Wave-induced Currents Research Articles

Evolutionary trend of the Gorgan Bay (southeastern Caspian Sea) during and post the last Caspian Sea level rise

The Gorgan Bay (GB) is a semi-confined sedimentary environment at the southeastern corner of the Caspian Sea (CS). High sensitivity to eustatic sea-level variations resulted in changes in the sedimentary facies and patterns of erosion/sedimentation for the GB in the last Caspian Sea-level cycle (1977–1995). Therefore, the evolutionary trend in coastal sedimentary environments was studied to determine the pattern of erosion and sedimentation related to sea-level fluctuation cycles. The sedimentology of the bay basin was studied in 500 km2 of the study area in 2001. In addition, coastal changes over the two past and post periods of sea-level rise were studied using satellite images (Landsat 7 with a resolution of 30 m) and ArcGIS 10.1 software. Waves, wave-induced currents and sediment transport were simulated using the MIKE-21 software package. Mixed sediments, particularly at the western and southern areas of the bay basin, were detected through reworking of coarser barrier island sediments into deeper areas. Well-sorted (0.35–0.5φ) sediments, with 98.31 ± 2.8% sand-size particles, were identified as the common texture along the wave-dominated coasts. Sea progradation, destruction of the beach profile and an increase in sea coverage of approximately 15,600 ha around the GB were other impacts of the CS-level rise. Additional impacts included severe erosion and submergence of a 9000 ha area of the flat coastal plains (slope~ 0.035%). The results demonstrate that water-level rise has strengthened the sediment accumulation in the bay inlet and basin at a mean rate of 0.430 MCM and 12.7 MCM, respectively. Both field measurements and simulation results revealed the notable shoaling of the bay entrance at a mean rate of 0.2 m. Simulations concluded that annual longshore transport toward the bay inlet has occurred at a net rate of 80,000 m3 during the last CS-level rise. Natural events after the eustatic cycle in the southeastern corner of the CS resulted in severe shoaling of the GB inlet and basin and restriction in the water exchange between the bay and open sea. Therefore, comprehensive management practices to restore the GB capacity and its natural habitats are critically needed.

Storm-wave development of shore-normal grooves (gutters) on a steep sandstone beach face

Shore-normal grooves (gutters) cut into the seabed have been reported widely from the marine geological record. Grooves commonly are spaced regularly across plane, consolidated surfaces in the littoral and sub-littoral zones and may be deeply incised. Despite their common occurrence in the rock record, there are few detailed descriptions of examples from modern environments. Previously reported examples have been ascribed to erosion by wave-induced currents, especially storm-driven near-shore flows. In particular, examples from beach faces have been related to either wave swash or backwash. However, no conceptual model exists to explain the presence of grooves, their morphology or their spacing alongshore.Herein, quasi-regularly spaced grooves on a soft sandstone beach face are described and interpreted to have formed due to wave breaking and swash zone processes consequent upon exceptional storms at sea. The groove morphologies are quantified using terrestrial laser scanning. Numerical modelling of the translation from offshore waves to nearshore breaking waves provides estimates of the swash zone parameters. A consideration of swash zone processes provides an explanation for formation of the grooves. In particular, the swash zone shear stress distribution and consequent bed erosion is a dome-shaped function of distance across the beach face, and this controls the cross-shore variability in groove depths. High-speed sheet flows, such as swash and backwash, develop periodic, shore normal, high and low speed streaks alongshore. Consequent streaky erosion produces the quasi-regular alongshore groove spacings. However, on any given beach face the specific spacing of grooves is likely a property, not only of the local sheet flow attributes, but also of larger-scale morphological forcing. This outcome suggests that spacing is an emergent property of the coupled sheet flow and larger-scale forcing, and thus specific spacings on any beach face remain unpredictable.

3D SPH porous flow model for wave interaction with permeable structures

A three-dimensional smoothed particle hydrodynamic (3D SPH) porous flow model for wave interaction with permeable structures is developed to assess the 3D effects around the coastal structures with complex geometrical boundaries. The Volume Averaged and Favre Averaged Navier-Stokes (VAFANS) equations along with the Sub Particle Scale (SPS) turbulence model are implemented as the governing equations to describe the fluid motion both inside and outside the permeable structure. The empirical frictional source terms are introduced to represent the resistance forces on the fluid flow induced by the solid skeleton of the porous structure. The permeable interface is treated as a transition zone and the porosity value changes continuously in this zone by using an interpolation algorithm over the background porosity points. The present model is validated by the available numerical results for dam-breaking wave impacting on a porous square prism and the experimental data for solitary wave interaction with a vertical porous breakwater. The validated model is then applied to investigate wave interaction with a detached shore-parallel breakwater of two layer porous media. The predicted 3D flow field inside and outside the permeable breakwater is analyzed. The spatial distributions of wave-induced current induced by wave breaking are also discussed.

Numerical simulations of rip currents off arc-shaped coastlines

The rip currents induced by waves off arc-shaped coastlines are seriously harmful to humans, but understanding of their characteristics is lacking. In this study, the FUNWAVE model was used to calculate the wave-induced currents in the Haller experiment and the ideal arc-shaped coast similar to Sanya Dadonghai, Hainan Province, China. The results showed that the FUNWAVE model has considerable ability to simulate the rip currents, and it was used to further simulate rip currents off arc-shaped coastlines to investigate their characteristics. The rip currents were found to be stronger as the curvature of arc-shaped coastline increased. Coastal beach slope exerts a significant influence on rip currents; in particular, an overly steep or overly mild slope is not conducive to creating rip currents. Furthermore, the rip currents were found to become weaker as the size of arc-shaped coast decreased. When the height and period of waves increase, the strength of rip currents also increases, and, in some cases, wave heights of 0.4 m may produce dangerous rip currents.

Modeling two-dimensional infragravity motions on a fringing reef

This study investigates infragravity motions on a two-dimensional fringing reef with a concave topography using a wave-resolving nonlinear Boussinesq wave model. The effect of bathymetric nonlinearity on spatial variations of infragravity waves is studied from shore-normal incident random waves. The model is first verified from cross-shore/alongshore significant wave height, wave setup and infragravity wave height measured in laboratory experiments. The modeled velocity is further examined to elucidate the infragravity-wave current field. Wavenumber-frequency velocity spectra show that cross-shore infragravity motions are controlled by the leaky waves, while alongshore infragravity motions exhibit edge waves characteristics. Additionally, high-mode edge waves prevail on the entire infragravity frequency band while low-mode edge waves are dominant at very low frequencies. Furthermore, the model results illustrate the spatial and temporal variability of wave-induced nearshore currents, alongshore and cross-shore flows accompanying with circulation cells and rip currents. The infragavity-wave current field is nearly identical to the mean current field and the circulations develop at the same spatial scale as the reef flat.

The numerical model of the sediment distribution pattern at Lampulo National fisheries port

The spatial distribution of sediment pattern was studied at Lampulo Fisheries Port, Krueng Aceh estuarial area, Banda Aceh. The research was conducted using the numerical model of wave-induced currents at shallow water area. The study aims to understand how waves and currents react to the pattern of sediment distribution around the beach structure in that region. The study demonstrated that the port pool area had no sedimentation and erosion occurred because the port was protected by the jetty as the breakwater to defend the incoming waves toward the pool. The protected pool created a weak current circulation to distribute the sediments. On the other hand, the sediments were heavily distributed along the beach due to the existence of longshore currents near the shoreline (outside the port pool area). Meanwhile, at the estuarial area, the incoming fresh water flow responded to the coastal shallow water currents, generating Eddy-like flow at the mouth of the river.

Surface current measurements using lagrangian Drifters in Anmok

In this study, surface currents measured by small lagrangian GPS drifters (Aquadrifter) in Anmok coastal waters were analysed to account for the variability of nearshore surface current and wave-induced current to understand sediment transport mechanism near the crescentic bars in the surf-zone and near Kangneung breakwater and submerged breakwater in Anmok. The 8 times lagrangian drifter experiments were conducted mostly during in 2nd, 3rd, 4th intensive measurements in winter, summer, and spring seasons with long-term wave observation at the station W1. The analysed surface currents near the breakwaters in Anmok show that wave-induced currents at the middle of the submerged breakwater were separated and flowed toward the shoreline but offshore currents were dominant through the channels between the breakwaters. The longshore currents near the shoreline were flowed to the northwest (southeast) depending on the incoming waves from ENE (NNE). The surface nearshore offshore currents were generated mostly by waves and winds in case of high and low wave energy environments. Using the small-size lagrangian surface drifter experiments, we successfully measured longshore and offshore wave-induced currents in the surf-zone and near submerged breakwater close to Kangneung breakwater. The drifter experiment results show the availability of direct observation of nearshore surface currents to understand the mechanism of sediment transport analysing observed wave-induced current and ebb-current in the surf-zone generated by incoming waves and local winds.

Stability of a micro-tidal inlet using semi-numerical approach

Tidal inlets get disconnected depending on the seasons due to the formation of sand bars near its mouth are termed as “seasonally open tidal inlets.” These inlets are usually small of width of about 100 m and occur in micro-tide (tidal range not exceeding 1 m). Since the east coast of India experiences a net littoral drift of up to about 0.8 Mm3/annum, which is one of the largest in magnitudes that needs to be considered in the analysis of modeling of the sand bar formation and the associated phenomena. Kondurpalem inlet situated along the South east coast of India is considered as a case study. A frequency domain wave model (STeady-state spectral WAVE) has been used to compute the nearshore wave climate. The wave-induced currents have been obtained, and the longshore sediment transport rate is obtained through empirical relations. The tidal prism is found from measured depth and tidal velocity by solving shallow water equations. The stability of the inlet is investigated by applying the criteria developed by Bruun (1986). The effect of a pair of training walls on maintaining the stability of the mouth is reassessed over the periods.

An Integrated Numerical Model for the Design of Coastal Protection Structures

In the present work, an integrated coastal engineering numerical model is presented. The model simulates the linear wave propagation, wave-induced circulation, and sediment transport and bed morphology evolution. It consists of three main modules: WAVE_L, WICIR, and SEDTR. The nearshore wave transformation module WAVE_L (WAVE_Linear) is based on the hyperbolic-type mild slope equation and is valid for a compound linear wave field near coastal structures where the waves are subjected to the combined effects of shoaling, refraction, diffraction, reflection (total and partial), and breaking. Radiation stress components (calculated from WAVE_L) drive the depth averaged circulation module WICIR (Wave Induced CIRculation) for the description of the nearshore wave-induced currents. Sediment transport and bed morphology evolution in the nearshore, surf, and swash zone are simulated by the SEDTR (SEDiment TRansport) module. The model is tested against experimental data to study the effect of representative coastal protection structures and is applied to a real case study of a coastal engineering project in North Greece, producing accurate and consistent results for a versatile range of layouts.

Shipwrecks and man-made coastal structures as indicators of historical shoreline position. An interdisciplinary study in the Sancti Petri sand spit (Bay of Cádiz, SW Spain)

Shoreline evolution studies are mostly performed by comparison of vertical images (e.g. aerial photographs and satellite imagery), being limited to the last decades. However, phenomena such as longer term climatic fluctuations may cause important secular coastal changes which are mostly unknown. The use of archaeological remains as shoreline proxies could overcome this limitation by allowing to expand back in time the historical shoreline record. The present study endorses the effectiveness of the use of shipwrecks and man-made structures as proxy data for analyzing historical shoreline evolution. This was confirmed by the evaluation of nearshore evolution (historical shorelines from 1787 to 1823 and recent changes from 1956 to 2013) and the reconstruction of the palaeobathymetry along Sancti Petri sand spit (SW Spain) by means of the analysis of historical documents, historical maps, modern aerial photographs and a recent bathymetry (2011), along with the archaeological prospection supported by the numerical modelling of the dispersion of archaeological remains. The analysis of historical maps has revealed a significant shoreline retreat over the medium term scale in Sancti Petri sand spit, averaging −1.2m·year−1. Results from historical maps and archaeological remains show slight differences with respect to the most recent retreat rates (−0.9m·year−1) obtained from aerial photographs for the period 1956–2013. Spatial variations in coastal retreat along the sandspit are closely linked to local patterns of wave height and wave-induced currents. Significant temporal variation in rates of shoreline change was observed, probably related to storminess variability in the study area, as indicated by the relation between the rates of coastal change for each analyzed period and the corresponding rate of change of winter NAO index.

Numerical simulation of the three-dimensional wave-induced currents on unstructured grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the threedimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.

Wave-induced current at Anmok Beach, Korea

Currents were measured at two stations on Anmok Beach, and were reproduced by a numerical model system CST3D-WA. Anmok area is known as wave-dominated coast, and the mean tidal range small. Field data with strong wave-induced current are rare, especially at shallow water depth. Measured currents were strong during three periods. The largest instantaneous current speed at a station during a period was 46 cm/s. CST3D-WA system simulated wave-induced current for the three periods, and compared with measurements. The deviation of the incident peak wave direction from the normal direction to the shoreline strongly affects the wave-induced current speed and direction. When the deviation angle crosses the normal direction, the wave-induced alongshore current direction changes between SE and NW. CST3D-WA is thought to have successfully reproduced the wave-induced current fields on this beach.

Three-dimensional wave-induced current model equations and radiation stresses

After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy’s wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.

Numerical modeling of hydrodynamics and sediment transport—an integrated approach

Point measurement-based estimation of bedload transport in the coastal zone is very difficult. The only way to assess the magnitude and direction of bedload transport in larger areas, particularly those characterized by complex bottom topography and hydrodynamics, is to use a holistic approach. This requires modeling of waves, currents, and the critical bed shear stress and bedload transport magnitude, with a due consideration to the realistic bathymetry and distribution of surface sediment types. Such a holistic approach is presented in this paper which describes modeling of bedload transport in the Gulf of Gdansk. Extreme storm conditions defined based on 138-year NOAA data were assumed. The SWAN model (Booij et al. 1999) was used to define wind–wave fields, whereas wave-induced currents were calculated using the Kolodko and Gic-Grusza (2015) model, and the magnitude of bedload transport was estimated using the modified Meyer-Peter and Muller (1948) formula. The calculations were performed using a GIS model. The results obtained are innovative. The approach presented appears to be a valuable source of information on bedload transport in the coastal zone.

Seasonal sediment dynamics on the Barcelona inner shelf (NW Mediterranean): A small Mediterranean river- and wave-dominated system

The seasonal pattern of sediment dynamics on an inner shelf characterized by the presence of sediment delivered by a small, mountainous river (with a “flash-flood” regime) was investigated. Near-bottom suspended sediment fluxes across the shelf (i.e. 20, 30 and 40m water depth) were estimated using observations from three benthic tripods deployed from September 2007 to June 2008. Near-bottom sediment resuspension was controlled by wave-induced currents and river-born sediment availability, whereas the shelf currents played a secondary role. Fourteen sediment transport events were identified (eight in autumn, two in winter and four in spring), with transport rates according to storm intensity and sediment availability. These few energetic events induced a large percentage of the cumulative sediment transport near the bottom. However, the lack of proportionality between suspended sediment transport rates and the combined wave-current bottom shear stress in some events highlights the importance of the sequence of events in sediment dynamics. Since wave activity, hydrography and river discharges display a strong seasonal pattern in the NW Mediterranean, the resulting sediment dynamics across the shelf also correspond to a seasonal cycle. This seasonal variability leads to a temporal evolution of the bottom grain size (coarser in winter) and the near-bottom sediment transport rates (higher in spring and autumn) which is consistent with the seasonal pattern of the hydrodynamic events and the river discharge load.

Numerical study on influences of breakwater layout on coastal waves, wave-induced currents, sediment transport and beach morphological evolution

This study provides a numerical model to investigate the influences of breakwater layout on coastal waves, wave-induced currents, sediment transport and beach morphological evolution in the vicinity of breakwater. The numerical model is developed based on the sub-models for nearshore wave, wave-induced current, sediment transport and beach morphological evolution. Nearshore wave is simulated based on the parabolic mild-slope equation considering wave refraction, diffraction and breaking effects. Wave-induced nearshore current is modeled using the nonlinear shallow water equations in which wave radiation stresses are provided by wave model for driving current. Then, the two-dimensional suspended sediment transport equation, bed-load equation and coast beach morphological evolution are coupled with the wave and current models for simulating sediment transport and morphological evolution in coastal waves and wave-induced currents. The numerical model is firstly tested by the experiment results for coastal waves, near-shore currents, sediment transport and beach morphological evolution around breakwater from the Large-scale Sediment Transport Facility at the US Army Corps of Engineer Research and Development Center (Gravens and Wang, 2007). Then the model is used to study the influences of breakwater layout on coastal waves, wave-induced currents, sediment transport and beach morphological evolution by set several breakwater layouts in the LSTF basin.

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

Wave-induced currents are an ubiquitous feature in coastal waters that can spread material over the surf zone and the inner shelf. These currents are typically under resolved in non-hydrostatic wave-flow models due to computational constraints. Specifically, the low vertical resolutions adequate to describe the wave dynamics – and required to feasibly compute at the scales of a field site – are too coarse to account for the relevant details of the three-dimensional (3D) flow field. To describe the relevant dynamics of both wave and currents, while retaining a model framework that can be applied at field scales, we propose a two grid approach to solve the governing equations. With this approach, the vertical accelerations and non-hydrostatic pressures are resolved on a relatively coarse vertical grid (which is sufficient to accurately resolve the wave dynamics), whereas the horizontal velocities and turbulent stresses are resolved on a much finer subgrid (of which the resolution is dictated by the vertical scale of the mean flows). This approach ensures that the discrete pressure Poisson equation – the solution of which dominates the computational effort – is evaluated on the coarse grid scale, thereby greatly improving efficiency, while providing a fine vertical resolution to resolve the vertical variation of the mean flow. This work presents the general methodology, and discusses the numerical implementation in the SWASH wave-flow model. Model predictions are compared with observations of three flume experiments to demonstrate that the subgrid approach captures both the nearshore evolution of the waves, and the wave-induced flows like the undertow profile and longshore current. The accuracy of the subgrid predictions is comparable to fully resolved 3D simulations – but at much reduced computational costs. The findings of this work thereby demonstrate that the subgrid approach has the potential to make 3D non-hydrostatic simulations feasible at the scale of a realistic coastal region.

EFFECT OF WAVE-CURRENT INTERACTION ON WAVES AND CIRCULATION OVER GEORGES BANK DURING STORM EVENTS

The coupled spectral wave and circulation model SWAN+ADCIRC was applied to investigate the wave-current interaction during storm events over Georges Bank, a large shallow submarine bank on the eastern seaboard of North America that separates Gulf of Maine from the North Atlantic Ocean. The current over the Georges Bank displays a rotary feature over a tidal cycle. The wave-induced current is in the same order as the wind-driven current and generally in the same direction as the depth-averaged tidal current, indicating strong nonlinear wave-current interaction. The magnitude of wave-induced current reaches 0.07 m/s at low tide and 0.2 m/s at the other three tidal phases. The effect of wave-current interaction on waves at the four tidal phases is also analyzed. The role of Georges Bank in dissipating wave energy is most significant at rising mid-tide and high tide, which is close to the storm peak. At rising mid-tide, the wave height is decreased by 0.3 m to 0.5 m over the majority of the bank when the wave propagates in the same direction as the current. At falling-mid tide, the wave height is increased by 0.5 m at the southern flank and decreased by 0.5 m at the northern flank of the bank.

Evolution of a beach nourishment project using dredged sand from navigation channel, Dunkirk, northern France

The largest beach replenishment project ever in France was completed in February 2014 in Dunkirk on the coast of northern France. A volume of 1.5 × 106 m3 of sand extracted from a navigation channel was placed on the beach to build up a 150 to 300 m wide supratidal platform in front of a dike, called « Digue des Allies », which protects several residential districts of Dunkirk from marine flooding. High resolution topographic surveys were carried out during 2½ years to monitor beach morphological changes, completed by a hydrodynamic field experiment conducted in February 2016. Approximately −138,200 m3 of sand, corresponding to 9.2% of the initial nourishment volume, were eroded over the nourishment area in about 2 years. An obvious decrease in erosion eastward with a shift from erosion to accumulation was observed, suggesting an eastward redistribution of sand. This longshore sand drift is beneficial for the eastward beach of Malo-les-Bains where most of the recreational activities are concentrated. Hydrodynamic measurements showed that waves and wave-induced currents play a major role on the longshore sand redistribution compared to tidal flows. Strong relationships were observed between cumulative offshore wave power and beach volume change during distinct beach survey periods (R2 = 0.79 to 0.87), with more significant correlations for northerly waves. A slight decrease in erosion during the second year compared to the first year after nourishment suggests that the loss of sand should decrease after an initial phase of rapid readjustment of the beach shape towards equilibrium.

Evolution of wave and tide over vegetation region in nearshore waters

Coastal wetlands are an important ecosystem in nearshore regions, where complex flow characteristics occur because of the interactions among tides, waves, and plants, especially in the discontinuous flow of the intertidal zone. In order to simulate the wave and wave-induced current in coastal waters, in this study, an explicit depth-averaged hydrodynamic (HD) model has been dynamically coupled with a wave spectral model (CMS-Wave) by sharing the tide and wave data. The hydrodynamic model is based on the finite volume method; the intercell flux is computed using the Harten–Lax–van Leer (HLL) approximate Riemann solver for computing the dry-to-wet interface; the drag force of vegetation is modeled as the sink terms in the momentum equations. An empirical wave energy dissipation term with plant effect has been derived from the wave action balance equation to account for the resistance induced by aquatic vegetation in the CMS-Wave model. The results of the coupling model have been verified using the measured data for the case with wave-tide-vegetation interactions. The results show that the wave height decreases significantly along the wave propagation direction in the presence of vegetation. In the rip channel system, the oblique waves drive a meandering longshore current; it moves from left to right past the cusps with oscillations. In the vegetated region, the wave height is greatly attenuated due to the presence of vegetation, and the radiation stresses are noticeably changed as compared to the region without vegetation. Further, vegetation can affect the spatial distribution of mean velocity in a rip channel system. In the co-exiting environment of tides, waves, and vegetation, the locations of wave breaking and wave-induced radiation stress also vary with the water level of flooding or ebb tide in wetland water, which can also affect the development and evolution of wave-induced current.