Journal of Waterway, Port, Coastal, and Ocean Engineering

Open boundary conditions significantly influence the results of a water wave numerical model based on the mild slope equation. An integral equation is written on an arc of a circle for a harbor area limited by two semi-infinite, fully reflective, straight dikes of any direction. This formulation, providing useful idealized tests for practical use, is compared with parabolic approximations in an analytical test case and for a schematic harbor. Parabolic approximations provide excellent results if the reflected wavefield generated from the exterior dikes is well known.

A numerical scheme was developed to solve the unsteady, two-dimensional Navier-Stokes equations and the exact free-surface boundary conditions for simulating the propagation of water waves over rigid rippled beds. A boundary-fitted coordinate system was used in this model. The accuracy of the numerical scheme was verified by comparing the numerical results for the velocity fields on the rippled bed with the experimental data. For the periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. To provide information for understanding the possible mechanism of sediment transport around the rippled bed, trajectories of the fluid particles with initial locations close to the ripples were determined. One of our main results showed that as a solitary wave passes over rigid ripples, the fluid particles near the bed are lifted by the primary vortices induced at the lee side of the ripple crest and are transported in the opposite direction from the wave. This is different from what occurs in the case of periodic waves, where the fluid particles are transported in the direction of the waves.

A nontidal, natural, mildly sloping, multiple, mostly four bar nearshore zone at the Coastal Research Station Lubiatowo, Poland is analyzed. It is made of fine sand with the mean grain size $D_{50}=0.22\mathrm{mm}\text{,}$ which is typical of the south Baltic coast. The bars oscillate about their average locations offering good prototype conditions for testing a method that could reproduce and predict this type of bed dynamics. The dataset represents four adjacent, shore normal profiles, spaced every 100 m and sampled every 10 m between 100 and 900 m offshore of the geodetic base once a year between 1987 and 1998. In all, 324 grid points, each with 12 realizations were incorporated, allowing use of the data intensive principal oscillation pattern (POP) technique to come up with a data-driven model of bed dynamics. It revealed three patterns that reasonably reproduced long-term bed dynamics, and the modeling results are fairly accurate at the locations of bars 2, 3, and 4, where bed evolution is slow enough to be grasped by annual records. Developments around innermost bar 1 turned out to be too fast for annual measurements to retain sufficient information and achieve satisfactory results with the POP method. The POP model outperformed dominant empirical orthogonal functions (EOF) modes by 6% in terms of the explained variance, but the EOF method is highly recommended prior to the POP analysis, because it can identify clear-cut orthogonal patterns; whereas, the POP method produces interdependent patterns whose interpretation is difficult without the EOF modes.

The new risk assessment model in which the second-order reliability method and the importance sampling Monte Carlo (ISMC) simulations were interrelated was implemented to Wiseman’s Bridge, Newport, and Broadhaven revetments in the Pembrokeshire Coast National Park, southwest Wales, United Kingdom. The tidal range of the site and the storm surge were randomly generated at the first stage of ISMC simulation from the probability distributions describing the phenomena. At the second stage, the damage probability was predicted by approximating the limit-state surface by a quadratic one having the identical curvature at the design point. Newport and Broadhaven revetments were safe, but the revetment at Wiseman’s Bridge needed strong maintenance. The risk assessment model reflected the effect of water level changes (circa 6 m above ordnance datum) on the reliability of rubble mound revetments by simulating the environmental conditions at the sites. As the uncertainties inherent in design parameters were extensive, such as variations associated with wave data, tidal range and storm surge, it was suggested to determine the reliability of revetments by using Monte Carlo simulation methods. On the other hand, such hard engineering structures in a National Park Coast where the emphasis is on natural beauty are questionable, especially when they protect just two buildings, such as the Wiseman’s Bridge revetment. It is ironic that pebble beaches abound in the area, and these are probably the best protection that can be given both to nature and structures.