Breaking Wave Conditions Research Articles

Optimizing Particle Density for Accurate Wave Simulation: A Comparative Study of Non-Breaking and Breaking Wave Conditions

This study investigates the optimal particle density for accurate wave simulation in non-breaking and breaking wave conditions using Smoothed Particle Hydrodynamics (SPH). Simulations were conducted using various particle densities, or particles per wavelength, to evaluate their impact on simulation accuracy and computational efficiency. In tests involving regular, non-breaking waves, particle densities in the range of np per L = 560 to 800 were found to provide satisfactory accuracy and computational efficiency. Increasing the particle density beyond np per L = 800 for more complex setups involving breaking waves did not significantly improve accuracy but resulted in much higher computational costs. Overall, the range of np per L = 560 to 800 offers the best balance between accuracy and efficiency, making it a practical choice for simulations with limited resources. This study underscores the trade-offs between accuracy and computational demand, providing guidance on the selection of particle density for various wave simulation scenarios.

Experimental investigation of equilibrium and temporal scour around the round head of the rubble mound breakwater in case of breaking and non-breaking waves

In this study, local sediment movements caused by regular wave effects around the head section of rubble mound breakwater were investigated experimentally. The experiments were performed in a wave channel with a length of 33 m, a width of 3.6 m and a depth of 1.2 m. A plunger-type wave generator was located at the offshore side, generating regular waves of varying heights and periods. Uniform sandbed material of three different grain sizes was used, alongside two distinct breakwater slopes and six different wave characteristics. Experiments were performed under both breaking and non-breaking wave conditions. Time-dependent scour depth and water level measurements were determined by using measuring equipment working with an ultrasonic method. In the paper, new empirical relations were derived for temporal relative scour depths and the non-dimensional time scale parameter and the non-dimensional time scale parameter. The determination coefficient and scatter index of these derived relations were calculated and evaluated statistically. It was observed that the relations are in good agreement with those obtained from experiments. Additionally, the findings indicate that wave breaking significantly reduces the equilibrium scour depth.

Sufficient conditions of blowup to a shallow water wave equation

The blow-up features of a shallow water wave equation on the line R are investigated. The L2 conservation law is utilized to derive several estimates of solutions for the equation. Sufficient conditions for wave breaking and lifespan of the solutions are established. Our main results contain parts of the wave breaking conditions for the Fornberg–Whitham and Degasperis–Procesi equations in the previous literatures.

An overtopping formula for shallow water vertical seawalls by SWASH

There is now wide evidence that phase-resolving numerical models can capture the general physics of the overtopping process even under complex hydrodynamics. Based on this outcome, an extensive parametric study has been carried out with the model SWASH, to develop a design formula that uniformly predicts the overtopping rate at vertical seawalls for both breaking and non-breaking wave conditions. The use of the numerical model has allowed to vary the experimental conditions smoothly, avoiding the typical limitation of laboratory experiments. Furthermore, particular tests have been performed to assess whether, and up to which extent, the mean overtopping discharge is affected by the low frequency components of the incident wave spectrum.The formula relates the overtopping rate to a new water level statistic, which represents the average of the highest one-fourth wave displacements at the toe of the wall; it has initially been derived for planar beaches and then extended to the case of slope varying foreshores. A comparison with an array of 200 laboratory experiments confirms that the new parametrization can reduce the scatter of data compared to the EurOtop equation.

Size-resolved aerosol at a Coastal Great Lakes Site: Impacts of new particle formation and lake spray.

The quantification of aerosol size distributions is crucial for understanding the climate and health impacts of aerosols, validating models, and identifying aerosol sources. This work provides one of the first continuous measurements of aerosol size distribution from 1.02 to 8671 nm near the shore of Lake Michigan. The data were collected during the Lake Michigan Ozone Study (LMOS 2017), a comprehensive air quality measurement campaign in May and June 2017. The time-resolved (2-min) size distribution are reported herein alongside meteorology, remotely sensed data, gravimetric filters, and gas-phase variables. Mean concentrations of key aerosol parameters include PM2.5 (6.4 μg m-3), number from 1 to 3 nm (1.80x104 cm-3) and number greater than 3 nm (8x103 cm-3). During the field campaign, approximately half of days showed daytime ultrafine burst events, characterized by particle growth from sub 10 nm to 25-100 nm. A specific investigation of ultrafine lake spray aerosol was conducted due to enhanced ultrafine particles in onshore flows coupled with sustained wave breaking conditions during the campaign. Upon closer examination, the relationships between the size distribution, wind direction, wind speed, and wave height did not qualitatively support ultrafine particle production from lake spray aerosol; statistical analysis of particle number and wind speed also failed to show a relationship. The alternative hypothesis of enhanced ultrafine particles in onshore flow originating mainly from new particle formation activity is supported by multiple lines of evidence.

Influence of wind and waves on ambient noise and bubble entrainment depth in the semi-enclosed Baltic Sea

Semi-enclosed, fetch-limited waters create unique conditions for wind wave development and breaking. Parameters of breaking waves influence bubble entrainment depth and associated noise, which is why they differ in semi-enclosed sea compared to open waters. While the established noise-wind speed relationship holds in oceanic conditions, it differs in land-constrained basins like the Baltic Sea. To explore noise level, bubble entrainment depth and wind speed relationships, we conducted noise and sub-surface bubble measurements, coupled with wind observations, in the selected area of the Baltic Sea during two consecutive summers. A novel method was employed to estimate bubble entrainment depth under conditions of strong backscatter. Model data of wave field parameters were employed to assess their influence on noise level and bubble entrainment depth. Results suggest stronger connections between noise level and wind speed, as well as wave height, compared to wave age and wind sea steepness. The same patterns hold true for the correlation between bubble entrainment depth and both wind speed and wave field parameters. The parameterized noise level-wind speed relationship differs from that obtained for oceanic conditions and also varies across measurement periods. Observed differences were shaped by varying wind-wave conditions, notably differences in wind speed, direction, wave height, and the presence of swell. The noise level-bubble entrainment depth relation is reported for the first time for Baltic Sea conditions. For a thorough analysis of the influence of these factors on noise and bubbles, longer measurements under diverse wind-wave conditions are required to account for site-specific wave field characteristics.

Wave breaking phenomenon in the unidirectional non-local wave model

In this paper, we investigate wave breaking phenomenon in the unidirectional non-local wave model. Making use of the L2-conservation law and fine structure of the model, we show a local-in-space wave breaking condition for the unidirectional non-local wave model.

Numerical investigation of breaking waves impact on vertical breakwater with impermeable and porous foundation

Three different types of breaking waves impact on a vertical breakwater with impermeable and porous foundations are studied using our in-house solver, DUTFOAM. The numerical model is based on the Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) method and the numerical results are compared with experimental data to obtain a reasonable agreement. The characteristics of flow fields inside and outside the porous region under different breaking wave conditions are discussed and compared. When considering the impermeable foundation, breaking waves that entrapped small air pockets pose the most extensive pressure and forces, while the broken waves exerted the minimum. The porous foundation, with varying porosity values, dramatically affects the flow field and resulting structural forces. Our findings demonstrate that more considerable peak pressures and higher acting positions with porous foundations than impermeable situations for all three breaking wave conditions. Moreover, a sharp increase in horizontal forces and overturning moments occurs in broken wave conditions when the porosity equals 0.5, which poses a threat to stability and deserves additional attention.

Dimensionless Parameterizations of Air-Sea <em>CO</em><sub>2</sub> Gas Transfer Velocity on Surface Waves

Accurate quantification of air-sea gas transfer velocity is critical for our understanding of air-sea CO2 gas fluxes, global carbon budget and climate responses. CO2 transfer velocity is predominantly subject to constraints of wave-related dynamic processes at the ocean surface layer but is typically parameterized with wind speed. This study proposes and compares two parameterizations which accommodate dimensionless wave terms. The validations are conducted using both laboratory and field measurements of CO2 transfer and wave statistics. A scaling of bubble-mediated gas transfer is implemented into the formula that is linked to wave breaking probability. The improved parameterizations are capable of collapsing combined laboratory and field data sets which comprise diversified conditions of wind, wave and wave breaking.

Characterizing breaking wave slamming loads on bridge piers with probabilistic models of slamming maxima, rise and decay times

The piers of sea-crossing bridges always suffer from considerable breaking wave loads. But the uncertainties and variability of wave slamming maxima and time history have yet been understood quantitatively. This paper conducted a series of experiments in a wave flume to investigate the slamming load of breaking waves on bridge piers with different cross-sections. Four piers with three kinds of cross-sections under three breaking wave conditions were employed in the experimental program. The time history of breaking wave slamming load was characterized by three parameters, i.e., slamming maxima, rise and decay times. To account for the statistical variability of breaking wave load, a pair-copula decomposed trivariate joint probability model was developed to determine the joint distribution of slamming maxima, rise and decay times. The effects of pier geometry on the probabilistic modeling of slamming maxima, rise and decay times are analyzed based on the experimental results. The slamming maxima, rise and decay times follow the generalized extreme value (GEV), log-logistic, and gamma distribution, respectively. Their marginal and joint probabilities are sensitive to the pier shape. This study provides an effective probability method to characterize breaking wave slamming loads based on the experimental results.

Shear Turbulence in the High-Wind Southern Ocean Using Direct Measurements

Abstract The ocean surface boundary layer is a gateway of energy transfer into the ocean. Wind-driven shear and meteorologically forced convection inject turbulent kinetic energy into the surface boundary layer, mixing the upper ocean and transforming its density structure. In the absence of direct observations or the capability to resolve subgrid-scale 3D turbulence in operational ocean models, the oceanography community relies on surface boundary layer similarity scalings (BLS) of shear and convective turbulence to represent this mixing. Despite their importance, near-surface mixing processes (and ubiquitous BLS representations of these processes) have been undersampled in high-energy forcing regimes such as the Southern Ocean. With the maturing of autonomous sampling platforms, there is now an opportunity to collect high-resolution spatial and temporal measurements in the full range of forcing conditions. Here, we characterize near-surface turbulence under strong wind forcing using the first long-duration glider microstructure survey of the Southern Ocean. We leverage these data to show that the measured turbulence is significantly higher than standard shear-convective BLS in the shallower parts of the surface boundary layer and lower than standard shear-convective BLS in the deeper parts of the surface boundary layer; the latter of which is not easily explained by present wave-effect literature. Consistent with the CBLAST (Coupled Boundary Layers and Air Sea Transfer) low winds experiment, this bias has the largest magnitude and spread in the shallowest 10% of the actively mixing layer under low-wind and breaking wave conditions, when relatively low levels of turbulent kinetic energy (TKE) in surface regime are easily biased by wave events. Significance Statement Wind blows across the ocean, turbulently mixing the water close to the surface and altering its properties. Without the ability to measure turbulence in remote locations, oceanographers use approximations called boundary layer scalings (BLS) to estimate the amount of turbulence caused by the wind. We compared turbulence measured by an underwater robot to turbulence estimated from wind speed to determine how well BLS performs in stormy places. We found that in both calm and stormy conditions, estimates are 10 times too small closest to the surface and 10 times too large deeper within the turbulently mixed surface ocean.

Three‐Dimensional Measurements of Air Entrainment and Enhanced Bubble Transport During Wave Breaking

AbstractWe experimentally investigate the depth distributions and dynamics of air bubbles entrained by breaking waves in a wind‐wave channel over a range of breaking wave conditions using high‐resolution imaging and three‐dimensional bubble tracking. Below the wave troughs, the bubble concentration decays exponentially with depth. Patches of entrained bubbles are identified for each breaking wave, and statistics describing the horizontal and vertical transport are presented. Aggregating our results, we find a stream‐wise transport faster than the associated Stokes drift and modified Stokes drift for buoyant particles, which is an effect not accounted for in current models of bubble transport. This enhancement in transport is attributed to the flow field induced by the breaking waves and is relevant for the transport of bubbles, oil droplets, and microplastics at the ocean surface.

Hydraulic stability of cube-armored mound breakwaters in depth-limited breaking wave conditions

Armor erosion due to wave attack has been studied intensively since it is considered the main failure mode of mound breakwaters. Cube-armored mound breakwaters in depth-limited breaking wave conditions are common in practice but have received limited attention in the literature. In this study, 2D physical tests were performed on non-overtopped double-layer randomly-placed cube-armored mound breakwater models with armor slope cotα = 1.5 and bottom slope m = 2% in breaking wave conditions. Using the experimental results, a new hydraulic stability formula was derived with a coefficient of determination R2 = 0.85 based on a power relationship between the armor damage and the stability number and the dimensionless water depth. A lower hydraulic stability was found for the front slope of non-overtopped cube-armored structures in breaking wave conditions when compared to formulas given in the literature.

Beach morphodynamic classification using high-resolution nearshore bathymetry and process-based wave modelling

Classification of beach morphodynamic state relies on accurate representation of breaking wave conditions, Hb (plus grain size and spring tidal range). Measured breaking wave data, however, are absent from all but a handful of sites worldwide. Here, we apply process-based wave modelling for propagating offshore waves to the breaking zone using high-resolution nearshore bathymetry, obtaining representative and accurate Hb values for multiple beaches at regional scale, and thereby derive meaningful morphodynamic classifications that accord with observed beach state. Ninety-five beaches on the north coast of Ireland were investigated, with observed beach types and states compared to predictions based on morphodynamic parameters determined using wave, tide and sediment data, obtained from field surveys and detailed numerical wave modelling. The coast is exposed to micro-through meso-tides (0.43–3.90 m) and low sea through high swell waves (Hb = 0.13–1.18 m) and is composed of fine to medium sand resulting in a full range of beach types (wave-dominated, tide-modified and tide-dominated) and most beach states, thereby providing a comprehensive field laboratory to undertake such a comparison. We found that modal beach types reside within their predicted Relative Tide Range (RTR) and modal beach states close to the predicted dimensionless fall velocity (Ω) range. The use of high-resolution nearshore wave modelling to determine Hb was deemed the most appropriate approach for deriving predicted beach classification. The work follows the investigation of the same coast by Jackson et al. (2005) who found shortcomings in relating beach types to breaker wave conditions. However, advances in inshore wave modelling and access to high-resolution nearshore bathymetry since then have enabled improved estimates of breaker height, producing more accurate results and enhancing previous work. The results highlight the need to obtain accurate estimates of Hb and Tp if they are to be used effectively in predicting beach parameters. This work therefore sets a precedence for other coastal sites worldwide where detailed nearshore bathymetry is available and Hb can be derived from process-based wave modelling, improving the classification and prediction of morphodynamic beach type and state.

Oil droplet formation and vertical transport in the upper ocean

The dispersion of oil droplets near ocean surface is important for evaluating the impact to the environment. Under breaking wave conditions, the surface oil experiences mainly two processes: the generation of oil droplets at/near the water surface, and the transport of oil droplets due to ocean dynamics. We investigated the vertical behavior by incorporating the transport equation and the VDROP model. The transport equation adopted the ocean dynamics by K-profile parameterization (KPP) and the impact of additional turbulence by imposing the energy dissipation rate on the ocean surface. The oil droplet distribution was obtained, and the entrained distribution and entrainment rate was computed. The results shows that although the entrained distribution and the entrainment rate shares certain consistency with previous studies, divergences are also noticed. Accordingly, the model that describes the physics should be adopted to avoid incorrect qualification of the oil concentration dispersed in the ocean.

On the evolution of magnetic shock wave in the mixture of gas and small solid dust particles

The paper aims to analyze the evolutionary behavior of weakly nonlinear waves propagating in one-dimensional unsteady flow of perfectly conducting compressible fluid subjected to a transverse magnetic field with dust particles. The method of progressive wave approach is utilized to determine the evolution equation characterizing the propagation of wave and also obtained the condition for first wave breaking at finite time. Further, we analyze the behavior of acceleration wave propagating in the medium considered. Also, the propagation of disturbances in the form of sawtooth wave (half N-wave) is studied here. It is observed that the presence of mass fraction of solid particles (kp) and β both causes to slow down the decay process. Also, the effect of axial magnetic field is to increase the growth rate of sawtooth wave (Half N-wave) as compared to in the absence of axial magnetic field. Further, the effect of magnetic field is to slow down the decay process in the presence of mass fraction of solid particles (kp).

Sensitivity of a one-line longshore shoreline change model to the mean wave direction

The sensitivity of a one-line longshore shoreline change model to the incident wave direction is evaluated at Narrabeen Beach (Australia). As previously observed, the application of the one-line model using wave conditions generated along the 10-m depth contour produces a long-term reorientation of the coastline, with an initial transition period and then a new stable equilibrium during the 10-year period from 2005 to 2015. However, this coastline change in shoreline planform shape is not observed in the shoreline position measurements. The source of this error is investigated by assuming that it is caused by biases in the incident wave direction and by using a Monte Carlo approach to search for the optimal set of wave angle bias corrections to apply at each cross-shore transect. The obtained optimal values enable the one-line model to reproduce accurately the shoreline planform, and they are coherent with estimates of the wave breaking angle obtained independently using a nearshore wave propagation model. Then, using the corrected wave angle time series as a reference, a second Monte Carlo analysis is completed to investigate the sensitivity of the model to errors in the mean wave direction drawn from Gaussian distributions with varying standard deviations. The analysis shows the range of expected errors in shoreline position for an estimated range of errors in the mean wave direction at Narrabeen beach. This work highlights the importance of considering the sensitivity of one-line longshore model simulations to errors in the incident wave angle, which can be relatively large given the uncertainties in spectral wave model estimates of wave direction, in wave buoy observations, and in wave propagation methods or input bathymetry used to estimate wave breaking conditions.

Experimental and Numerical Study on the Wave, Surge, and Structure Interactions on a Coastal Residential Building

Lee, D.; Park, H.; Shin, S., and Cox, D.T., 2021. Experimental and numerical study on the wave, surge, and structure interactions on a coastal residential building. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 156–160. Coconut Creek (Florida), ISSN 0749-0208. Residential structures in the low-lying coastal region are often suffered from devastate coastal disasters, like storms and tsunamis. To minimize the loss and improve the resilience of a coastal community, it is crucial to understand structural damage and failure mechanism under extreme from extreme coastal events. Large-scale laboratory experiments of wood-framed residential houses were conducted to investigate the wave and surge effect on the structure and the structural failure mechanism. The tests were conducted by changing a surge level, wave period, and wave height condition, and measure hydro-kinematics and structural damage process. LIDAR scanning was conducted to collect the data of damage proportion on the structure during series of wave and surge conditions. A three-dimensional RANS model, olaFlow, was used to verify our numerical model, and applied to understand hydrodynamics near the structure. Three different wave breaking conditions, including non-breaking, breaking, and broken wave are tested and consequent wave induced forces on structure are compared for both undamaged structure and damaged structure conditions. The numerical model results showed a good agreement with the experimental results in water surface and velocity. The numerical results of wave induced force in damaged conditions showed 28∼43% smaller than those in undamaged conditions. This finding highlight that the damage level of a structure could affect predicting wave load on the structure.

Experimental study of erosion by waves on the lakeshore of lateritic soils

Many countries use hydropower as their main source of power generation. One of the factors responsible for erosion in hydroelectric reservoir margins is the action of wind-induced waves, which increases sedimentation and reduces their storage capacity. Despite potential economic and environmental damages, research into wave erosion processes on reservoir margins are found mainly in cohesive soils from cold regions. Research on erosion by waves of cohesive soils from savannah regions, which are commonly found in tropical reservoirs, is incipient; studies evaluating breaking and non-breaking wave conditions on this type of erosion are especially important. This work presents the results from 18 water wave channel experiments which were conducted to investigate the erosional processes by waves on lateritic soils, under breaking wave and non-breaking wave conditions, as well as determining the spatial distribution of the resulting sediments. Lateritic soil samples were placed on the wave channel and different conditions were tested. Wave frequencies varied from 0.272 to 0.999 Hz on four different beach slope angles of 22.50, 30.00, 45.00, and 60.00 degrees. In 80% of the tests, the erosion rate varied positively in a nonlinear form with the increase of the accumulated wave power. However, when the waves broke, erosion rate sometimes varied negatively and the sediment production tended to be reduced. High precision 3D surveys showed a good agreement between the maximum depth of the eroded surfaces and the power increase of the waves. The average roughness of the samples increased in 90% of the tests. The spatial distribution of sediments and their grain size distributions were also investigated. The waves’ driving forces were incapable of transporting the sediments away from their source of origin and, therefore, were not able to change the natural distributions of the grains with the simulated conditions.

Armor Damage of Overtopped Mound Breakwaters in Depth-Limited Breaking Wave Conditions

Armor damage due to wave attack is the principal failure mode to be considered when designing conventional mound breakwaters. Armor layers of mound breakwaters are typically designed using formulas in the literature for non-overtopped mound breakwaters in non-breaking wave conditions, although overtopped mound breakwaters in the depth-induced breaking wave zone are common design conditions. In this study, 2D physical tests with an armor slope H/V = 3/2 are analyzed in order to better describe the hydraulic stability of overtopped mound breakwaters with double-layer rock, double-layer randomly-place cube and single-layer Cubipod® armors in depth-limited breaking wave conditions. Hydraulic stability formulas are derived for each armor section (front slope, crest and rear slope) and each armor layer. The front slope of overtopped double-layer rock structures is more stable than the front slope of non-overtopped mound breakwaters in breaking wave conditions. When wave attack increases, armor damage appears first on the front slope, later on the crest and, finally, on the rear side. However, once the damage begins on the crest and rear side, the progression is much faster than on the front slope, because more wave energy is dissipated through the armored crest and rear side.