Plunging Breaking Waves Research Articles

Experimental study on plunging breaking waves impacting a vertical cylinder with three different model scales

Scale effects, which can influence the reliability and effectiveness of experimental results, are often unavoidable but seldom explored, particularly in the context of plunging waves. To investigate the scale effects of plunging wave impacts on a vertical cylinder, experiments were conducted in a wave flume at model scales of 1:20, 1:30 and 1:40. The wavemaker movements were scaled based on the Froude-similarity law and the pressures on the front surface of the cylinder were analyzed. The results indicated that plunging waves were generated across these three scales, with fine agreement in overall wave elevations and a local waveform similarity of 80–90%. The analysis of pressures showed that the distribution of peak pressures on the cylinders remained consistent across different scales; however, scale effects were closely related to the intensity of wave impacts. Specifically, in cases of relatively weak impact, such as when the wavefront struck the cylinder before breaking or even after an intense wave breaking with intense gas-liquid mixtures, the pressure discrepancies were less than 20% among these different scales. This discrepancy can exceed 50% near the wave peaks during the vertical wave front or early jet formation stages with strong impacts.

Wave height distribution for plunging breakers induced by air bubbles

This study highlights the wave height distributions based on plunging breaking waves and air bubble effects in the surf zone. Wave height distributions predicted previously by different models have been reformulated in terms of air bubble effects. Some of the most commonly applied wave height distributions are judged using laboratory observations in a custom-built wave flume. Results have revealed a notable deviation from the Rayleigh distribution, with the proposed model demonstrating a closer match to experimental data, particularly for larger wave heights. Probability densities of larger wave heights are reduced significantly by entrained air bubbles, leading to measured wave heights below Rayleigh distribution predictions. In addition, the different wave height parameters derived from the proposed model exhibited good agreement with laboratory data compared to the Rayleigh distribution. Furthermore, theoretical analysis shows the scale parameter's dependence on the decay coefficient, aligning well with measurements and simplifying the proposed distribution to a one-parameter model. Again, based on the error analysis, the proposed model's results show good performance compared to others.

Flow characteristics and bubble statistics during the fragmentation process of the ingested main cavity in plunging breaking waves

Flow characteristics and bubble statistics during the fragmentation process of the ingested main cavity in plunging breaking waves

Numerical study of bubble rise in plunging breaking waves

During the occurrence of plunging wave breaking, a substantial number of multi-scale bubbles are generated. These submerged bubbles persist for extended periods and contribute to the distinct acoustic and optical characteristics of the wake. In this study, we utilize high-fidelity simulations, combined with the adaptive refinement strategy to accurately track bubbles of multi-scales during the entire rising stage. Unlike previous studies, our emphasis is specifically on investigating the process of bubble rising during plunging wave breaking. Comprehensive statistical analyses are performed and characteristics of bubbles across various scales are also provided. Our findings reveal that most bubbles are concentrated in small scales, while larger bubbles rapidly ascend to the surface or undergo fragmentation into smaller bubbles through breaking cascades eventually. A distinct stratification of bubble size distribution along the depth direction is observed. Bubble velocity distributions are also important characteristics that are frequently neglected in studies of plunging wave breaking. Bubbles primarily spread along the spanwise direction, with a uniform distribution of velocity in this dimension. The velocity distribution of bubbles displays asymmetric tails that extend to higher velocities, and within this high-velocity regime, a power law behavior is observed, similar to the size distributions. Ultimately, the flow field is left with only a few small bubbles, moving at an exceedingly low speed. Furthermore, dynamical evolution of bubble rise in plunging wave breaking is described in detail and we analyze the intricate interactions between bubbles and turbulent flows. We observe that vortices are predominantly generated in close proximity to the bubbles, and bubble motion plays a crucial role in initiating turbulent flows. Simultaneously, these vortices contribute to the fragmentation of large-scale bubbles, transforming them into smaller counterparts due to turbulent fluctuations.

Large eddy simulations of bubbly flows and breaking waves with smoothed particle hydrodynamics

For turbulent bubbly flows, multi-phase simulations resolving both the liquid and bubbles are prohibitively expensive in the context of different natural phenomena. One example is breaking waves, where bubbles strongly influence wave impact loads, acoustic emissions and atmospheric-ocean transfer, but detailed simulations in all but the simplest settings are infeasible. An alternative approach is to resolve only large scales, and model small-scale bubbles adopting sub-resolution closures. Here, we introduce a large eddy simulation smoothed particle hydrodynamics (SPH) scheme for simulations of bubbly flows. The continuous liquid phase is resolved with a semi-implicit isothermally compressible SPH framework. This is coupled with a discrete Lagrangian bubble model. Bubbles and liquid interact via exchanges of volume and momentum, through turbulent closures, bubble breakup and entrainment, and free-surface interaction models. By representing bubbles as individual particles, they can be tracked over their lifetimes, allowing closure models for sub-resolution fluctuations, bubble deformation, breakup and free-surface interaction in integral form, accounting for the finite time scales over which these events occur. We investigate two flows: bubble plumes and breaking waves, and find close quantitative agreement with published experimental and numerical data. In particular, for plunging breaking waves, our framework accurately predicts the Hinze scale, bubble size distribution, and growth rate of the entrained bubble population. This is the first coupling of an SPH framework with a discrete bubble model, with potential for cost-effective simulations of wave–structure interactions and more accurate predictions of wave impact loads.

Greenwater due to plunging breaking wave impingement on a deck structure. Part 1: Experimental investigation on fluid kinematics

This study experimentally investigates the kinematics of greenwater resulting from plunging breaking wave impacts on a deck structure. Two impingement scenarios, characterized by different breaking points, were considered. The ensemble-averaged flow fields were obtained by applying both PIV (particle image velocimetry) and BIV (bubble image velocimetry) techniques to 50 repeated tests. The study examines flow patterns, velocity fields, and derived quantities from velocity data to identify differences in flow behaviors, variations in velocity magnitude, and potential distribution of peak impact pressures. The presented results provide useful information and indication for assessing concentrated loadings and enhancing our understanding of hydrodynamic behaviors. Additionally, the validity of applying Ritter dam break solutions to describe the horizontal velocity distribution of greenwater flows is examined, and prediction equations based on self-similar horizontal velocity distribution are derived.

WAVE TRANSFORMATION ON CORAL REEFS: COMPARISON OF A CFD MODEL AND PHYSICAL MODEL TESTS OF A MALDIVIAN REVETMENT

Designing optimized coastal structures on islands bordered by coral reefs has proven to be a challenging task due to the complex reef and wave interaction (Jensen, 1991; Jensen, Sloth and Jacobsen, 1998). Often the reefs in these tropical regions have a steep seaward profile until a certain depth, whereafter the reef suddenly becomes flat with a mild slope. When offshore waves reach the reef, it can result in plunging wave breaking, a wave set-up, and energy transfer from the peak frequency to lower frequencies resulting in long period wave motions. Under these conditions, it is difficult to predict the rate of overtopping as the complex hydrodynamics are not covered in standard overtopping formulas. Furthermore, the standard spectral wave models, on which the overtopping formulas often are based, cannot describe the transformation of offshore waves over the reef as the models are not able to resolve the physics of this violent water motion. In connection with the hydraulic study for a detailed design of a revetment on Fuvahmulah in the Maldives, the OpenFOAM CFD model is applied to obtain the hydrodynamic design parameters. The wave dynamics on the reef, the revetment overtopping rates, and hydrodynamic forces derived from the numerical model are compared with results from a physical model conducted by the Danish Hydraulic Institute (DHI).

Plunging breakers. Part 2. Droplet generation

An experimental study of the dynamics and droplet production in three mechanically generated plunging breaking waves is presented in this two-part paper. In the present paper (Part 2), in-line cinematic holography is used to measure the positions, diameters ($d\geq 100\ \mathrm {\mu }{\rm m}$), times and velocities of droplets generated by the three plunging breaking waves studied in Part 1 (Erininet al.,J. Fluid Mech., vol. 967, 2023, A35) as the droplets move up across a horizontal measurement plane located just above the wave crests. It is found that there are four major mechanisms for droplet production: closure of the indentation between the top surface of the plunging jet and the splash that it creates, the bursting of large bubbles that were entrapped under the plunging jet at impact, splashing and bubble bursting in the turbulent zone on the front face of the wave and the bursting of small bubbles that reach the water surface at the crest of the non-breaking wave following the breaker. The droplet diameter distributions for the entire droplet set for each breaker are fitted with power-law functions in separate small- and large-diameter regions. The droplet diameter where these power-law functions cross increases monotonically from 820 to 1480$\mathrm {\mu }{\rm m}$from the weak to the strong breaker, respectively. The droplet diameter and velocity characteristics and the number of the droplets generated by the four mechanisms are found to vary significantly and the processes that create these differences are discussed.

Plunging breakers. Part 1. Analysis of an ensemble of wave profiles

An experimental study of the dynamics and droplet production in three mechanically generated plunging breaking waves is presented in this two-part paper. In the present paper (Part 1), the dynamics of the three breakers are studied through measurements of the evolution of their free surface profiles during 10 repeated breaking events for each wave. The waves are created from dispersively focused wave packets generated with three wave maker motions that differ primarily by small changes in their overall amplitude. Breaker profiles are measured with a cinematic laser-induced fluorescence technique covering a streamwise region of approximately one breaker wavelength and over a time of 3.4 breaker periods. The aligned profile data is used to create spatio-temporal maps of the ensemble average surface height and the standard deviation of both the local normal distance and the local arc length relative to the instantaneous mean profile. It is found that the mean and standard deviation maps contain strongly correlated localized features and indicate that the transition from laminar to turbulent flow is a highly repeatable process. Regions of high standard deviation include the splash created by the plunging jet impact and subsequent splash impacts at the front of the breaking region as well as the site where the air pocket entrained under the plunging jet at the moment of jet tip impact comes to the surface and pops. In Part 2 (Erinin et al., J. Fluid Mech., vol. 967, 2023, A36), these features are used to interpret various features of the distributions of droplet number, diameter and velocity.

A numerical study of aeration characteristics of a plunging solitary wave on a slope

In this paper, the characteristics of aerated flow under a plunging solitary wave on a 1:20 sloping beach are investigated numerically. The numerical model solves the Reynolds-averaged Navier–Stokes equations for mean flow. The turbulence is described by the k−ε model, in which the turbulence production and dissipation modified by entrained air bubbles are considered by an additional term. A transient equation is solved for air bubble transportation. The numerical model is validated by comparing the air bubble concentration, mean flow velocities, and turbulent kinetic energy against experimental data, demonstrating its capability for simulating transient aerated flows under breaking waves. The validated model is further applied to reveal the detailed interaction of the entrained air bubbles and the turbulent free surface flows during the wave breaking process. Plunging breaking wave consists of four stages, namely, the wave front steepening, the initiation of overturning, the transitional stage, and the quasi-steady bore propagation stage. The results reveal that the overturning and breaking wave front is the main source for turbulence generation and air entrainment in the initiation and transitional stage of breaking wave, respectively. The entrained air bubbles are mainly transported backward and downward by turbulence structures and forming distinct bubble vortex rollers near the bottom. The distribution of air bubble concentration shows a linear correlation to the distribution of turbulence quantities in the initial and transitional stage of breaking wave, demonstrating the important role of local turbulent structures on air entrainment and transportation.

Development, calibration and validation of a phase-averaged model for cross-shore sediment transport and morphodynamics on a barred beach

Simulating cross-shore sediment transport and associated sandbar migration is still a challenging task for phase-averaged coastal morphological models. Numerical studies have mostly relied on beach morphology prediction for calibration and validation, without examining in much detail the underlying hydrodynamics, sediment concentrations and transport rates. This paper reports on a new three-dimensional coastal morphodynamic model based on the hydrodynamic model of Zheng et al. (2017), combined with an advection-diffusion type suspended sediment transport model and the extended SANTOSS near-bed sediment transport formula of Van der A et al. (2013), to represent the key cross-shore transport mechanisms. The model is are calibrated based on comprehensive measurements from a large-scale laboratory experiment involving regular plunging breaking waves over an evolving sandbar, covering detailed comparisons on hydrodynamics, sediment suspension, transport rates, and bed level evolution. Separate validation using large scale wave flume experiments were also conducted to confirm the model's performance on different conditions. Good agreements are obtained between measurements and model results, which demonstrates the model's ability to reproduce cross-shore sediment transport processes under breaking waves correctly, given that the appropriate parameterizations for intra-wave processes are included. Model results also reveal the onshore near-bed transport is related to wave-induced near-bed streaming, wave skewness and asymmetry, and bed slope effects at different locations across the beach surface. Wave breaking-induced turbulence enhances the near-bed transport within the bed boundary layer which needs to be taken into account in order to achieve good model prediction skills.

On Doppler Shifts of Breaking Waves

Field-tower-based observations were used to estimate the Doppler velocity of deep water plunging breaking waves. About 1000 breaking wave events observed by a synchronized video camera and dual-polarization Doppler continuous-wave Ka-band radar at incidence angles varying from 25 to 55 degrees and various azimuths were analyzed using computer vision methods. Doppler velocities (DVs) associated with breaking waves were, for the first time, directly compared to whitecap optical velocities measured as the line-of-sight projection of the whitecap velocity vector (LOV). The DV and LOV were found correlated; however, the DV was systematically less than the LOV with the ratio dependent on the incidence angle and azimuth. The largest DVs observed at up-wave and down-wave directions were accompanied by an increase of the cross-section polarization ratio, HH/VV, up to 1, indicating a non-polarized backscattering mechanism. The observed DV was qualitatively reproduced in terms of a combination of fast specular (coherent) and slow non-specular (incoherent) returns from two planar sides of an asymmetric wedge-shaped breaker. The difference in roughness and tilt between breaker sides (the front face was rougher than the rear face) explained the observed DV asymmetry and was consistent with previously reported mean sea surface Doppler centroid data and normalized radar cross-section measurements.

Effects of spanwise length and side-wall boundary condition on plunging breaking waves

A systematic study of the effect of the spanwise length and the sidewall boundary condition of a numerical wave flume (NWF) on direct numerical simulation of a plunging breaking wave is performed. To deal with the topological changes of free surfaces, a high-fidelity numerical model is employed to solve the Navier–Stokes equations together with the volume of fluid function. After verification by two-dimensional (2D) simulations of a plunging breaker on a sloping beach, ten NWFs with different spanwise extents and sidewall boundary conditions are studied. Special attention is devoted to the three-dimensionality of the plunging breaker. Compared with three-dimensional (3D) models, the 2D model accurately reproduces the dynamics of a breaking solitary wave in the early stage, but it is inadequate for the study of the post-breaking process. For a 3D NWF with nonslip sidewall boundary condition, the wave domain can be divided into two regions with different physical properties. In the near-wall region, the nonslip boundary condition on the sidewall plays a crucial role in the wave hydrodynamics, while in the central region, the properties of the breaking wave are similar to those for the periodic boundary condition, which provide a closer representation of the real sea environment. The spanwise length of the NWF plays only a minor role in simulations under the periodic boundary condition. Furthermore, lateral boundaries and spanwise length show more influences on a plunging breaker with larger incident wave steepness. This study provides valuable support for the design of numerical simulations of wave breaking.

Performance of a coupled level-set and volume-of-fluid method combined with free surface turbulence damping boundary condition for simulating wave breaking in OpenFOAM

In the present study, an extension of the volume-of-fluid (VOF) method used in the open-source computational fluid dynamics (CFD) software OpenFOAM was developed, taking the advantages of the VOF and the level-set (LS) methods with an additional free surface turbulence damping (FSTD) boundary condition to restrict the overprediction of turbulence near the free surface. The coupled level-set and volume-of-fluid (CLSVOF) method has been developed, scripted, validated and proposed. The free surface elevation with the proposed CLSVOF method was validated in a developed numerical wave tank (NWT) against turbulence models used so far in OpenFOAM. Further, the validity of the present numerical model was evaluated for the case of plunging breaking waves against relevant experimental and numerical data. The outcome of this study demonstrates that the performance of the wave generation is improved with the proposed numerical model compared to existing turbulence models in OpenFOAM, creating a useful simulation add-on that generates long-term waves without unphysical dissipation, wave damping, and wave decay. The overprediction of turbulence created due to the significant difference in the fluid's density close to the free surface is limited by applying the FSTD boundary condition leading to a better representation of the flow field.

Transient analysis of the slamming wave load on an offshore wind turbine foundation generated by different types of breaking waves

In this study, a computational fluid dynamics model was employed to simulate the impact of a breaking wave on the foundation of an offshore wind turbine. The accuracy of the numerical simulation was validated in comparison with published experimental results for the Large Wave Channel (GWK) at Hannover, Germany. To understand the influence of the wave-breaking location on the monopile support structure, a series of shoaling waves with different spilling and plunging breaking wave types were considered in terms of the surf-similarity parameter (ξ0) and relative breaking distance (xb′). After processing the total wave load with an empirical mode decomposition method and a low-pass filter, the instantaneous nature of the slamming wave load generated by different breaking wave types was obtained. Subsequently, an exponential-type refined dynamic model was established to consider the characteristics of the filtered slamming wave load. ξ0 and xb′ were found to be dominant factors for the run-up phenomena, slamming characteristics, and wave-dependent parameters. The results demonstrated that these two coefficients can be applied to determine the nature of the run-up and slamming wave loads.

Reynolds stress turbulence modelling of surf zone breaking waves

Computational fluid dynamics is increasingly used to investigate the inherently complicated phenomenon of wave breaking. To date, however, no single model has proved capable of accurately simulating the breaking process across the entirety of the surf zone for both spilling and plunging breakers. The present study newly considers the Reynolds stress–$\omega$turbulence closure model for this purpose, where$\omega$is the specific dissipation rate. Novel stability analysis proves that, unlike two-equation closures (at least in their standard forms), the stress–$\omega$model is neutrally stable in the idealized potential flow region beneath surface waves. It thus naturally avoids unphysical exponential growth of turbulence prior to breaking, which has plagued numerous prior studies. The analysis is confirmed through simulation of a progressive surface wave train. The stress–$\omega$model is then applied to simulate a turbulent wave boundary layer, demonstrating superior accuracy relative to a two-equation model, especially during flow deceleration. Finally, the stress–$\omega$model is employed to simulate spilling and plunging breaking waves, with seemingly unprecedented accuracy. Specifically, the present work marks the first time that a single turbulence closure model collectively: (1) avoids turbulence over-production prior to breaking, (2) accurately predicts the breaking point, (3) provides reasonable evolution of turbulent normal stresses, while also (4) yielding accurate evolution of undertow velocity structure and magnitude across the surf zone, for both spilling and plunging cases. Differences in the predicted Reynolds shear stresses (hence flow resistance) are identified as key to the improved inner surf zone performance, relative to a state-of-the-art two-equation model.

Experimental investigation of oxygen transfer efficiency in hydraulic jumps, plunging jets, and plunging breaking waves

Abstract The scope of the paper is to analyse the different similarities of air entrainment among the hydraulic jumps, plunging jets, and plunging breaking waves and to discuss current practices. The measured data are reexamined and scrutinised to investigate the gas exchange phenomena through an air-water interface. In particular, oxygen transfer efficiency and penetration depth by air bubbles are discussed. The calculated results highlight that the oxygen transfer efficiency is decreased with the increase of energy dissipation rate both in plunging jets and breaking waves. In contrast, it is shifted almost parallel in the case of hydraulic jumps. In addition, the aeration lengths in the hydraulic jumps and penetration depths both in plunging jets and plunging breaking waves were dependent on the jet impact velocity.

Wave Energy Dissipation of Spilling and Plunging Breaking Waves in Spectral Models

On the basis of field experiments and modeling, the dependence of the dissipation of the energy of waves breaking by plunging and spilling on the frequency of wave spectra was investigated. It was shown that the modeling of wave breaking should take into account the compensation of the nonlinear growth of higher wave harmonics, which occurs in different ways for waves breaking with different types and for different methods of modeling a nonlinear source term. The study revealed that spilling breaking waves have a frequency selectivity of energy dissipation at frequencies of second and third harmonics for the Boussinesq and SWAN models for any method of modeling a nonlinear source term. Plunging breaking waves have a quadratic dependence of the dissipation coefficient on frequency in the Boussinesq model and SWAN model with the SPB approximation for a nonlinear source term. The SWAN model with default LTA approximation for plunging breaking waves also assumes frequency-selective energy dissipation. The discrepancy between the LTA default method and others can be explained by the overestimation of the contribution of the second nonlinear harmonic and by inaccurate approximation for the biphase. It is possible to improve the accuracy of LTA and SPB methods by tuning SWAN model coefficients.

A combined volume of fluid and immersed boundary method for free surface simulations induced by solitary waves

A combined volume of fluid and immersed boundary method is developed to simulate free surface flow induced by solitary waves. The simulations of problems involving free boundaries with large deformations are known to be challenging due to the discontinuity of density and momentum flux across the interface. In order to reduce the spurious velocities and prevent unphysical tearing of the interface, an extra velocity field is designed to extend the velocity of the water into the air and to enforce a new boundary condition near the free surface. The free surface is captured using a new Volume of Fluid (VOF) method and a boundary layer is built on the air side by an immersed boundary method. A density-weight smoothing approach is used to reconstruct the velocities inside the boundary layer. The accuracy of the new solver is verified by two benchmark problems, the propagation of a solitary wave in constant depths and run-up of a solitary wave on a slope. The performances of the new solver are compared with the original VOF solver, analytical solutions and one-phase flow solver results, and better results are obtained. The simulation of a plunging wave breaking on a slope further demonstrates the capability of the new solver to capture strong air-water interactions. It is shown to improve the robustness and stability of two-phase flow simulations and higher accuracy can be obtained on a relatively coarse grid compared to the original volume of fluid method.

Focused Plunging Breaking Waves Impact on Pile Group in Finite Water Depth

Abstract Accuracy estimation of wave loading on cylinders in a pile group under different impact scenarios is essential for both the structural safety and cost of coastal and offshore structures. Differing from the interaction of waves with a single cylinder, less attention has been paid to pile groups under different arrangements. Numerical simulations of interactions between plunging breaking waves and pile group in finite water depth are performed using the two-phase flow model in REEF3D, an open-source computational fluid dynamics program to investigate the wave loads and flow kinematics characteristics. The Reynolds-averaged Navier–Stokes equation with the two equation k − ω turbulence model is adopted to resolve the numerical wave tank. The model is validated by comparing the numerical wave forces and free surface elevation with measurements from experiments. The computational results show fairly good agreement with experimental data. Four cases are simulated with different relative distances, numbers of cylinders, and arrangements. Results show that the wave forces on cylinders in the pile group are effected by the relative distance between cylinders. The staggered arrangement has a significant influence on the wave forces on the first and second cylinder. The interaction inside a pile group mostly happens between the neighboring cylinders. These interactions are also effected by the relative distance and the numbers of the neighboring cylinders.