A 3D unstructured grid nearshore hydrodynamic model based on the vortex force formalism

Acknowledgments This work was partly supported by joint Engineering and Physical Science Research Council (EPSRC) UK and Technology Foundation STW Netherlands funded SINBAD (EP/J005541/1) project. P. Zheng was supported by the China Scholarship Council during his four-year PhD study at the University of Liverpool. We would like to thank Prof. C.S. Chen of the University of Massachusetts-Dartmouth for providing the source code of FVCOM and also the SWAN developers for developing and providing this open source code. We would also like to thank the staff and personnel involved in collecting and maintaining the DUCK’94 experiment dataset and the anonymous reviewers for their constructive comments and suggestions. Computational support was provided by the Chadwick High Performance Computer at University of Liverpool and also the facilities of N8 HPC Centre of Excellence, provided and funded by the N8 consortium and EPSRC (EP/K000225/1).Peer reviewedPublisher PD

Gourds: A Sliding-Block Puzzle with Turning

We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single empty cell on a board and forms a natural extension of the 15-puzzle to include rotational moves. We analyze the puzzle and completely characterize the cases when the puzzle can always be solved. We also study the complexity of determining whether a given set of colored pieces can be placed on a colored hexagonal grid board with matching colors. We show this problem is NP-complete for arbitrarily many colors, but solvable in randomized polynomial time if the number of colors is a fixed constant.Comment: 15 pages + 3 pages appendix, including 18 figure

Near-Bed Turbulent Kinetic Energy Budget Under a Large-Scale Plunging Breaking Wave Over a Fixed Bar

Hydrodynamics under regular plunging breaking waves over a fixed breaker bar were studied in a large-scale wave flume. A previous paper reported on the outer flow hydrodynamics; the present paper focuses on the turbulence dynamics near the bed (up to 0.10 m from the bed). Velocities were measured with high spatial and temporal resolution using a two component laser Doppler anemometer. The results show that even at close distance from the bed (1 mm), the turbulent kinetic energy (TKE) increases by a factor five between the shoaling, and breaking regions because of invasion of wave breaking turbulence. The sign and phase behavior of the time-dependent Reynolds shear stresses at elevations up to approximately 0.02 m from the bed (roughly twice the elevation of the boundary layer overshoot) are mainly controlled by local bed-shear-generated turbulence, but at higher elevations Reynolds stresses are controlled by wave breaking turbulence. The measurements are subsequently analyzed to investigate the TKE budget at wave-averaged and intrawave time scales. Horizontal and vertical turbulence advection, production, and dissipation are the major terms. A two-dimensional wave-averaged circulation drives advection of wave breaking turbulence through the near-bed layer, resulting in a net downward influx in the bar trough region, followed by seaward advection along the bar's shoreward slope, and an upward outflux above the bar crest. The strongly nonuniform flow across the bar combined with the presence of anisotropic turbulence enhances turbulent production rates near the bed

Sand suspension and fluxes by wave groups and equivalent monochromatic waves

We thank the technical staff of the UPC CIEMLAB and Sjoerd van Til for their contributions to the experiments, and the editor and an anonymous reviewer for their useful feedback on the manuscript. The experimental work was supported by the European Community's Seventh Framework Programme through the grant to the budget of the Integrating Activity HYDRALAB IV within the Transnational Access Activities, Contract no. 261520, with additional funding from the Dutch Technology Foundation STW (project 12058) and the UK’s Engineering and Physical Sciences Research Council (EPSRC, grant number EP/J00507X/1) through the SINBAD project. JvdZ was funded through the European Community’s H2020 Programme HYDRALAB+ (Contract no. 654110). The presented data are stored in the 4TU online data repository (https://doi.org/10.4121/uuid:30496cc3-9803-4c18-8a6f-85513bb29c3d).Peer reviewedPostprin

Experimental study on a breaking-enforcing floating breakwater

Floating breakwaters are moored structures that attenuate wave energy through a combination of reflection and dissipation. Studies into floating breakwaters have been generally restricted to optimising the attenuation performance. This study presents a novel floating breakwater type that was developed to have good attenuation performance while keeping wave drift loads as small as possible. The floating breakwater was designed as a submerged parabolic beach that enforces wave energy dissipation through breaking. The design was tested in a 3D shallow-water wave basin in captive and moored setups for regular and irregular wave conditions. Results are presented in terms of attenuation performance, motions, and (mooring) loads. The results show that the breaking of waves improves the attenuation performance of the floater in captive setup. However, in moored setup, the attenuation performance was dominated by diffraction and radiation of the wave field, with breaking being of secondary importance. This shows that breaking-enforcing floating breakwaters have potential, but require a high vertical hydrostatic and/or mooring stiffness in order to enforce intense breaking. Mean wave drift loads on the object showed significant difference between breaking and non-breaking waves in both setups, with breaking waves leading to lower normalized loads. This is attributed to breaking-induced set-up and set-down of the water level. As a result, the new breakwater design has a more favourable balance between wave attenuation and drift loads than common (i.e., box-, pontoon-, or mat-type) floating breakwater designs. Tests with varying surface roughness showed that floating breakwaters may benefit from dual-use functions that naturally increase the roughness (e.g., shellfish, vegetation), which have a marginal effect on the attenuation performance, but increase the added mass and hydrodynamic damping and as such, reduce mooring line loads

The influence of wave groups and wave-swash interactions on sediment transport and bed evolution in the swash zone

Large scale laboratory measurements of sediment dynamics in the swash zone are presented. Two bichromatic wave group conditions were generated, having the same energy content but different wave group period (Tg = 15.0 s and 27.7s). For the shortest wave group, due to bore focusing, the shoreline fluctuates predominantly at the time scale, showing a large runup and the presence of wave–swash interactions with strong momentum exchange. In contrast, for the longer wave groups, the swash excursion is dominated by the individual waves. The uprush generally promotes onshore sediment advection with consequent erosion at the rundown location but accretion close to the runup. On the contrary, the backwash promotes seaward sediment advection and accretion at the rundown location. The presence of repeated wave–swash interactions modifies these patterns slightly. A wave overrunning a previous uprush promotes a reduction in onshore sediment advection while weak wave–backwash interactions reduce seaward advection. Consequently, the measured sediment dynamics shows stronger intra–swash cross–shore sediment advection for the swash events produced by the short wave groups. Measurements of the sheet flow layer near the shoreline show that for the shortest wave groups the vertical structure of the concentration is influenced by horizontal advection, leading to large sheet-flow layer thickness. However, for the longer wave groups, the local vertical exchange of sediment in the sheet–flow layer is dominant, with the presence of a pick–up and mirroring upper layer similar to oscillatory sheet–flow measurements. These results reaffirm the important effects of the wave group structure and the wave–swash interactions on the swash zone sediment dynamics and beach face evolution.Peer ReviewedPostprint (author's final draft

Wave boundary layer hydrodynamics and sheet flow properties under large-scale plunging-type breaking waves

Wave boundary layer (WBL) dynamics are measured with an Acoustic Concentration and Velocity Profiler (ACVP) across the sheet flow-dominated wave-breaking region of regular large-scale waves breaking as a plunger over a developing breaker bar. Acoustic sheet flow measurements are first evaluated quantitatively in comparison to Conductivity Concentration Meter (CCM+) data used as a reference. The near-bed orbital velocity field exhibits expected behaviors in terms of wave shape, intrawave WBL thickness, and velocity phase leads. The observed fully turbulent flow regime all across the studied wave-breaking region supports the model-predicted transformation of free-stream velocity asymmetry into near-bed velocity skewness inside the WBL. Intrawave concentration dynamics reveal the existence of a lower pickup layer and an upper sheet flow layer similar to skewed oscillatory sheet flows, and with similar characteristics in terms of erosion depth and sheet flow layer thickness. Compared to the shoaling region, differences in terms of sheet flow and hydrodynamic properties of the flow are observed at the plunge point, attributed to the locally enhanced wave breaker turbulence. The ACVP-measured total sheet flow transport rate is decomposed into its current-, wave-, and turbulence-driven components. In the shoaling region, the sand transport is found to be fully dominated by the onshore skewed wave-driven component with negligible phase lag effects. In the outer surf zone, the total net flux exhibits a three-layer vertical structure typical of skewed oscillatory sheet flows. However, in the present experiments this structure originates from offshore-directed undertow-driven flux, rather than from phase lag effects.Peer ReviewedPostprint (published version

Large scale experiments on beach evolution induced by bichromatic wave groups with varying group period

New large scale experimental data have been presented showing the wave group influence on beach morphodynamics at the surf and swash zones. Bichromatic wave conditions were generated varying the modulation bandwidth but keeping the wave energetic content constant within the experimentation limits. The wave group influence in the surf zone is observed in the form of the cross-shore location of the breaker bar respect to the initial still water level (SWL) location, which has been shown to increase as increases the wave group period. This influence is explained in terms of differences on the surf zone width induced by the varying wave group periods. In the swash zone, time dependent bed level elevation measurements were done using a newly developed conductivity technique, the CCM+ system. Bed level time variations at the swash zone have shown to be composed of a long scale trend and bed level oscillations of shorter frequencies related to the wave group forcing. A good spectral correlation has been found between the water surface elevation and bed level variation at the wave group period for every bichromatic component indicating an important influence of wave groups on the swash zone morphodynamics