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This study employs an existing finite-difference model based on the hyperbolic form of the modified mild slope equation (MMSE) to investigate wave reflection near bathymetric depressions such as dredged borrow pits and nearshore canyons. First, the model is tested for numerical limitations on the higher order bottom slope and curvature terms using idealized cases of a simple depth transition and a symmetric trapezoidal trench, with comparisons of the MMSE to both the traditional mild slope equation (MSE) solution and a shallow water analytic solution. It is demonstrated that the model gives accurate solutions on slopes as steep as 1 : 1, and that the solutions from all three models agree in the shallow water region. However, for waves in intermediate depths, predicted wave reflection from nearshore depressions is shown to differ significantly between the MMSE and MSE models. Next, geometrical data from a wide range of existing and proposed borrow pits and a submarine canyon are gathered and analyzed for whether wave reflection is an important process near realistic nearshore depressions. The geometric data show that realistic nearshore depressions lie within the tested range of the MMSE model and that borrow pits are generally not in shallow water, which means it is important to use a MMSE-type model to calculate reflection from these features. In addition, storm conditions on average lead to a 50% increase in reflection coefficient in comparison to the mean wave conditions, due to the increase in wave period. Finally, the results also indicate borrow pit design criteria that can be used to ensure minimal reflection. DOI: 10.1061/(ASCE)0733-950X(2008)134:1(1) CE Database subject headings: Wave reflection; Nearshore; Dredging; Numerical models.

This paper describes the hydrodynamic characteristics of a pile-supported vertical wall breakwater, the upper part of which is a vertical wall, and the lower part consisting of an array of vertical piles. For regular waves, using the eigenfunction expansion method, a numerical model has been developed that can compute wave transmission, reflection, and run-up, and wave force acting on the breakwater. For irregular waves, the regular wave model is repeatedly used for each frequency component of the irregular wave spectrum. The wave period is determined according to the frequency of the component wave, while the root-mean-squared wave height is used for all the component waves to compute the energy dissipation between piles. To examine the validity of the developed models, large-scale laboratory experiments have been conducted for pile-supported vertical wall breakwaters with a constant spacing between piles but various drafts of the upper vertical wall. Comparisons between measurement and prediction show that the numerical model adequately reproduces most of the important features of the experimental results for both regular and irregular waves. The pile-supported vertical wall breakwater always gives smaller transmission and larger reflection than a curtain wall breakwater with the same draft as that of the upper wall, or a pile breakwater with the same porosity as that of the lower part, of the pile-supported vertical wall breakwater. DOI: 10.1061/(ASCE)0733-950X(2006) 132:2(83) CE Database subject headings: Breakwaters; Laboratory tests; Wave forces; Wave reflection.