Breaking Wave Conditions Research Articles

Predicting Breaking Wave Conditions Using Gene Expression Programming

The forces and loading resulting from shallow water breaking waves are one of the most important drivers in coastal engineering design and morphological change. The importance of accurately and precisely predicting breaking wave conditions cannot be overstated. Using a novel dataset of laboratory and field scale breaking wave conditions, this study assesses the performance of widely applied empirical relationships for breaking waves and uses newly available artificial neural networks and gene expression programming (GEP) numerical methods to develop an accurate and easily applied predictor of breaking conditions for coastal engineers and planners. A novel GEP model is developed and shown to: provide excellent predictive ability at all scales, greatly improve prediction compared with previous works at laboratory scale, and clearly identify the relevant importance of seafloor slope and the water depth to wavelength ratio.

LIDAR-based detection of the post-typhoon recovery of a meso-macro-tidal beach in the Beibu Gulf, China

Because of global sea-level rising with frequent storm activities, most beaches in the world experience widespread erosion, which poses a significant hazard to beach management. The morphodynamic process of the evolution of a beach in response to storm activities is of increasing concern. Using a terrestrial laser scanner, the topography of Yintan beach was continuously observed for 33days with a 25cm spatial resolution digital elevation model (DEM) of that covered an area of 15ha before and after typhoon Rammasun. The short-term beach recovery was explored using a comprehensive approach, which included grey relational analysis, terrain analysis, Gaussian fitting, Gamma fitting, and Delft3D wave simulation methods. The results show that the Yintan beach recovery process can be divided into three stages with two transition points. Stage one began at the end of Rammasun, which indicated a weakly stable state with an average daily net erosion of −588m3, a mean beach slope that ranged from 0.96° to 1.28°, and a landform with no obvious alterations. After the vast accretion of 6874m3 of first transition, stage two, which was characterized by oscillations, occurred in the region with an average daily net erosion of −396m3 and a conspicuous beach slope reconstruction in the range of 0.94°–2.16°. During this stage, sandbar reconstruction played a key role. The second transition event arose at the end of stage two with a vast accretion of 5762m3. Afterwards, the daily net accretion of 200m3 and the beach slope range of 0.93°–1.74° dominated the region during stage three, and the beach surface became similar to that of the pre-Rammasun. Within the entire observation period, intense beach elevation changes that ranged from −15cm to −6cm and 6cm to 15cm mainly occurred in the sandbar and foreshore zones, respectively. Additionally, slight elevation changes (ranging from −4cm to 4cm) were densely distributed in the backshore and dunes, and moderate elevation changes (ranging from −6cm to −4cm and 4cm to 6cm) emerged along the entire beachface. It was concluded that the spatial distribution of the bottom shear stress that was induced by wave action was responsible for the reconstruction of the foreshore and sandbar after Rammasun, whereas the short-term beach recovery process was affected by the beach states in various wave breaking conditions.

On the imprint of surfactant‐driven stabilization of laboratory breaking wave foam with comparison to oceanic whitecaps

AbstractSurfactants are ubiquitous in the global oceans: they help form the materially‐distinct sea surface microlayer (SML) across which global ocean‐atmosphere exchanges take place, and they reside on the surfaces of bubbles and whitecap foam cells prolonging their lifetime thus altering ocean albedo. Despite their importance, the occurrence, spatial distribution, and composition of surfactants within the upper ocean and the SML remains under‐characterized during conditions of vigorous wave breaking when in‐situ sampling methods are difficult to implement. Additionally, no quantitative framework exists to evaluate the importance of surfactant activity on ocean whitecap foam coverage estimates. Here we use individual laboratory breaking waves generated in filtered seawater and seawater with added soluble surfactant to identify the imprint of surfactant activity in whitecap foam evolution. The data show a distinct surfactant imprint in the decay phase of foam evolution. The area‐time‐integral of foam evolution is used to develop a time‐varying stabilization function, and a stabilization factor, , which can be used to identify and quantify the extent of this surfactant imprint for individual breaking waves. The approach is then applied to wind‐driven oceanic whitecaps, and the laboratory and ocean distributions overlap. It is proposed that whitecap foam evolution may be used to determine the occurrence and extent of oceanic surfactant activity to complement traditional in‐situ techniques and extend measurement capabilities to more severe sea states occurring at wind speeds in excess of about 10 m/s. The analysis procedure also provides a framework to assess surfactant‐driven variability within and between whitecap coverage data sets.

Assessing the performance of formulations for nonlinear feedback of surface gravity waves on ocean currents over coastal waters

This study presents applications of a two-way coupled wave-circulation modelling system over coastal waters, with a special emphasis of performance assessments of two different methods for nonlinear feedback of ocean surface gravity waves on three-dimensional (3D) ocean currents. These two methods are the vortex force (VF) formulation suggested by Bennis et al. (2011) and the latest version of radiation stress (RS) formulation suggested by Mellor (2015). The coupled modelling system is first applied to two idealized test cases of surf-zone scales to validate implementations of these two methods in the coupled wave-circulation system. Model results show that the latest version of RS has difficulties in producing the undertow over the surf zone. The coupled system is then applied to Lunenburg Bay (LB) of Nova Scotia during Hurricane Juan in 2003. The coupled system using both the VF and RS formulations generates much stronger and more realistic 3D circulation in the Bay during Hurricane Juan than the circulation-only model, demonstrating the importance of surface wave forces to the 3D ocean circulation over coastal waters. However, the RS formulation generates some weak unphysical currents outside the wave breaking zone due to a less reasonable representation for the vertical distribution of the RS gradients over a slopping bottom. These weak unphysical currents are significantly magnified in a two-way coupled system when interacting with large surface waves, degrading the model performance in simulating currents at one observation site. Our results demonstrate that the VF formulation with an appropriate parameterization of wave breaking effects is able to produce reasonable results for applications over coastal waters during extreme weather events. The RS formulation requires a complex wave theory rather than the linear wave theory for the approximation of a vertical RS term to improve its performance under both breaking and non-breaking wave conditions.

Hydraulic stability of rock armors in breaking wave conditions

Armor layers of mound breakwaters are usually designed with empirical formulas based on small-scale tests in non-breaking wave conditions. However, most rubble mound breakwaters are constructed in the depth-induced breaking zone, where they must withstand design storms having some percentage of large waves breaking before reaching the structure; in these cases, the design formulas for non-breaking wave conditions are not fully valid. To characterize double-layer rock armor damage in breaking wave conditions, 2D physical model tests were carried out with a bottom slope m = 1/50. In order to develop a simple method to determine the wave parameters in the depth-induced breaking zone, experimental wave measurements were compared to the numerical estimations given by the SwanOne model. An analysis was conducted to select the best characteristic wave height to estimate rock armor damage when dealing with depth-induced breaking waves; the spectral significant wave height, Hm0, estimated at a distance of 3hs seaward from the structure toe, was found to be the most adequate. A new hydraulic stability formula is proposed for double-layer rock armors in breaking wave conditions, considering the observed potential 6-power relationship between the equivalent dimensionless armor damage and the Hm0 at 3hs seaward distance from the structure toe.

NUMERICAL MODELLING OF BREAKER DEPTH INDEX

The breaker depth index, γb, is commonly used to determine the wave height to water depth ratio where the wave will break (Horikawa, 1988). In the present study, γb has been calculated using a fully nonlinear Boussinesq Type Equations (BTE) wave model with implemented BCI (Breaking Celerity Index). The BCI is a phase-resolving type breaking criterion for calculating the incipient wave breaking conditions (D’Alessandro and Tomasicchio, 2008). The model suitability in predicting γb has been verified against physical data from an experimental investigation conducted with incident regular waves propagating along uniform 1:20 and 1:50 slope beaches (G.V. dos Reis, 1992), and estimates of γb from five existing empirical formulae (Battjes, 1974; Ostendorf and Madsen, 1979; Singamsetti and Wind, 1980; Smith and Kraus, 1990; Goda, 2010). The comparisons showed that BCI presents a better agreement with the physical data with respect to the other investigated formulae in determining the value of γb, independently from the breaker type. In addition, the verification of the BCI in determining γb has been extended to the observed data from a large-scale laboratory experiment on wave hydrodynamics performed over a fixed-bed barred beach (Tomasicchio and Sancho, 2002).

Estimation of slamming coefficients on local members of offshore wind turbine foundation (jacket type) under plunging breaker

In this paper, the slamming coefficients on local members of a jacket structure under plunging breaker are studied based on numerical simulations. A 3D numerical model is used to investigate breaking wave forces on the local members of the jacket structure. A wide range of breaking wave conditions is considered in order to get generalized slamming coefficients on the jacket structure. In order to make quantitative comparison between CFD model and experimental data, Empirical Mode Decomposition (EMD) is employed for obtaining net breaking wave forces from the measured response, and the filtered results are compared with the computed results in order to confirm the accuracy of the numerical model. Based on the validated results, the slamming coefficients on the local members (front and back vertical members, front and back inclined members, and side inclined members) are estimated. The distribution of the slamming coefficients on local members is also discussed.

An algorithm for modeling entrainment and naturally and chemically dispersed oil droplet size distribution under surface breaking wave conditions

A surface oil entrainment model and droplet size model have been developed to estimate the flux of oil under surface breaking waves. Both equations are expressed in dimensionless Weber number (We) and Ohnesorge number (Oh, which explicitly accounts for the oil viscosity, density, and oil-water interfacial tension). Data from controlled lab studies, large-scale wave tank tests, and field observations have been used to calibrate the constants of the two independent equations. Predictions using the new algorithm compared well with the observed amount of oil removed from the surface and the sizes of the oil droplets entrained in the water column. Simulations with the new algorithm, implemented in a comprehensive spill model, show that entrainment rates increase more rapidly with wind speed than previously predicted based on the existing Delvigne and Sweeney's (1988) model, and a quasi-stable droplet size distribution (d<~50μm) is developed in the near surface water.

Novel Methods for Optically Measuring Whitecaps under Natural Wave-Breaking Conditions in the Southern Ocean

AbstractTraditional methods for measuring whitecap coverage using digital video systems mounted to measure a large footprint can miss features that do not produce a high enough contrast to the background. Here, a method for accurately measuring the fractional coverage, intensity, and decay time of whitecaps using above-water radiometry is presented. The methodology was developed using data collected in the Southern Ocean under a wide range of wind and wave conditions. Whitecap quantities were obtained by employing a magnitude threshold based on the interquartile range of the radiance or reflectance signal from a single channel. Breaking intensity and decay time were produced from the integration of and the exponential fit to radiance or reflectance over the lifetime of the whitecap. When using the lowest magnitude threshold possible, radiometric fractional whitecap coverage retrievals were consistently higher than fractional coverage from high-resolution digital images, perhaps because the radiometer captures more of the decaying bubble plume area that is difficult to detect with photography. Radiometrically obtained whitecap measurements are presented in the context of concurrently measured meteorological (e.g., wind speed) and oceanographic (e.g., wave) data. The optimal fit of the radiometrically estimated whitecap coverage to the instantaneous wind speed, determined using robust linear least squares, showed a near-cubic dependence. Increasing the magnitude threshold for whitecap detection from 2 to 4 times the interquartile range produced a wind speed–whitecap relationship most comparable to the concurrently collected fractional coverage from digital imagery and previously published wind speed–whitecap parameterizations.

Nonlinear relativistic plasma resonance: Renormalization group approach

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

Oil slicks on water surface: Breakup, coalescence, and droplet formation under breaking waves

The ability to calculate the oil droplet size distribution (DSD) and its dynamic behavior in the water column is important in oil spill modeling. Breaking waves disperse oil from a surface slick into the water column as droplets of varying sizes. Oil droplets undergo further breakup and coalescence in the water column due to the turbulence. Available models simulate oil DSD based on empirical/equilibrium equations. However, the oil DSD evolution due to subsequent droplet breakup and coalescence in the water column can be best represented by a dynamic population model. This paper develops a phenomenological model to calculate the oil DSD in wave breaking conditions and ocean turbulence and is based on droplet breakup and coalescence. Its results are compared with data from laboratory experiments that include different oil types, different weathering times, and different breaking wave heights. The model comparisons showed a good agreement with experimental data.

Physical modelling of tsunami onshore propagation, peak pressures, and shielding effects in an urban building array

Wave experiments were conducted on a 1:20 length scale to measure water surface elevations and extreme pressures on and around idealized structural elements and arrays of structures. Experiments varied offshore wave characteristics and onshore structural configurations. Conditions in which waves broke on or just before the specimen caused maximum impulsive pressures. Pressures measured under nonbreaking wave conditions agreed with predicted values using design equations suggested by the Japanese Cabinet Office; however bare-earth water surface elevation inputs produced nonconservative estimates in breaking wave trials. Shielded structures experienced pressure reductions of 40–70% under breaking wave conditions. Results indicate that shielding elements constructed nearshore may reduce wave-induced damage. This dataset may be used to validate numerical models of tsunami propagation through urban environments.

Prediction of Incipient Breaking Wave-Heights Using Artificial Neural Networks and Empirical Relationships

The accurate prediction of shallow water breaking heights is paramount to better understanding complex nonlinear near shore coastal processes. Over the past 150 years, numerous empirical relationships have been proposed based on scaled laboratory datasets. This study utilizes a newly available field collected full-scale dataset of breaking wave conditions to investigate the accuracy of published empirical models and a novel artificial neural networks (ANN) model in predicting the final breaking wave-height for laboratory-scaled and full-scaled ocean waves. Performance is measured by comparison against both the field datasets and 465 separate datasets from 11 independent laboratory studies. The relationship of Rattanapitikon and Shibayama [2000 “Verification and modification of breaker height formulas,” Coastal Eng. J. 42 (4), 389–406.] outperformed all available empirical models when tested against only laboratory datasets, but was superseded by the relationship of Robertson et al. [2015 “Remote sensing of irregular breaking wave parameters in field conditions,” J. Coastal Res. 31 (2), 348–363.] when tested against only field datasets. However, this study noted that models developed based on scaled laboratory tests tend to underestimate the ocean full-scale breaking wave-heights. The training and testing of the ANN model were accomplished using 75% and 25% of the combined field and laborartory datasets. The ANN models consistently outperformed predictive accuracy of empirical models. Sensitivity analysis of the trained ANN models quantified the relative impact of individual wave parameters on the final breaking wave-height.

TTP로 피복된 경사식구조물의 처오름높이 산정식: 사면경사 1:1.5 조건

The runup height is an important design parameter to determine the crest elevation of coastal structures and seawalls. In this study, two dimensional wave runup tests for rubble-mound structure covered by tetrapods were conducted. Incident waves at the toe include nonbreaking, breaking and broken random wave conditions. A empirical formula to predict runup elevation of rubble-mound structure with 1:1.5 front slope was proposed on the basis of physical model test results using a surf similarity parameter. The test results from this study were compared with those from van der Meer and Stam(1992).

Observations of megaripples in the surf zone

Abstract Bedform measurements were obtained under shoaling and breaking wave conditions using a pencil-beam sonar in the intertidal zone at Skallingen, Denmark. Measurements were made during four individual tidal cycles starting from flat bed conditions at low tide and as the tide rose and the instruments entered the surf zone, megaripples appeared when the mobility number exceeded 240, which equates to the classic flat-bed criterion proposed by Dingler and Inman (1976). The megaripples were oriented cross-shore and their wavelength scaled with the wave orbital diameter. Wave ripples were observed when the mobility number was smaller which occurred mainly under shoaling waves. Since all bedforms were erased as the seabed became dry at low tide and perpendicular longshore currents were occasionally strong, the megaripples were of small amplitude but their dimensions were consistent with predictions from the literature. Their migratory behaviour in the first few hours of existence appeared more strongly related to self-organisation rather than to ambient hydrodynamics. A clear gap in bedform spacing at λ = 120 cm was identified between wave ripples and megaripples.

Influence of surface forcing on near-surface and mixing layer turbulence in the tropical Indian Ocean

An autonomous upwardly-moving microstructure profiler was used to collect measurements of the rate of dissipation of turbulent kinetic energy (ε) in the tropical Indian Ocean during a single diurnal cycle, from about 50m depth to the sea surface. This dataset is one of only a few to resolve upper ocean ε over a diurnal cycle from below the active mixing layer up to the air–sea interface. Wind speed was weak with an average value of ~5ms−1 and the wave field was swell-dominated. Within the wind and wave affected surface layer (WWSL), ε values were on the order of 10−7–10−6Wkg−1 at a depth of 0.75m and when averaged, were almost a factor of two above classical law of the wall theory, possibly indicative of an additional source of energy from the wave field. Below this depth, ε values were closer to wall layer scaling, suggesting that the work of the Reynolds stress on the wind-induced vertical shear was the major source of turbulence within this layer. No evidence of persistent elevated near-surface ε characteristic of wave-breaking conditions was found. Profiles collected during night-time displayed relatively constant ε values at depths between the WWSL and the base of the mixing layer, characteristic of mixing by convective overturning. Within the remnant layer, depth-averaged values of ε started decaying exponentially with an e-folding time of 47min, about 30min after the reversal of the total surface net heat flux from oceanic loss to gain.

Surface weathering and dispersibility of MC252 crude oil

Results from a comprehensive oil weathering and dispersant effectiveness study of the MC252 crude oil have been used to predict changes in oil properties due to weathering on the sea surface and to estimate the effective “time window” for dispersant application under various sea conditions. MC252 oil is a light paraffinic crude oil, for which approximately 55wt.% will evaporate within 3–5days when drifting on the sea. An unstable and low-viscosity water-in-oil (w/o) emulsion are formed during the first few days at the sea surface. This allows a high degree of natural dispersion when exposed to breaking wave conditions. Under calm sea conditions, a more stable and light-brown/orange colored water-in-oil (w/o) emulsion may start to form after several days, and viscosities of 10,000–15,000mPas can be achieved after 1–2weeks. The “time window” for effective use of dispersants was estimated to be more than 1week weathering at sea.

Pressure variations in a cryogenic liquid storage tank subjected to periodic excitations

The pressure change in a partially filled liquid nitrogen tank, subjected to periodic lateral forces, has been investigated experimentally. The cylindrical tank has a radius of R=0.148m and is filled up to 69% of the total volume (43×10−3m3). Six different sloshing conditions were considered, with the wave amplitude b of the first asymmetric mode ranging from b/R=0.12 up to wave breaking conditions of b/R⩾0.54. The tank was pressurized with nitrogen vapor and the pressure at sloshing initiation was in general pi≈250kPa. Pressure drops in the order of 100kPa have been measured and the dependency of these pressure drops on wave amplitude has been determined. The integrated temperature sensors allowed to measure the vapor temperature change and, with a high resolution, the thermal boundary layer in the liquid. The effective diffusion coefficient model of Das and Hopfinger (2009) [2] has been extended and allows calculating the temperature distribution in the thermal boundary layer, as well as the pressure drop as a function of the effective diffusion coefficient. A novel result is that the calculated temperature distribution in the thermal boundary layer deviates from the measured one, relating to a stop in the pressure drop. The sloshing Nusselt number NuS=De/D0 is shown to correlate well with a Reynolds number that contains the wave amplitude.

ライフサイクルコスト最小化による防波堤の目標整備水準の検討

This study discusses the evaluation method of target safety level of composite breakwaters and breakwaters covered with wave dissipating concrete blocks in view of minimum life cycle cost. Authors evaluated target safety levels of breakwaters under various conditions on waves and disaster loss costs. As the results, it was found that effect of disaster loss cost is smaller than that of wave conditions on target safety level. Target safety level was found to be strongly dependent on wave breaking conditions.

STABILITY OF RUBBLE MOUND BREAKWATERS IN SHALLOW WATER AND SURF ZONE : AN EXPERIMENTAL STUDY

Rubble-mound breakwaters are often pre-designed with empirical formulae allowing the estimation of armour stone size or weight, taking into account the wave conditions (mainly a characteristic wave height and a characteristic period), the type and density of stone or block used, the slope of the mound, the acceptable level of damage, etc. In deep water conditions, the existing formulas are rather well established (e.g. Hudson and Van der Meer formulas&#x0D; among others). They use as input data wave parameters that are well defined (e.g. the significant wave height H1/3 or sometimes the height H1/10) and easily accessible, from in situ measurements or from numerical wave models. In shallow water however, and in particular in breaking wave conditions (where most of the small breakwaters are built), a number of physical processes (refraction, shoaling and breaking) significantly modify the incoming waves.&#x0D; They also lead to changes in the wave height distribution (which can no longer be regarded as being of Rayleightype) and in the shape of the wave spectrum. This, combined with the fact that most of the models used nowadays for nearshore wave propagation are spectral wave models (e.g. SWAN, TOMAWAC, etc.) and thus provide spectral parameters as output (typically the spectral significant wave height Hm0 and the peak period Tp or the mean energetic&#x0D; period Tm-1,0) has raised the question of which characteristic wave parameter should be used in stability formulas for rubble-mound breakwaters in shallow water. This has led to the consideration of more representative wave parameters such as H2% or Tm-1,0 which are sometimes less accessible from existing wave database or numerical modelling studies. The objective of the present study is to review and compare several available methods to calculate armour stone weight in shallow waters, and to provide some insight into the applicability and limitations of these methods based on a series of wave flume experiments.