estimated soil erodibility characteristics were used, in combination with the estimated wave-induced flood face velocities, to estimate the magnitude of lateral erosion. This case study identified that soil erodibility characteristics directly impact coastal flood protection levee performance, grass/turf armoring provides erosion protection for a limited duration, and identification and evaluation of pre-overtopping wave-induced erosion is an important failure mode to be considered in order to ensure reliable coastal flood protection.