Wave overtopping can cause severe erosion on the crest and landward slope of a dike. Accurate erosion prediction requires resolving the spatiotemporal evolution of overtopping flow, which remains insufficiently understood. This study investigates the behavior of overtopping flow along the crest and landward slope using a new, efficient numerical model based on the Steep-Slope Shallow Water Equations. The model was validated against measurements from field experiments using a wave overtopping simulator. The model was applied to a typical dike geometry (Bc = 5 m; tan(α) = 1V:3H), where the overtopping flow is imposed at the waterside crest line based on a schematization using empirical equations from literature and insights from small-scale overtopping experiments. The spatiotemporal evolution of the flow was analyzed along the crest and landward slope for different overtopping volumes. The flow was observed to stretch in time along both the crest and slope while the wavefront steepens, causing the peak flow thickness (hpeak) to decrease significantly. The peak flow velocity (upeak) decreases along the crest but initially accelerates on the slope due to gravitational forcing. As the flow becomes progressively thinner and faster downslope, frictional forcing increases, reducing the acceleration. Eventually, gravitational and frictional forces balance, causing upeak to decelerate and then decrease. Overall, the model captures key spatiotemporal dynamics such as flow stretching, wavefront steepening, and deceleration of upeak on long slopes, which are absent in time-independent analytical models. It offers a computationally efficient approach that provides a practical middle ground between simplified analytical methods and full CFD simulations.

The dynamics of coastal dunes are often affected by a combination of environmental conditions and human interventions. During storms and calm periods, marine and aeolian flows cause sediment transport that results in sedimentation and erosion. Dunes typically grow due to aeolian transport of sediment and erode due to marine forcing by waves and currents. Shoreface nourishments can increase the sediment budget in the coastal profile which may influence the marine and aeolian sediment transport. To what extent shoreface nourishments influence sediment transport and the connected dynamics of coastal dunes is yet unknown. In this paper we investigate coastal dune volume change from yearly profile measurements and relate this to a shoreface nourishment program. The measured dune growth along the entire Dutch sandy coastline is characterized at most places by a break in slope where the dune growth increases after a specific ‘breakpoint’ year. The derived breakpoint years generally correspond with the start of the nourishment program with a delay of several years (1–5 years). These results provide a starting point for further elaborating on the relationship between the dynamics of coastal dunes and nourishments. The next step would be to delineate the potential influence of nourishments on either the growth of dunes through aeolian sediment transport or the erosion due to marine events.

Nature-based solutions are increasingly recognized as effective and multifunctional components of climate-resilient flood protection. While tropical mangroves have received substantial attention, temperate riparian forests, particularly willow systems, offer comparable wave attenuation and biodiversity benefits, yet remain understudied. This study assesses the ecological and protective value of three types of willow floodplain forests: a so-called wild-grown willow forest, a pollard willow forest, and a willow plantation. Using field data from the Biesbosch National Park (the Netherlands), we quantified forest structure, ground-dwelling invertebrate diversity, and modelled wave attenuation under storm scenarios. Structural complexity and biodiversity were highest in the wild-grown forest, with significantly greater invertebrate order richness, larger body sizes, and more heterogeneous canopy architecture. The pollard forest showed the highest wave attenuation efficiency due to their dense, low-lying crown structures. The plantation forest showed lower values across both axes. We integrated these findings into a trade-off model evaluating ecological value, flood protection efficiency, and a 50-year simple cost analysis of each forest type as a hybrid solution alongside traditional dikes. While the pollard forest is the most spatially efficient for flood attenuation, the wild-grown system provides greater ecological value at lower lifecycle cost. Our results underscore the importance of tailoring hybrid flood defense strategies to local priorities - balancing biodiversity, spatial constraints, and economic feasibility. The framework developed here can inform ecosystem-based design in delta regions worldwide, supporting integrated climate adaptation that aligns safety with ecological resilience.

Salt marshes provide critical coastal protection by attenuating waves, yet their performance under extreme storm conditions and subsequent recovery have lacked quantitative assessment. This study quantifies temporal variations in wave attenuation capacity across a complete storm cycle (before-during-after) at a Scirpus mariqueter marsh in the Yangtze Estuary, and evaluates cumulative impacts under storm sequences through numerical modeling. Our results show: (1) Storm landfall led to significant reduction in wave attenuation capacity of salt marshes, with wave damping coefficient (β) decreasing substantially in the post-storm period; (2) The weakened wave attenuation capacity of salt marshes was attributed to storm-induced vegetation damage in stem density, with recovery taking more than a few weeks; (3) Under the scenario of storm sequences, cumulative damage in stem density caused significant decline in wave attenuation capacity of salt marshes, with β gradually decreasing until the vegetation disappeared completely. This study reveals the vulnerability of salt marsh wave attenuation to storm disturbances, particularly under storm sequences, providing critical insights for coastal wetland management under increasing storm frequency.

Mangrove forests are vital for flood reduction, yet their failure mechanisms during storms are poorly known, hampering their integration into engineered coastal protection. In this paper, we aimed to unravel the relationship between the resistance of mangrove trees to overturning and root distribution and the properties of the soil, while avoiding damage to natural mangrove forests. We therefore (i) tested the stability of 3D-printed tree mimics that imitate typical shallow mangrove root systems, mimicking both damaged and intact root systems, in sediments representing the soil properties of contrasting mangrove sites, and subsequently (ii) tested if the existing stability models for terrestrial trees are applicable for mangrove tree species, which have unique shallow root systems to survive waterlogged soils. Root systems of different complexities were modeled after Avicennia alba, Avicennia germinans, and Rhizophora stylosa, and printed at a 1:100 scale using material densities matching those of natural tree roots, to ensure the geometric scaling of overturning moments. The mimic stability increased with the soil shear strength and root plate surface area. The optimal root configuration for mimic stability depended on the sediment properties: spreading root systems performed better in softer sediments, while concentrating root biomass near the trunk improved stability in stronger sediments. An adapted terrestrial tree resistance model reproduced our measurements well, suggesting that such models could be adapted to predict the stability of shallow-rooted mangroves living in waterlogged soils. Field tree-pulling experiments are needed to further confirm our conclusions with real-world data, examine complicating factors like root intertwining, and consider mangrove tree properties like aerial roots. Overall, this work establishes a foundation for incorporating mangrove storm damage into hybrid coastal protection systems.

During severe storms, waves can overtop dikes, leading to erosion of the crest and landward slope, which may ultimately result in breaching. To accurately model this erosion, the overtopping flow needs to be described in a time-dependent manner for each individual wave overtopping event. The peak flow velocity (upeak) and peak flow thickness (hpeak) are critical boundary conditions in this context. Previous studies have shown that these flow characteristics are related to the overtopping volume, yet often propose deterministic models that overlook the variability and interdependency between these characteristics.

The goal of this study is to address these gaps by explicitly quantifying the variation and interdependence of upeak and hpeak, using data from small-scale FlowDike experiments. We propose generalized distributions to describe the variation in these flow characteristics, with upeak varying by 13% to 23%, depending on the waterside slope angle, and hpeak varying by approximately 20%. Furthermore, the interdependency between upeak and hpeak is modeled using a Student-t copula (ν=9.361, ρ=−0.497), revealing a moderate negative correlation. This suggests that overtopping events with a high upeak are less likely to have a large hpeak, and vice versa.

The findings of this study can be directly applied to improve models that describe the loading caused by overtopping waves and the resulting erosion. By incorporating the variation and interdependence of upeak and hpeak, these models can provide a more detailed representation of the peak flow characteristics of overtopping waves. Furthermore, these insights can be applied to the design of wave overtopping simulators, enabling the simulation of more realistic overtopping flows by incorporating more of their natural variation.

This research investigates how salt marshes contribute to both wave energy dissipation and spectral period transformation, advancing their role as a nature-based solution for coastal protection. Using laboratory simulations with a scaled barren foreshore, salt marsh and dike model, we examine the interactions between vegetation, water depth, and wave properties under varied conditions, including storm scenarios with irregular waves. Results indicate a case specific threshold at which the salt marsh model attenuates energy optimally, as for very shallow water depths wave energy is predominantly dissipated by the barren foreshore. The spectral wave period T m − 1 , 0 increases when waves propagate from deep to shallow water depths, as a result of wave breaking and generation of infragravity waves. The presence of salt marsh vegetation further enhances this effect by preferentially damping high frequency components. This highlights that an increase in T m − 1 , 0 in vegetated environments may not always correspond to an increased hydrodynamic load on the dike.

Mangroves have been used for coastal protection in Bangladesh since the 1960s, but their integration with embankment designs has not been fully explored. This paper investigates the effect of existing mangroves on required embankment performance, with a focus on the wave-damping effect of mangroves. Existing mangroves reduce the required thickness of embankment revetment by up to 16–30% in the west, 47–82% in the central region, and 53–77% in the east. Notable mangrove sites include the belt south of polder 45 (Amtali), with an average width of 1.77 km, and the Kukri-Mukri polder, with an average width of 1.82 km. These mangroves reduce the need for thick slope protection, allowing the replacement of concrete revetments with softer materials, such as clay or grass, combined with mangrove foreshore. Additional large mangrove belts are found in Sandwip and Mirersarai. By replacing or reducing revetment requirements, mangrove forests can minimize carbon emissions from construction while providing carbon sequestration and other ecosystem services. This study can inform future sustainable investments in coastal protection systems by identifying areas where mangroves offer the greatest wave-damping benefits, which could be focus of follow-up feasibility studies.

Saltmarshes are a promising nature-based alternative for conventional flood protection. However, saltmarshes can erode under storm conditions, whereby the seaward edge of the saltmarsh often forms a vertical cliff. Despite its importance, the effect of storm conditions on erosion at the saltmarsh cliff remains understudied, especially when waves traverse over a cliff. This research investigates the complex flow patterns around a saltmarsh cliff non-intrusively using Particle Image Velocimetry (PIV) conducted through a series of scaled monochromatic wave flume experiments. We adopted realistic foreshore configurations (e.g. cliff heights) and hydraulic loading conditions from the Dutch Wadden Sea. Results show two local near-bed velocity maxima on top of the saltmarsh, created during different wave phases by water depth contraction, wave transmission and interaction between flow and vortices that are shed from the cliff. Under the wave crest, high onshore-directed near-bed velocities were measured at approximately 2.5–4 times the cliff height onshore from the cliff. Under the wave trough, high offshore-directed velocities were found at the marsh edge. Both onshore- and offshore-directed velocities increase with increasing cliff height, larger wave height or lower water depth. Vegetation on top of the marsh reduces both the incoming and outgoing velocities in front of the cliff. Increasing the cliff height resulted in a greater reduction in velocities by the vegetation. These results demonstrate how local near-bed velocity maxima and location are influenced by the presence of a cliff and the interaction with vegetation on top of the saltmarsh. This research highlights the vulnerability of the cliff even during inundation of the cliff and will help to implement saltmarshes as nature-based solutions for flood defence.

During extreme high-water events in river systems, the load on a levee section may exceed its resistance, initiating the breaching process which eventually leads to levee failure. The success of an emergency measure to intervene in the initial phases of levee failure is mainly dependent on its timely application. Quick action is required to prepare and deploy an emergency measure before damages to the levee section have become irreparable. In this study, we investigate the key parameters for successful application of an emergency measure, focusing on the BresDefender case study. The BresDefender is a floating pontoon used by the Dutch military, which is intended to avoid or postpone levee failure. A model has been developed taking the operational steps in the implementation of the emergency measure during a high water and the (uncertainty) in the duration of these processes into account. The model is used to quantify the probability of successful operation to prevent levee failure due to overflow or slope instability. The probability of successful application of the BresDefender has been simulated for river flood situations in the Netherlands. For the river Rhine, where the examined cases were prone to slope instabilities, the probability of arriving in time was found to be 70%. But for the Meuse case, where the examined cases were prone to overflow, the probability of arriving in time was found to be only 0%. The critical steps in the process after the occurrence of damage to the levee are damage detection, the decision to repair the damage, the transport of the emergency measure, and the placement of the measure. By incorporating emergency measures in emergency preparedness procedures, the time required for the critical steps will be decreased and the probability of successful application of the emergency measure, i.e., its contribution to flood risk reduction, will be enhanced.

Rock groins in the Elbe Estuary are constructed to maintain proper water levels for navigation and for embankment erosion protection. At certain localities, significant damages to rock groins have been observed due to the primary ship-generated waves. Primary waves are generated along the ship's hull and then propagate toward the river banks and groin fields, appearing in the interaction with the structures as a turbulent overflow phenomenon. Eventually, this overflowing may cause damages mainly to the crest and leeward side of the groins. Since this overflowing is the most pronounced with large primary waves at certain water levels, the estimation of the probabilities of extreme primary waves is a key element for a safe and reliable design of groins. For this goal, nonparametric Bayesian networks (NPBNs) are used here to infer the probability distribution function of the extreme primary wave heights at the tip of a groin in the Elbe Estuary. Results demonstrate the suitability of the NPBN in their prediction. The model framework allows the designer to predict the probabilities of primary ship-generated waves at groins when the information of ship dimensions, nautical parameters, and waterway geometry is available. These probabilities can later be used for design purposes for current and future conditions.

Marine pollution is a major global environmental problem. The transport and dispersion of marine pollution is driven by a wide range of hydrodynamic processes, including wave-induced currents (e.g., Stokes drift) that are generated by free-surface and internal gravity waves in density-stratified fluids. While the (Lagrangian-mean) Stokes drift is known to fundamentally change transport patterns, wave-induced Eulerian-mean currents, such as those generated in the presence of the Coriolis force due to the Earth's rotation, are generally less well understood. To address this, the Delta Transport Processes Laboratory (DTP-Lab), a multi-purpose lab with novel facilities and state-of-the-art equipment, is being constructed in the Hydraulic Engineering Laboratory at TU Delft. The DTP-Lab combines multiple components: a 4.40-m diameter turntable, which can support a (removable) 5-m long flume; a 12.7-m long stainless steel flume; a piston-type, wet-back, force-controlled surface wave generator; a pumping system to create any type of density stratification; and a 3D Particle Tracking Velocimetry (PTV) system. The design and construction of these components along with technical validation and performance tests are presented in this technical note. A scaling analysis demonstrates the suitability of the laboratory to investigate wave-induced current under rotation. The DTP-Lab will pioneer the combined experimental study of surface waves, density stratification and Coriolis forces. The DTP-Lab is presented here with the objective of giving practical information to future users and to describe its novelty and range of applications.

The passage of ships in confined waterways creates a stern wave that can overflow bank protection structures such as groins. This overflow, due to the long-period primary ship-induced waves, can be high in velocity, especially at the lee-side slope of groins, potentially causing significant damage to the structure. This study derives an equation to express overflow velocities, intended as a design tool for groins exposed to these types of waves. A detailed experimental investigation was performed on four physical models of groins with different slopes and stone sizes in the armor layer under the influence of different hydraulic heads. Particle image velocimetry (PIV) was used to measure the flow velocities at the crest and lee sides of the structure. All PIV measurements were performed thrice under free-flow conditions with no initial water level at the lee side of the structure. The depth- and time-averaged flow velocities (Uavg) were extracted from four positions along the lee-side slope and accelerated from 0.7 to 2.2 m/s. A dimensionless equation of the overflow velocities was obtained as a function of the hydraulic head (h), slope (θ), freeboard (Rc), and nominal rock diameter (dn50).

Initial damage, caused by previous wave loading or other events, might affect the hydraulic stability of pattern-placed revetments. Three common types of damage are considered in this study. The effect of this assumed initial damage on the hydraulic stability and failure probability of revetments is quantified using a FEM model. This model is developed using data from large-scale flume and field experiments. Using results from the FEM model, surrogate models are created to predict the effect of each type of initial damage on the hydraulic stability and failure probability. Through the use of these surrogate models, it is demonstrated that S-shaped deformation caused by filter migration around the wave impact zone has the largest effect on the hydraulic stability decreasing up to 30%, and failure probability per year increasing up to 10,000 times. When the granular filling between the joints of the columns is washed-out, the stability decreases up to 29% and the failure probability increases up to 700 times. A missing column has a limited effect on the hydraulic stability and failure probability when there is no other (structural) damage. However, if it originates from underlying damage, it might be an initial sign of total failure of the revetment. This study demonstrates the effectiveness of finite element modeling for studying (damaged) revetments, which can be used to complement flume experiments. The results can be used to prioritize maintenance efforts in risk-based maintenance of pattern-placed revetments.

Vegetation in front of levees, dikes and seawalls can decrease wave energy and therefore contribute to the safety against flooding. However, wave damping predictions by vegetation are still inaccurate due to measurement and modelling uncertainties. Many studies focused on finding reliable predictive tools using scaled flume tests with vegetation mimics. Scaling down vegetation can however lead to discrepancies with realistic scales, known as scale errors. In this work scaled tests were conducted on 3D-printed elastic replicas of willow trees and compared with real-scale experiments. We identified differences in measured wave dissipation between the scaled hydraulic model (1:10) and its real-scale prototype with 5m high live willow trees under storm conditions (1:1). The maximum measured wave damping (30%) was roughly 1.5 times higher than the real-scale experiments (20%). Following the same trend of the real-scale experiments, this amount of wave height damping declined for larger water levels. Largest effects are argued to be due to increased viscous damping (smaller branch Reynolds numbers) and non-exact flexibility scaling. These significant deviations illustrate that full-scale experiments, although expensive, are still needed to validate the results of scaled experiments for woody vegetation. Alternatively, accounting for these discrepancies can make scaled experiments more reliable and expensive real-scale experiments less needed for wave damping studies on woody vegetation.

Nature-based flood defences receive increasing interest as a viable option for improving flood safety worldwide. A contemporary case is using the ability of saltmarshes to attenuate waves during storm conditions for strengthening coastal flood defences. To ensure a long-term reinforcement of flood protection, it is important to understand the erosion mechanisms of saltmarshes during storms. One of the critical locations for erosion is at the transition between the saltmarsh and the bare mudflat, often characterized by a vertical step or cliff. These cliffs vary between 0.2 to 2.0 m in height, depending on soil characteristics and local hydrodynamics. However, wave-induced hydrodynamics that controls the (mass) erosion at the saltmarsh cliff are not fully understood. Also the role of saltmarsh vegetation on these near-cliff hydrodynamics are not clearly quantified. In this research, we present high-resolution measurements of wave-induced hydrodynamics at a saltmarsh cliff performed in a scaled wave flume experiment.

During berthing operations of large vessels, the bow thruster jet deflecting on the quay wall and the bed can lead to high flow velocities near the bed. This may scour the bed when it is left unprotected, causing instability of the adjacent quay wall. Due to the complex flow field of the reflected jet, the decay in near-bed flow velocities perpendicular to the quay wall is unknown. This results in uncertainties in the design of bed protections, especially in the required width.

In this research, the decay of the near-bed flow velocity perpendicular and parallel to the quay wall induced by a 4-channel bow thruster is studied. Field measurements have been conducted in the North Sea Port of Gent with one of the largest Dutch inland vessels. The near-bed flow velocities have been measured at multiple distances from the quay wall.

For the flow velocity measurements four main parameters have been varied: the applied bow thruster power, quay wall clearance, number of thrusters, and the lateral distance between jet axis and measurement sensors.

The highest flow velocities were measured near the quay wall, rapidly declining while moving away from the quay. Comparison of the measurement results to the Dutch and German guidelines generally leads to the conclusion that these guidelines are conservative. In addition, the dependency of the velocity on the total travelled distance by the jet as given in the Dutch method is not reflected in the measurement results. Furthermore, fundamentally different outcomes on the influence of the quay wall clearance on the near-bed flow velocity have been found.

When the measured near-bed flow velocities are used as the sole input to calculate the required bed protection, significantly smaller rock sizes and asphalt mattress thickness would be necessary to withstand the hydraulic load of the jet in comparison to current guidelines. Further studies with different vessels and direct measurement of the efflux velocity of the thrusters are recommended.

Physical model tests have been performed to study static stability of rock-armoured mild slopes. Current stability design formulae for steeper rock-armoured slopes focus on plunging and surging waves. Slopes of 1:6 and milder usually have more spilling breakers which decreases the load. Also, on mild slopes displaced rocks more often remain present in the wave attack zone, which increases the strength. These aspects lead to an overdesigned structure when existing formulae for steep rock-armoured slopes are used. The present wave flume tests were used to understand the processes and develop a design formula for rock-armoured mild slopes with an impermeable core. These tests were performed for statically stable rock-armoured slopes of 1:6 to 1:10. The tests confirmed that not all existing damage parameters are able to accurately describe the static stability on milder slopes. For mild slopes it is more accurate to describe the damage based on the eroded depth rather than on the eroded area or number of moved stones. In this study, a design formula and guidelines are provided for practicing engineers that design or evaluate the stability of mild rock-armoured slopes.

During extreme high-water events, the phreatic water level in levees will rise over time due to infiltration of water. This can promote slope instability or internal erosion, and eventually lead to structural failure. A potential solution is the application of an impermeable seal, such as a geotextile, to the levee’s outer slope to locally reduce the inflow of water. In this study, the spatiotemporal effect of a seal on the phreatic surface level is investigated experimentally, both at laboratory scale for a homogeneous sand levee, and at full-scale for a more realistic levee design. On the two-dimensional laboratory scale, it was found that application of a seal does not significantly change the steady-state phreatic level, as expected from a theoretical perspective. However, the time for the phreatic surface level to reach steady state after a sudden external water rise was found to increase 25% to 50% in the cases with a seal. Similar results were found for the full-scale three-dimensional experiments, which showed that details of the soil-structure interface significantly influenced the effectiveness of the impermeable seal, increasing the time to steady state between 12% and 25%. A simple numerical transient groundwater flow model confirms that the quality of the seal governs the response of the phreatic level. This model required the inclusion of an interface layer to properly model the imperfect soil-seal conditions. It is concluded that application of an impermeable seal to a levee before sudden water rise does not influence the new steady-state phreatic level. However, the seal slows down the infiltration process, especially for a case where the outer slope is damaged.

The presence of marine pollutants such as marine plastics has increased significantly over the last decades and poses a major environmental problem, in both the coastal and offshore area. Marine pollutants are transported, mixed and diffused in the ocean, which means the understanding and modelling of marine transport is key for mitigation purposes (Moulton et al., 2022). Additional to large scale and planetary currents that play a major role in marine transport, free surface waves, internal gravity waves in density stratified fluids and the Coriolis force due to the rotation of the Earth are also fundamental drivers of transport that need to be accounted for. The fundamental fluid mechanics processes associated with these are often not resolved in large-scale models, but are instead included in a parametrised form. However, some fundamental processes associated with wave-induced currents (e.g., Stokes drift) in rotating, density-stratified fluids with a free surface remain unclear and untested. In addition, parametrisation for different environments, forcings and time scales must be developed and tested before being implemented into models for them to reliably predict transport, accumulation and storage of marine pollutants. For this purpose, the Delta Transport Processes Laboratory (DTPLab) is being developed at TUDelft Hydraulic Engineering Laboratory. This laboratory pioneers the combined experimental study of surface waves, density stratification and Coriolis forces in a single laboratory. The DTPLab was designed with a multi- users and purposes vision, with interchangeable facilities and state-of-the-art measurement devices. This paper presents the DTPLab facilities (under construction) and equipment that make this laboratory unique in the world, and describes, as an example of what is feasible, a novel experiment that will be performed in this lab.</jats:p>