Wave Run-up Research Articles

Numerical study of higher-harmonic wave loads and runup on monopiles with and without ice-breaking cones based on a phase-inversion method

Ice-breaking cones are commonly used in the design of marine structures in cold regions. This study investigates the effects of higher-harmonic wave loads and wave runup on a 5-MW offshore wind turbine with and without ice-breaking cones under extreme wave conditions on the Liaodong Peninsula in China. Two ice-breaking cones (upward-downward and inverted types) are considered. The numerical model adopts a two-phase flow by solving unsteady Reynolds-averaged Navier-Stokes (URANS) equations using the volume of fluid (VOF) method. A phase decomposition method through a ‘Stokes-like’ formulation was adopted to obtain the parameters for each harmonics. The presence of the conical part is seen to increase the second-harmonic wave loads by up to 40%, but it has only limited influence on the fourth and fifth harmonics. The upward-downward-type ice-breaking cone increases the third harmonic, while the inverted-type ice-breaking cone decreases the third harmonic. Due to the phase difference between the first-harmonic and higher harmonics, the largest wave runup occurs at 0°, and 135° is the location with the smallest wave runup. This is because at the 135-degree location, the linear component is positive but the other nonlinear components are negative. For the 0-degree location, all harmonics are positive. By contrast, the inverted type has little effect. The high harmonic wave runup of the minimum point is backwards compared with that of the monopile, and most nonlinear wave runups are different upstream of the monopile.

Efficiency and Wave Run-Up of Porous Breakwater with Sloping Deck

In order to protect fragile shoreline and coastal assets during extreme storms, a combined floating breakwater-windbreak has been proposed to reduce both wind and wave energies in the sheltered area. The 1 km-long breakwater has a porous hull with internal tubes to allow free passage of water; thereby further dissipating wave energy. The deck of the structure is designed to have a slope of 25 degrees facing the upstream side, and arrays of cylindrical tubes are placed on the sloping deck to form a windbreak. A reduced-scale (1:50) model test was carried out in a wave flume to examine wave sheltering performance under significant wave heights Hs = 3.0 m to 7.5 m and peak wave periods Tp = 9.4 s to 14 s sea states. Both regular and random wave conditions with different wave heights were considered. It is found that transmission coefficients ranging from 0.4 to 0.6 can be achieved under tested wave conditions. Porous breakwater hull increases the wave dissipation coefficients and is effective in reducing the wave reflection at the upstream side. The wave run-up length is dependent on the Iribarren number if the reduction induced by vertical freeboard is considered. Based on experimental data, empirical formulae have been proposed to predict the wave run-up responses in regular waves, probability of non-zero wave run-up occurrence, modified Weibull distribution of the wave run-up peaks and extreme wave run-up in random waves.

Numerical Analysis of Wind Effect on Wave Overtopping on a Vertical Seawall

Onshore wind significantly affects wave run-up and overtopping, thereby representing a major variable to account for in the design process. The aim of this study is to analyze the ability of numerical models to properly reproduce the wind effect on the overtopping at vertical seawall and to use them to understand how the wind influences the overtopping process as well. We use the RANS model, FLOW-3D, and the NLSW model, SWASH; both model the action of wind through the shear stress that it exerts on the sea surface. Although a simplified modelling of wind has been adopted, the CFD model has led to physically consistent results. On the other hand, SWASH seems to be unsuitable for reproducing the enhancement of the overtopping rate due to wind. CFD numerical results show that the wind affects only the lower overtopping regime (i.e., q < 1 l/s/m); as the mean overtopping discharge decreases, the influence of wind increases. Specifically, wind plays a key role in pure “white overtopping”, where the advection of spray is the predominant mechanism of the overtopping process. The effects of wind thus seem to be important in the design of seawalls, but are difficult to quantify through hydraulic models because of the unknown scaling laws. Therefore, we have found that a full-scale numerical approach is suitable to study the influence of wind on wave overtopping and to evaluate the wind factor to take into account in the design process.

Risk Assessment of Wave Over-Topping Based on Smoothed-Particle Hydrodynamics Method

FETSWCM-SWAN and DualSPHysics models are used to study the storm flooding process of Dazuo Seawall in Quanzhou city, Fujian province, China. Firstly, a storm over-topping assessment method is proposed. Secondly, the water level and storm wave at the foot of Dazuo Seawall calculated by FETSWCM-SWAN during the process of Typhoon Usagi in 2013 and Typhoon Dujuan in 2015. Finally, the typical wave and storm run-up processes at Dazuo Seawall are modeled by DualSPHysics. The results show that the typical wave run-up of Dazuo Seawall is less than 2 m, but the storm wave run-up can reach 6.85 m under Usagi. The risk is high when high tide is encountered. The risk of storm flooding is classified into three grades. This risk assessment could provide decision-making support to government departments in warning against storm flooding threats.

Wave induced coastal flooding along the southwest coast of India during tropical cyclone Tauktae

The coastal flood during the tropical cyclone Tauktae, 2021, at Chellanam coast, Kerala, India, has invited wide attention as the wave overtopping severely affected coastal properties and livelihood. We used a combination of WAVEWATCHIII and XBeach to study the coastal inundation during high waves. The effect of low-frequency waves and the rise in the coastal water level due to wave setup caused the inundation at Chellanam, even during low tide with negligible surge height. Wave setup raised the water level at the coast with steep slopes to more than 0.6 m and peaked during low tide, facilitating wave breaking at the nearshore region. The coastal regions adjacent to these steep slopes were subjected to severe inundation. The combined effect of long and short waves over wave setup formed extreme wave runups that flooded inland areas. At gently sloping beaches, the longwave component dominated and overtopped the seawalls and damaged households along the shoreline. The study emphasizes the importance of longwave and wave setup and its interaction with nearshore bathymetry during the high wave. The present study shall lead to the development of a coastal inundation prediction system for the low-lying hot spots using the combination of WAVEWATCHIII and XBeach models.

Field observations and numerical modeling of swash motions at an engineered embayed beach under moderate to energetic conditions

Wave run-up is a key factor for the assessment of coastal flood risk during large swell events. The behavior of swash motions along embayed beaches is strongly influenced by particular features such as rocky headlands, irregular morphology, or tides, that have not received much attention in the past. In the present paper, swash motions along an engineered embayed beach were investigated under moderate to energetic wave conditions through field observations and numerical computations. Using pressure sensors and video-derived run-up data a Boussinesq-type nearshore wave model was found to capture the relevant wave transformation and swash zone processes reasonably well. The tidal water level variations were found to have a significant impact on the overall swash amplitudes and to condition the respective role of short- and long-wave components to the swash motions. In the studied configuration, the tidal level rise was shown to cause a transition from a very dissipative to a reflective or intermediate beach configuration depending on incident wave energy. Moreover, swash amplitudes were observed to vary significantly alongshore with differences of up to a factor of 2.2. Numerical results suggest that both the foreshore slope and the sub-tidal morphology play a key-role in the alongshore swash distribution.

On the selection of turbulent model for the nearshore hydrodynamics modeling of coral reefs: Insight from an inter-comparison study

Natural coral reefs generally have rough and undulating topography. Due to the steep and variable topography from the deep to shallow water near the starting point of reef flats, the wave motion is quite complex and there are severe wave rolling and breaking on reef flats. To credibly simulate the wave evolution on reef flats, and the hydrodynamic performance of revetment breakwaters built on coral reefs, a suitable turbulence model is needed in the numerical simulation. In this study, a series of hydrodynamic numerical simulations with various RANS turbulence models are conducted adopting OlaFlow solver as the computational platform. The numerical results from three turbulence models, i.e. the standard k-ε, the buoyancy-modified k-ω SST, and the stabilized k-ω SST, are analyzed and evaluated utilizing different grid systems, where the grid number is 1.40, 2.37 and 3.52 million, respectively. By comparing the numerical results from the three different turbulence models, it is found that the stabilized k-ω SST turbulence model could give consistent and good results for the complex evolution process of waves on reef flats, and give acceptable results for the wave impact on structures. In contrast, the numerical results from the standard k-ε and the buoyancy-modified k-ω SST models present significant grid dependencies, indicating that the credibility of these results is doubtful. On the aspect of capturing the wave breaking and run-up, the results from the buoyancy-modified k-ω SST and the stabilized k-ω SST models are remarkably better than that from the standard k-ε model. As for the overtopping volume over breakwater, all three turbulence models present serious grid dependence and fail to obtain consistent numerical results. Finally, it is recognized that the stabilized k-ω SST model is a suitable turbulence model for the nearshore hydrodynamics modeling of coral reefs.

Numerical Study of Influences of Onshore Wind on Hydrodynamic Processes of Solitary Wave over Fringing Reef

Many post-disaster surveys have reported on the natural function and effectiveness of fringing reef in preventing the shoreline from the inundation caused by severe weather events. Prior studies mainly focus on the wave propagating, transforming, and breaking on the fringing reefs by assuming that ocean waves propagate in an ideal environment where the wind is absent. However, in the real severe ocean environment, huge surges and waves always occur simultaneously with the strong winds. The wave profile can be easily reshaped by the strong winds, which can also significantly affect the way that ocean waves propagate on the fringing reefs. Therefore, it is necessary to study the hydrodynamics of fringing reefs under the combined action of wind and waves. To study the influences of the onshore wind on the hydrodynamics of solitary wave on the fringing reef, the finite volume method is applied to solve the governing equations of two-phase incompressible flow and a high-resolution numerical wind-wave tank is established in this study. Effects of several main factors are analyzed in detail. The research results show that the onshore wind can significantly increase the maximum wave runup height (maximum by 38.49%) and decrease the wave reflection coefficient of solitary wave (maximum by 8.66%). It is hoped that the research results of this study can enhance the understandings on the hydrodynamics of ocean waves on the fringing reefs during severe weather events.

Wave‐Driven Hydrodynamic Processes Over Fringing Reefs With Varying Slopes, Depths, and Roughness: Implications for Coastal Protection

AbstractWave breaking on the steep fore‐reef slopes of shallow fringing reefs can be effective at dissipating incident sea‐swell waves prior to reaching reef shorelines. However, wave setup and free infragravity waves generated during the sea‐swell breaking process are often the largest contributors to wave‐driven water levels (wave runup) at the shoreline. Laboratory flume experiments and a two‐dimensional vertical phase‐resolving nonhydrostatic wave‐flow model, which includes a canopy model to predict drag forces generated by roughness elements, were used to investigate wave‐driven water levels for along‐shore uniform fringing reefs. In contrast to many previous studies, both the laboratory experiment and the numerical model account for the effects of large bottom roughness. The numerical model reproduced the observations of the wave transformation and runup over both smooth and rough reef profiles. The numerical model was then extended to quantify the influence of reef geometry and compared to simulations of plane beaches lacking a reef. For a fixed offshore forcing condition, the fore‐reef slope controlled wave runup on reef‐fronted beaches, whereas the beach slope controlled wave runup on plane beaches. As a result, the coastal protection utility of reefs is dependent on these slopes. For our examples, with a fore‐reef slope of 1/5 and a 500 m prototype reef flat length, a beach slope of ∼1/30 marked the transition between the reef providing runup reduction for steeper beach slopes and enhancing wave runup for milder slopes. Roughness coverage, spacing, dimensions, and drag coefficient were investigated, with results indicating the greatest runup reductions were due to tall roughness elements on the reef flat.

Numerical Simulation of Wave Overtopping of an Ecologically Honeycomb-Type Revetment with Rigid Vegetation

Traditional concrete revetments can destroy the ecological environment and the water landscape. An increasing number of ecological revetment structures have been applied in coastal, lake, and river regulation projects. It has been found that honeycomb-type revetments display a better performance in the attenuation of wave overtopping when compared to experimental data collected using the Eurotop and Muttray’s formula; recording a 40% decrease in the wave run-up in comparison to the latter. To further investigate the wave run-up and overtopping of the ecologically vegetated honeycomb-type revetment, based on OpenFOAM, an open source computational fluid dynamics software, a three-dimensional numerical wave tank was established. The Discrete Particle Method (DPM) was used to simulate gravel movement, and the flexible plant move boundary model was developed to simulate vegetation. The results of wave run-up calculated by the numerical model and those obtained by the experiments were in good agreement, with errors less than 20%. The modeled results of wave overtopping were within the same order of magnitude as those from the experiments; however, critical limitations were noticed due to effects of plant generalization and grid restrictions imposed by DPM methods. The results showed that wave overtopping increased with increasing wave period and wave height. However, with an increase in the wave overtopping, the influence of the wave period on wave overtopping decreased. The increase in vegetation density effectively reduced wave overtopping. Furthermore, an empirical formula for wave overtopping, considering the effects of vegetation density, was proposed.

Assessing Drivers of Coastal Tundra Retreat at Point Hope, Alaska

AbstractShoreline erosion over the last few decades along the Point Hope, Alaska, USA coastline has led to considerable loss of tundra behind the beach. Analysis of available remote sensing, morphology, and hydrodynamic datasets are used to inform the time scales and mechanisms of coastal land loss at Point Hope, in part through integration of these data into an analytical retreat model originally developed for coastal foredunes. At shorter time scales, these analyses indicate that steeper local beach slopes influence higher wave runup that can enhance the scale of tundra retreat at a particular section of coast. Coastal stretches that are most vulnerable to wave attack of the tundra scarp appear to shift with time related to complex spatio‐temporal variability in shoreline change rates. These local beach erosion rates primarily control the retreat of the tundra at decadal scales. However, independent of the fronting beach morphology, the largest erosion events throughout the region generally occur when there is the coincidence of both high wave energy and elevated still water levels. Additional exploratory modeling results indicate that future changes to sea level and changes in wave energy will further enhance the magnitude of tundra erosion.

The momentum conservative scheme for simulating nonlinear wave evolution and run-up in U-shaped bays

The momentum conservative scheme for simulating nonlinear wave evolution and run-up in U-shaped bays

An improved method for calculating the wave run-up on a vertical cylinder based on the velocity stagnation head theory

The estimation of wave run-up is a concern in the design of certain marine engineering structures. Accurate estimation of the wave run-up is important for the safety and cost of the structure. To better predict the wave run-up on structures, a series of physical experiments for wave run-up on vertical cylinder under regular waves and focusing waves were conducted in this study. The influences of the wave steepness kA, relative structural scale ka, and A/D on the wave run-up were analyzed. By fitting the experimental data, a semi-empirical formula that calculates the wave run-up, based on the velocity stagnation head theory, is proposed. In the improved formula, a second order theory is employed to calculate the wave velocity in the crest, and the two important factors, viz., the relative structural scale ka and A/D, are also considered. The formula was evaluated by utilizing certain experimental data in the literature, demonstrating that it can provide a satisfactory wave run-up prediction. Furthermore, the wave run-up on the cylinder under the focused waves was predicted by the new formula. It can predict it well as local wave steepness is small.

Viscous Flow Fields Induced by the Run-Up of Periodic Waves on Vertical and Sloping Seawalls

Unsteady two-dimensional Reynolds Averaged Navier-Stokes (RANS) equations coupled with the k−ε turbulence model was developed to simulate the viscous flow field near seawalls. The complex free-surface configuration was captured using the particle level set method (PLSM). An innovative solid-fluid coupling method was employed to mimic the solid-fluid interaction on fixed Cartesian grids. The proposed numerical model was applied to investigate the viscous flow fields induced by periodic waves propagating on three different seawalls, including vertical and steep seawalls, which are commonly designed in Taiwan with slopes of 1:2 and 1:5. The results reveal that the wave run-up height is closely related to Iribarren number and breaking wave. Partial standing wave or asymmetric recirculating cells in front of a steep seawall lose symmetry with increasing slope. The wave pressure on the seawall face increases as the Ursell number or seawall slope increases. The undertow caused by breaking waves has a significant effect on the bottom shear stress in front of the seawall.

An analytical study of scattering of water waves by a surface-piercing bottom-mounted compound porous cylinder placed on a porous sea-bed

The scattering problem of a bottom-mounted surface-piercing compound porous cylinder located on a porous sea-bed is theoretically investigated under the assumption of small amplitude wave theory. The compound cylinder is comprised of an impermeable upper cylinder and a porous lower cylinder beneath it. The boundary conditions on the porous boundaries follow Darcy’s law by assuming fine pores in the porous structure. The whole fluid region is split into three bounded and an unbounded sub-regions, within which the individual velocity potentials are found by using eigenfunction expansion technique. Further, utilization of the matching conditions along the boundaries of individual successive regions leads to a semi-analytical solution of the proposed problem. The impact of the non-dimensional porous-effect parameter of the cylindrical wall, the draft ratio, radius ratio and the sea-bed porosity on waveloads and wave run-ups are studied. The results show that suitable consideration of porosity and structure parameters enhance the efficiency of the proposed compound cylinder in mitigating wave impact. Furthermore, the hydrodynamic waveload acting on the lower as well as upper cylinder can be reduced by the suitable positioning of the annular spacing of the system, which will provide explicit information for the purpose of engineering design in the coastal area.

Numerical investigation of wave run-up and impact forces on large offshore jacket platforms

This paper focuses on wave interactions with large deep-sea jacket platforms. A numerical wave tank is designed and developed to simulate the wave-structure interactions, and the accuracy and precision of this numerical wave tank are verified by the theoretical values and LWI experimental tests. Then the processes of wave run-up along with the legs and impact the lower deck of a large deep-sea jacket platform located at the South China Sea are simulated, analyzed, and discussed. The results show that the greater the wave steepness, the stronger the wave run-up ability. The wave run-up processes are mainly concentrated within a radius R around the legs, and the maximum wave run-up ratio reaches 1.56 on the front side of leg 1 when the wave steepness is 0.03. Due to the interference, reflection, and superposition effects, all the legs show different wave run-up characteristics, and additional high-frequency side wave peaks are observed around the legs, which are mainly focused on 0–0.6 Hz in the frequency domain. With the increase of wave steepness λ, the wave drag forces increase significantly during the wave run-up processes. Especially, when the waves impact the lower deck under case 3, it will cause huge vertical wave impact loads, and the maximum value reaches 46.59 MPa, which will cause further attenuation to the vertical and lateral resistance of the jacket platform.

Beach Profile, Water Level, and Wave Runup Measurements Using a Standalone Line-Scanning, Low-Cost (LLC) LiDAR System

A prototype rapidly deployable, Line-scanning, Low-Cost (LLC) LiDAR system (USD 400 per unit; 2020) was developed to measure coastal hydro-morphodynamic processes. A pilot field study was conducted at the U.S. Army Corps of Engineers, Field Research Facility (FRF) in Duck, North Carolina, USA to evaluate the efficacy of the LLC LiDAR in measuring beach morphology, wave runup, and free-surface elevations against proven approaches. A prototype LLC LiDAR collected continuous cross-shore line scans for 25 min of every half hour, at ~7 revolutions/s and ~1.3° angular resolution, at two locations (one day at each location), spanning 12 m (i) on the backshore berm (35 scans; Series B) and (ii) in the swash/inner surf zone (28 scans; Series C). LLC LiDAR time-averaged beach profiles and wave runup estimates were compared with the same quantities derived from the continuously sampling terrestrial LiDAR scanner installed atop the dune at the FRF (DUNE LiDAR). The average root-mean-square difference (RMSD) between 17 (6) time-averaged LLC and DUNE LiDAR beach profiles was 0.045 m (0.031 m) with a standard deviation of 0.004 m (0.002 m) during Series B (Series C). Small-scale (cm) swash zone bed level changes were resolved over 5-min increments with the LLC LiDAR. The RMSD between LLC- and DUNE LiDAR-derived wave runup excursions over two 25-min segments was 0.542 m (cross-shore) and 0.039 m (elevation) during the rising tide and 0.366 m (cross-shore) and 0.032 m (elevation) during the falling tide. Between 72–79% of the LLC LiDAR wave runup data were more accurate than the RMSD values, thereby demonstrating the LLC LiDAR is an effective, low-cost instrument for measuring wave runup and morphodynamic processes. Co-located water levels were measured with a continuously sampling (16 Hz) RBRsolo3 D|wave16 pressure logger during Series C. LLC LiDAR free-surface elevations at the nadir during one high tide (4.5 h) compared well with pressure-derived free-surface elevations (RMSD = 0.024 m, R2 = 0.85).

Wave run-up on composite bucket foundation due to random waves: Model tests and prediction formulae

Wave run-up around foundations is a hot research topic in offshore wind engineering, particularly for novel composite bucket foundations (CBFs). This study investigates wave run-up on a CBF due to random waves via physical model experiments. The variation in wave run-up around a CBF and the influence of relative wave height on the maximum relative wave run-up is analysed. The experimental results show that the maximum relative wave run-up is found at the 0° marking, and the lowest wave run-up heights occur between the 108° and 144° markings. Moreover, the velocity stagnation head theory (VSH theory) and M5ʹ model tree are employed to predict the wave run-up and obtain an optimum prediction model. Statistical indicators, including the coefficient of determination, agreement index, scatter index, and bias, were used to evaluate the performance of the generated formulae. The prediction formula developed by the VSH theory combined with the second-order Stokes wave theory based on the particle velocity at the mean free surface has good performance in the prediction of wave run-up on the CBF due to random waves. The performance of the formula for relative wave run-up was developed using the M5ʹ model tree based on the scatter parameter, relative wave height, and wave steepness and was optimal according to statistical indicators. The relative wave height plays a crucial role in wave run-up prediction. The relative wave run-up height increases with an increase in the scatter parameter, relative wave height, and decrease in wave steepness. These two methods are recommended for predicting wave run-up on CBF owing to random waves.

The influence of submerged coastal structures on nearshore flows and wave runup

Engineered and natural submerged coastal structures (e.g., submerged breakwaters and reefs) modify incident wave fields and thus can alter hydrodynamic processes adjacent to coastlines. Although submerged structures are generally assumed to promote beach protection by dissipating waves offshore and creating sheltered conditions in their lee, their interaction with waves can result in mean wave-driven circulation patterns that may either promote shoreline accretion or erosion. Here, we analyse the mean flow patterns and shoreline water levels (wave runup) in the lee of idealised impermeable submerged structures with a phase-resolved nonhydrostatic numerical model. Waves propagating over submerged structures can drive either a 2-cell mean (wave-averaged) circulation, which is characterised by diverging flows behind the structure and at the shoreline, or 4-cell circulation, with converging flows at the shoreline and diverging flows in the immediate lee of the structure. The numerical results show that the mode of circulation can be predicted with a set of relationships depending on the incoming wave heights, the structure crest level, and distance to the shoreline (or structure depth). Qualitative agreement between the mean flow and proxies for the sediment transport using an energetics approach suggest that the mean flow can be a robust proxy for inferring sediment transport patterns. For the cases considered, the submerged structures had a minimal influence on shoreline wave setup and wave runup despite the wave energy dissipation by the structures due to alongshore wave energy fluxes in the lee. Consequently, these results suggest that the coastal protection provided by the range of impermeable submerged structures we modelled is primarily due to their capacity to promote beach accretion. • A phase-resolved model simulates hydrodynamic interactions with submerged structures. • Waves can drive 2-cell or 4-cell mean circulation and sediment transport patterns. • Bottom shear stresses presented an overall similar pattern to the mean currents. • We develop a predictor for the flow patterns based on wave and structure parameters. • The submerged structures had limited influence on shoreline setup and wave runup.

On the mean overtopping rate of rubble mound structures

Estimation of the mean overtopping discharge is a major task in the design and assessment of the crest level of rubble mound structures such as breakwaters and seawalls. The tolerable mean overtopping rates are given based on the associated risk and wave characteristics. Several empirical formulas have been developed for the prediction of mean overtopping discharge at coastal structures. These formulas can be applied to a wide variety of coastal structures, but have limited accuracy and/or do not reflect the physics of the phenomena. The main aim of this study is to overcome these issues for rubble mound structures by considering the physics of the process in the formula development. To achieve this, first, the references used in the extended CLASH database (also called the EurOtop-2018 database), were scrutinized, the reported wave characteristics were corrected (if required) and the rubble mound structure subset was extended using a recent study. Then noting that overtopping occurs when the wave runup exceeds the freeboard, the difference between the maximum wave runup and crest freeboard was considered as the governing parameter in the mean overtopping discharge formula. In the developed formula, a semi-empirical relationship between the mean overtopping and wave runup has been established. The performances of the developed formulas and existing ones were evaluated both qualitatively and quantitively. Accuracy metrics such as RMSE and BIAS indicated the superiority of the developed simple formula. Finally, a design formula to consider uncertainty and some guidelines are provided for practitioners. • A robust formula was derived for the mean overtopping of rubble mound structures. • The formula has a compact form and includes effects of governing parameters such as the wave runup and crest width. • The formula was evaluated for a wide range of cases such as oblique waves and wave walls as well as prototype data. • A probabilistic formula was also given to include the uncertainty and safety in the design.