In coastal areas, variable bottom effects significantly enhance wave nonlinearity and complicate wave propagation. It is of practical interest to characterize the nonlinear effect on the statistics of free surface displacements and particle kinematics. In this work, we take advantage of a fully nonlinear potential flow model to investigate the statistics of unidirectional irregular waves propagating over an uneven bottom. By confronting the simulated results with existing experimental results (free surface elevation and horizontal velocity beneath the mean sea level) in the temporal, spectral, and statistical domains, we show the high fidelity of the model in predicting the nonlinear irregular wave kinematics. As the relative importance of low-frequency harmonics becomes lower for acceleration, the model performance in predicting the measured horizontal acceleration is even better than that for the measured horizontal velocity. The empirical statistical distributions of velocity and acceleration in both horizontal and vertical directions are compared with both the normal (Gaussian) and the log-normal (LN) distributions. The latter requires skewness as an input in addition to the mean and standard deviation of the signal. We notice that, unlike the free surface displacement generally of positive skewness, the signal of velocities and accelerations are sometimes characterized by negative skewness. In such cases, the negative LN distribution should be adopted. Although the LN distribution has rarely been used for short-term statistics of wave elevation and kinematics, the detailed comparisons presented here demonstrate very good performance for all kinematic variables. In particular, in the area following a rapid reduction of water depth, where the sea-state is out-of-equilibrium, the heavy tails in the distributions are well reproduced by the LN model, indicating some generality and merits of this model.
The role of infragravity waves (IG waves) in beach and dune erosion or in flood hazard has been extensively studied on open beaches. In contrast, the detailed characterization of IG waves and their contribution to the Total Water Level (TWL) along the shore of inlets received little attention so far. In such environment, there is a real lack of in situ observations of waves and hydrodynamics conditions at appropriate spatial and temporal coverage to study the role of infragravity (IG) waves (long waves of frequency typically ranging between 0.004 Hz and 0.04–0.05 Hz) on coastal hazards. This contribution is based on field observations collected at the Arcachon Lagoon, a shallow semi-enclosed lagoon connected to the ocean by a large tidal inlet, located in southwest France. Analyses combine observations made at several locations during storm events within the inlet and the lagoon with numerical simulation with the XBeach surfbeat model to explore the spatial variability of IG waves and simulate observed, historical, and idealized storm conditions. The results show that IG waves are substantial during typical winter storms at the inlet and range from Hm0 = 0.8 to over 1 m across the ebb delta and about 0.4–0.6 m in the inner part of the inlet. At the lagoon entrance, IG waves remain substantial (about 0.1–0.2 m) and decrease to a few centimeters at the lagoon shore. The spatial variability and magnitude of IG waves along the inlet coast, simulated for the historical storms, are quite comparable to those observed during classical winter, and do not increase linearly with offshore wave energy. However, both observations and simulations reveal local amplifications of IG waves in the inner part of the inlet, especially along the sheltered coast were IG waves dominate the variance of free surface elevation, reaching about 0.6–0.7 m during common storms and more than 1 m for an extreme storm scenario. A numerical experiment indicates that IG wave reflection from one coast to the other contributes up to 35–40% of the measured IG wave height at a hot spot located along the sheltered coast. Finally, the contribution of IG waves to TWL at the shore on both sides of the inlet has been estimated to be about 0.4–0.6 m for a common storm and 0.6–0.9 m for an extreme scenario, locally peaking at 0.74 and 1.1 m respectively and overpassing the contribution of wave-induced setup. This work provides new insights into the contribution of IG waves to TWL and its implications for overtopping flooding hazard and overwash processes at large inlets, highlighting the need to consider IG waves in Early Warning Systems or hazard mapping for flood prevention plans in these environments.
Earthquake induced tsunamis pose devastating threat to coastal communities worldwide. Accurate description of tsunami generation by kinematic fault rupture is of importance to investigate earthquake events and evaluate tsunami impacts. The paper develops a multi-layer non-hydrostatic model with a kinematic bottom boundary condition and conducts comprehensive validation to examine the model’s capability in resolving seismic tsunami generation. The two-dimensional governing equations of the multi-layer non-hydrostatic free-surface flow system equipped with kinematic seafloor displacement is first introduced in Cartesian coordinates. A combined finite difference and finite volume scheme is utilized to discretize the governing equations with flow variables arranged on a staggered Arakawa C-grid. Application of pressure correction technique to the discretized formulations yields Poisson-type equations from which the non-hydrostatic pressure is solved for the next time step to complete the temporal integration. Based on existing analytical solutions, four groups of tsunami generation cases considering broad ranges of source parameters, including horizontal scale, rise time, and rupture velocity, are designed to demonstrate performance of the proposed non-hydrostatic model with one-, two-, and three-layers as well as the hydrostatic one. Comparison of 59 generation cases including extreme scenarios indicates the non-hydrostatic model performs better than the hydrostatic model in reproducing the entire waveform and predicting the maximum wave amplitude. High modeling accuracy can be achieved through incorporation of more layers. The proposed multi-layer non-hydrostatic model is a powerful tool for investigating earthquake source mechanisms and evaluating coastal tsunami hazards.
Understanding the seasonal variations of vegetation drag coefficients is crucial for improving wave attenuation predictions and adapting to climate impacts. This study explores the seasonal changes in drag coefficients within salt marsh vegetation, using data from a year-long series of field measurements at the Chongming Dongtan Wetland. It uncovers the complex seasonal variations of drag coefficients. Results demonstrate that incorporating a nonlinear equation for characteristic flow velocity and effective vegetation length significantly improves the precision of drag coefficient predictions, ensuring a closer match with field observations. Furthermore, it introduces a refined drag coefficient formula that incorporates adjustments for vegetation stiffness and relative submergence, offering a more accurate representation of the seasonal variability in drag forces exerted by salt marsh vegetation. This enhanced formula is crucial for accurately assessing vegetation's role in wave attenuation, providing critical insights for the design and implementation of coastal defense and wetland conservation initiatives.
The recession of a berm breakwater is a key parameter in ensuring its stability, and functionality, to protect coastal areas against wave impacts. Consequently, consideration of the expected recession in structural design is required to ensure the required objectives of the structure. In this study, physical model laboratory experiments were conducted to measure the recession of two-class armour berm breakwaters in response to varying sea state conditions (wave height, wave period, storm duration, and water depth at the structure's toe) and geometrical parameters (berm elevation from still water level, berm width, and rock size). A total of 110 tests were conducted under irregular wave forcing and the results were compared with those of existing formulae, derived specifically for mass armour and Icelandic-type berm breakwaters. Of the existing formulae, the Sigurdarson and Van der Meer (2013) formula that is derived for both mass armour and Icelandic-type berm breakwater outperforms the other formulas. Subsequently, a new empirical formula was developed to estimate the erosion depth based on the dimensionless water depth. The findings from this study could be instrumental for the structural design of two-class armour berm breakwaters under different sea states and geometrical configurations.
Storm surges pose a significant threat to coastal communities, necessitating rapid and precise storm surge prediction methods for long-time risk assessment and emergency management. High-fidelity numerical models such as ADCIRC provide accurate storm surge simulations but are computationally expensive. Surrogate models have emerged as an alternative option to alleviate the computational burden by learning from available numerical datasets. However, existing surrogate models face challenges in capturing the highly non-stationary and non-linear patterns of storm surges, resulting in over-smoothed response surfaces. Moreover, the dry–wet status of nearshore nodes has not been informatively considered in the training process.
This study proposes Surge-NF, a novel point-based surrogate model inspired by Neural Fields (NF) from computer graphics. Surge-NF introduces two key innovations. A positional encoding module is proposed to mitigate over-smoothing of high-frequency peak storm surge spatial dependencies. A multi-task learning framework is proposed to simultaneously learn and predict the dry–wet status and peak surge values, leveraging task dependencies to improve prediction accuracy and data efficiency. We evaluate Surge-NF on the NACCS database with comparison to state-of-the-art alternative surrogate models. Surge-NF consistently reduces RMSE/MAE by 50% and achieves 4–5 times computational cost gain over baselines, requiring only 50 training storms to produce accurate predictions. The complementary benefits of the positional encoding and multi-task learning modules are evident from the improved prediction capability with their combined use.
Overall, Surge-NF represents a significant advancement in storm surge surrogate modeling, offering its novel and unique ability to capture high-frequency spatial variations and leverage task dependencies. It has the potential to greatly enhance storm surge risk assessment and emergency response management, enabling effective decision-making and mitigation strategies to safeguard coastal communities from the devastating impacts of storm surges.
Oyster shell-filled bags have been used in engineered reefs and living shorelines as a nature-based solution to attenuate wave energy and stabilize shorelines. However, due to limited scientific data, uncertainties persist in accurately predicting the performance of these reefs, which can hinder a more widespread adoption. In particular, there is a lack of information on wave transmission through, and the stability of, oyster shell-filled bag berms with different configurations and relative freeboards. To address this knowledge gap, a full (1:1) scale experimental flume study was conducted to measure the wave transmission and stability of six different oyster shell-filled bag berms under a range of incident wave conditions and water levels. The findings from the experimental tests were used to propose empirical equations for wave transmission and stability, which can assist practitioners in predicting the performance of these engineered reefs.
Beaches are a natural defense against extreme events, such as storms and hurricanes, whose intensity and frequency are expected to increase in the future due to climate change. In this context, models that forecast the morphological evolution of coastal areas can be used to anticipate the effects of future scenarios, allowing early action to mitigate the damage caused by extreme events. Hence, this study included data from three different monitoring programs in data models to simulate the seasonal morphological evolution of several Portuguese beaches. Two different data models were implemented using the Random Forest algorithm. One was fed with profile data and wave conditions while the other considered also sediment size data. Both models achieved suitable performances, but the inclusion of sediment data reduced the model errors and variance, and thus improved model performance. It was demonstrated that combining data from multidisciplinary campaigns can be a solution to generate reliable and robust morphological forecasting models.
Nature-based coastal protection that integrates vegetated wetlands for wave attenuation and erosion mitigation shows great potential. However, there is a lack of consensus on whether longer wave periods contribute to an increase or a reduction in the attenuation of waves in vegetated wetlands, which is primarily due to the disregard of vegetation submersion states. In the current study, we modified a classic model to pinpoint the conditional role of the period. Wave attenuation by vegetation is quantified as the product of two terms: wave decay rate and time of wave group travel through a unit length. By tracing the dynamics of these two terms, the model is in good agreement with the measurements and can well explain why wave attenuation increased with longer period (from 2 to 10 s) in submerged canopies (up to 10 times) but decreased in emergent canopies (by 75%). A maximum response period (2 - 10 s) was found, beyond which period has no effect on wave attenuation. Furthermore, we found that in field conditions, the variation in wave period can lead to a sharp reduction in wave dissipation. which is critical for coastal safety. For instance, a 62% decrease in wave period at Galveston Island corresponded to a 40% drop in wave dissipation. This work provides a comprehensive understanding on the role of wave period in wave dissipation by wetland vegetation, which would assist in safely implementing wetlands for coastal defence.