Benchmark experimental study on wave run-ups of fixed four-rounded-square-column array in regular waves

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

Vortex-induced motions (VIM) of offshore floaters occur when the frequency of the vortex shedding is close to the natural frequency in the transverse direction of the unit subjected to the current, and this can severely affect the fatigue life of mooring lines and risers. Literatures in recent years have shown an increasing interest in the VIM behavior of semi-submersibles (SS), the geometry of which implies a more complex VIM phenomenon. In the case of multi-column semi-submersibles, the vortices shed around each column. Thus the shape of the columns, circular or square, and the wake interference different for each current heading, characterize the VIM of the unit. Based on verification by the VIM towing tests for a semi-submersible with four rounded square columns, VIM simulations were conducted using CFD method in the model scale for four semi-submersibles with different column designs: a SS model with four rounded square columns (SRC-SS), a SS model with four circular columns (CC-SS), a SS model with two tandem rounded square columns and two tandem circular columns (SRCT-CCT-SS), and a SS model with two staggered rounded square columns and two staggered circular columns (SRCS-CCS-SS). The current headings ranged from 0° to 180° and reduced velocities of 4 up to 14 were considered. Different semi-submersibles present different VIM performances owing to the influence of the column design. The most significant transverse motions of the CC-SS model occur at the 0° current heading with the largest nominal transverse amplitudes around 74% of the column diameter. On the other hand, the maximum amplitudes in the transverse direction of the SRC-SS model, approximately 63% of the column width, are observed at the 45° current heading. Additionally, the VIM responses could be mitigated when the semi-submersible consists of combined circular-section and square-section columns.

In the interaction between waves and structures, the maximum wave run-up height on the surface of the structure and the wave field distribution around the cylinder are important factors to be considered in the design of marine structures. In this paper, the open source software OpenFOAM is used to simulate the wave run-up phenomenon of a truncated cylinder under regular waves by solving the Reynolds-averaged Navier–Stokes equation. The established numerical model is verified with the experimental data, and the good consistency demonstrates the accuracy in simulating the interaction between waves and fixed truncated cylinders. The numerical results show that the draft of the cylinder under regular waves has little effect on its maximum wave run-up height, but has a significant effect on the horizontal wave force. At the same wave steepness, the radial dimensionless run-up height increases with the increase of scattering parameters ka, where k is the wave number and a is the cylinder radius. The radial run-up height decreases gradually along the radial direction in the upstream, and increases gradually along the radial direction in the downstream.

The analytical solutions for the diffraction of the short-crested wave, the cnoidal wave, and the solitary wave incident on a composite bucket foundation of an offshore wind turbine are derived in this paper. The analytical expressions for the pressure, wave run-up, and wave force on the composite bucket foundation are obtained. Based on the numerical results, it is found that the short-crested wave run-up is affected by the wave phase, the cnoidal wave run-up is affected by the wave parameter λ, and the solitary wave run-up is affected by the wave parameter χ. For a composite bucket foundation, the long-crested wave force is larger than the short-crested wave force and the solitary wave force is larger than cnoidal wave force in certain shallow water conditions. Moreover, the short-crested wave force may first increase and then decrease with the increase in the water depth, while the cnoidal wave force and the solitary wave force monotonically increase with the increase in the water depth. In the design of the offshore wind turbine with composite bucket foundation, it will be more conservative if the formula derived from the plane waves is used as design criteria in a short-crested sea, and the wave force in shallow water should be determined by the solitary wave and the cnoidal wave together.

The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.

In this study, the wave energy dissipation over a horizontal slotted plate with a leeside vertical seawall was extensively investigated by analytical and numerical approaches. The analytical model was developed by using the matched eigenfunction expansion method and the energy dissipation model with a porosity-dependent drag coefficient estimated by computational fluid dynamics (CFD) results from the 2D channel flow with symmetric slats. The energy dissipation of a horizontal slotted plate was assessed by analyzing the variation of the reflection coefficient, wave run-up, vertical wave force on the plate, and horizontal wave force on the vertical wall for different submergence depths, porosities, plate lengths, and wave steepnesses. Results from the analytical model were compared extensively with those from CFD simulations. CFD computations were performed by using an incompressible turbulence model based on Reynolds averaged Navier–Stokes equations and volume of fluid method. Overall, a good agreement was observed between the analytical and CFD results. A qualitative numerical analysis showed that the wave dissipation over a horizontal slotted plate was caused by the generation of higher-harmonic waves, wave breaking, and vortices formation near the slotted plate. The presented analytical and numerical models would provide a mutually complementary tool for the accurate and efficient design of a horizontal slotted plate for reducing the reflection coefficients, wave forces, and wave run-up on seawalls.

Wave run-up is an important phenomenon that should be considered in ocean structure design. In this study, the wave run-up of a surface-piercing circular cylinder was calculated in the time domain using the three-dimensional linear and fully nonlinear numerical wave tank (NWT) techniques. The NWT was based on the boundary element method and the mixed Eulerian and Lagrangian method. Stokes second-order waves were applied to evaluate the effect of the nonlinear waves on wave run-up, and an artificial damping zone was adopted to reduce the amount of reflected and re-reflected waves from the sidewall of the NWT. Parametric studies were conducted to determine the effect of wavelength, wave steepness, and the draft of the cylinder on the wave run-up of the cylinder. The maximum wave run-up value occurred at 0°, which was in front of the cylinder, and the minimum value occurred near the circumferential angle of 135°. As the diffraction parameter increased, the wave run-up increased up to 1.7 times the wave height. Furthermore, the wave run-up was 4% higher than the linear wave when the wave steepness was 1/35. In particular, the crest height of the wave run-up increased by 8%.

Full-scale experimental study on wave reflection and run-up at stepped revetments

Wave run-up prediction for composite bucket foundation due to regular wave and current

This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-shore structure of the long-wave motion is presented, and the observations are critically compared with existing theories for two-dimensional surf-beat generation. The surf beat shows a strong dependency on normalized surf-zone width, consistent with long-wave forcing by a time-varying breakpoint, with little evidence of the release and reflection of incident bound long waves for the random-wave simulations considered. The seaward-propagating long waves show a positive correlation with incident short-wave groups and are linearly dependent on short-wave amplitude. The phase relationship between the incident bound long waves and radiated free long waves is also consistent with breakpoint forcing. In combination with previous work, the present data suggest that the breakpoint variability may be the dominant forcing mechanism during conditions with steep incident short waves.

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

: Wave runup and overtopping on inclined coastal structures and wave runup on beaches are reviewed together to examine the ranges of wave runup processes occurring on slopes of different inclinations. Laboratory experiments on regular wave runup and overtopping on coastal structures are reviewed first to provide historical perspec- tive. More recent laboratory experiments on irregular wave runup and overtopping on coastal structures are summarized to show the improved quantitative understanding due to the improved capabilities for irregular wave experiments. Field experiments on wave runup on beaches are then reviewed to discuss the possible dominance and causes of low frequency shoreline oscillations on gently sloping beaches. The recent development of time dependent numerical models is reviewed to indicate the rapid progress of the numerical capabilities of predicting irregular wave runup on inclined coastal structures and beaches. This review indicates that the improved quantitative understanding of irregular wave runup and overtopping on inclined coastal structures and irregular wave runup on beaches has essentially been limited to normally incident waves on coastal structures and beaches of alongshore uniformity. Future experimental and numerical studies are suggested in this review.

Estimation of regular wave run-up on slopes of perforated coastal structures constructed on sloping beaches

Coastal zones are vital to economies and societies, supporting diverse ecosystems, human settlements, and critical infrastructure. However, these areas face increasing threats from storm surges and coastal flooding. Traditional engineering solutions like seawalls and groins often disrupt natural processes and encourage unsustainable development, leading to a growing interest in Nature-based Solutions (NbS) such as wetlands and coastal vegetation. An assessment of the protective function of these NbS requires improved understanding of their influence on coastal processes, including wave runup. Despite the availability of many empirical equations for predicting wave runup on bare beaches, comparable equations for vegetated beaches remain largely undeveloped. This study develops empirical equations for predicting short wave runup on vegetated beaches through integrated numerical modeling and expression programming techniques. The research investigates four key parameters: significant wave height ( H s ), peak wave period ( T p ), beach slope ( S ) and vegetation density ( N v ) across two vegetation types: rigid and flexible. Orthogonal sampling generates 768 simulation scenarios per vegetation type. The XBeach Non-Hydrostatic is then utilized to simulate wave runup under the generated wave and vegetation scenarios. To develop runup equations, dimensional analysis transforms parameters into three dimensionless variables: Iribarren number, wave steepness, and vegetation characteristics (number of stems). The Artificial Bee Colony Expression Programming ( ABCEP ) algorithm derives vegetation-specific runup empirical equations from the resulting dataset. Results demonstrate acceptable predictive performance with R² values exceeding 0.94 for both vegetation types. Validation against independent numerical data confirms superior performance compared to widely-used wave runup formulations established for non-vegetated beaches. The empirical equations developed in this research provide coastal engineers and practitioners with tools explicitly incorporating vegetation density for short wave runup prediction.

On the accuracy of large-steepness regular wave generation, propagation and run-up on a cylinder