Journal of Waterway, Port, Coastal, and Ocean Engineering

Spilling breaking over beach profiles of varying slopes was studied numerically using an immersed-boundary/level-set method where both the bed profile and the free surface were immersed in a Cartesian grid. The combined water/air flow was governed by the incompressible Navier-Stokes equations and a Smagorinsky model for the subgrid scale stresses. The numerical model was validated by comparison to experimental data of waves breaking over a constant-slope beach. The examined beach profiles consisted of an outer region where the slope was constant and an inner region, which included the breaking point and the surf zone, where the slope was varying and the bed shape was concave. Eight cases were examined, and the main results are: (a) the decay coefficient of the wave-energy flux in the surf zone is correlated to the beach slope in the outer region; (b) the vorticity generation at the free surface and its distribution in the surf zone, as well as the intrawave velocity, the streaming boundary layer, and the undertow in the surf zone, are affected significantly by the varying slope in the inner region only for the cases of milder beach slope in the outer region; and (c) the effect of the normalized eddy-viscosity of the mean flow in the surf zone on the undertow profile is of the same order to the effect of the normalized net momentum gradient.

The development and implementation of a stabilized finite-element model for the simulation of large-scale geophysical flows using the shallow water equations (SWEs) is presented. The model is derived from the mass and momentum conservative forms of the SWE, with wetting–drying implemented using a front tracking algorithm. Transient hydrodynamic phenomena are resolved using run time h-mesh adaption, such that the initial grid resolution only needs to capture bathymetric features. Cartographic mapping is used to allow the use of Cartesian master elements when the meshing is performed in spherical coordinates. The model is validated using five applications designed to test mass conservation and robustness of the wet–dry scheme, and the cartographic mapping is implemented. The presented finite-element model numerical scheme for large-scale geophysical flows overcomes the limitations of mass conservation that have plagued older finite-element model schemes dependent on the generalized wave continuity equation (GWCE). The presented numerical model derives its novelty from the combination of a mass and momentum conservative finite-element model framework, true wetting–drying, and implicit time stepping with a spatially adaptive mesh and temporally adaptive time integration scheme. To the author’s knowledge, no prior finite-element model works exist with this combination of features in the realm of shallow water simulations for large-scale geophysical flows.

The Golden Horn estuary (GH) is a historic inlet in the northwest direction of the Bosphorus. It is a unique region that has valuable biological resources and provides living space for a wide variety of organisms. The GH suffers symptoms of poor circulation because of low river discharges upstream. Mixing by tidal or wind stress is also negligible in the estuary. Water exchange via the Bosphorus is the main factor that controls the circulation. In this study, a three-dimensional (3D) hydrodynamic model was set up and calibrated to predict the exchange flows between the waters of the Bosphorus and the eastern part of the GH. The numerical model was simulated for 2 months, January and August, which correspond to the extreme and gentle flow regimes, respectively. The mean negative and positive exchange flows were calculated. In addition, the influence of various driving forces on GH circulation was investigated using the calibrated 3D hydrodynamic model. The results show that the difference in water-surface elevation between the Marmara Sea and the Black Sea and the density-driven circulation account for almost 80% of the exchange flows in the GH. An attempt to estimate the residence time (τ) characteristics in the GH was also made using a 3D numerical model and a simplified box model, and the results were compared.

This study quantitatively assessed the risk in the overtopping performance of berm breakwaters due to sea level rise (SLR). To achieve this, a recent overtopping prediction formula that includes the influence of water depth on the estimated overtopping rate was used for the analysis. Additionally, the probabilities of failure in terms of the overtopping rate for different SLR scenarios were estimated using the Monte Carlo simulations, and the optimal maintenance intervals were determined. The increase in the crest freeboard, required to maintain the design overtopping rate, was estimated to be less than the increase needed in berm width for the different sea level rise scenarios considered. Furthermore, the required crest freeboard was influenced less by the initial configuration of the berm width. Shorter maintenance intervals were required for structures with an initially wide berm compared to those with a high crest freeboard. The results indicated that the future design and maintenance of berm breakwaters need to consider the effects of SLR on the overtopping performance, especially in shallow water zones.

The generation of shallow water tides (overtides) may influence shoaling processes in shallow embayments and harbors. A simplified, conceptual model is developed to simulate the generation of overtides and tidal asymmetries in small inlet/bay systems. The model’s formulation assumes a weakly nonlinear, pumping-mode response and includes effects of four generating mechanisms: quadratic bottom friction (QB), elevation-effect of friction (EEF), nonlinear continuity (NC), and advective acceleration (AA). QB generates primarily odd harmonics, including a second overtide component (M6) that reduces/distorts peak flood/ebb currents symmetrically. The first overtide component (M4) is generated primarily by NC, EEF, and AA. NC, AA, and QB mechanisms are associated with flood-dominant distortion patterns, whereas the EEF mechanism is associated with a shift toward ebb dominance in the special case in which NC contributions are reduced (e.g., large basin tidal flats) and AA is small. Solutions for the M4 tide indicate phase-locking, and distortion patterns consistent with previous studies. A maximum flood-dominant response can occur when the ocean forcing frequency is half the Helmholtz frequency, which is a condition that may cause flood shoals to develop.