Breaker Line Research Articles

Contaminant transport in the surf zone

Dispersion of dissolved contaminants introduced at various locations within and just outside the surf zone are investigated. It is shown that the Longuet-Higgins model of surf-zone hydrodynamics adequately describes the distribution of longshore currents measured at the laboratory scale. Relations are derived between the longitudinal and transverse dispersion coefficients and the influencing parameters. The maximum longitudinal dispersion coefficients are associated with tracer releases near the breaker line, and longitudinal dispersion coefficients generally increase with travel time for distances up to at least 10 surf-zone widths. In contrast, transverse dispersion coefficients remain relatively constant for increasing travel time. The longitudinal and transverse dispersion coefficients can be significantly influenced by assumed values of local turbulent diffusion and cross-shore shear dispersion.

REDUCED COMPLEXITY MODELING OF SHORELINE RESPONSE BEHIND OFFSHORE BREAKWATERS

Prediction of the shoreline response behind offshore breakwaters is essential for coastal protection projects. Due to the complexity of the processes behind the breakwaters (e.g., wave diffraction, currents, longshore transport), detailed modelling needs high computational efforts. Therefore, simplifying the process effect in a simpler coastline model could be efficient. In this study, the coastline evolution model ShorelineS is used. A new routine was implemented in the model to adjust the wave heights and angles behind the offshore breakwaters. Two approaches from the literature and a newly introduced one were tested in this study. The model free grid system was used to simply track the breaker line; such an advantage also helped to form tombolo, which is not common for these types of models. The tests showed promising results for single and multi breakwaters systems; however, the newly introduced approach still needs further testing and refinement for better performance and less computational cost.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/mdCpmSQFO1Y

Trapped Low Frequency Waves on the Northern Israeli Continental Shelf

AbstractTime series of sea level measurements from different instruments deployed around the Haifa Bay area are analyzed. All observations indicate the existence of persistent low frequency oscillations with periods corresponding to approximately 1 hour and to approximately 30 minutes. These oscillations are persistent throughout most of the year and reached maximal wave heights of around 30 cm, a comparable value to tidal variations, making these oscillations an important factor in determining the average sea level elevation. The work identifies the phenomenon as resonant trapped waves, which are normal modes of the continental shelf extending from Haifa promontory to Achziv Canyon. Their temporal and spatial characteristics are learned through field measurement data analysis, wavelet analysis, numerical simulations, and exploration of an analytic solution. Finally, possible mechanisms for the generation of these waves are discussed. Such waves, which are commonly not surveyed, can be an important factor affecting coastal dynamics such as breaker line and coast line locations. Furthermore, the resonance behavior found has the capability of increasing the deep‐to‐shallow amplitudes in up to two orders of magnitude depending on incident angle. Noting that seismic or atmospheric events can agitate oscillation with similar wave periods, the intensification poses a hazard to Haifa Bay and coastal area.

Sediment transport under oscillatory flows

The results of Direct Numerical Simulations of the oscillatory flow over a cohesionless bed of spherical particles, mimicking sediment grains, are described. The flow around the sediment particles is explicitly computed by using the immersed boundary method, which allows the force and torque acting on the particles to be evaluated along with their dynamics. Different values of the Reynolds number and different values of the ratio between the grain size and the thickness of the boundary layer are considered such that the results are useful to quantify the sand transport generated by sea waves in the region offshore of the breaker line. Therefore, the results are used to test the capability of empirical sediment transport formulae to predict the sediment transport rate during the oscillatory cycle.

Experimental Observations of Turbulent Events in the Surfzone

In coastal dynamics, large-scale eddies transport and spread smaller turbulent vortices both towards the sea surface, thus contributing to the processes of air-water gas transfer, and towards the sea bottom, inducing sediment pick-up and resuspension. The mechanical role of the breaking-induced vortices to the redistribution of turbulence and turbulent kinetic energy is still unclear and needs a more thorough study, possibly supported by more measurements in this field. Based on this, the present paper aims to investigate the effects of experimental breaking waves in the surf zone. Two regular breaking waves, a spiller and a plunger, which propagate on a fixed slope, were generated in a laboratory channel and were examined shoreward to the breaker line. The measurements of their velocities in the cross-shore plane were assessed by means of a 2D Laser Doppler Anemometer. At the same time and location, elevation data were also acquired using a resistive wave gauge. Here, the principal characteristics are addressed in terms of turbulent intensities, turbulent kinetic energy, length scales and coherent motions. Our results could thus contribute to better define conceptual models used in typical engineering applications in coastal areas.

An Analytical Solution for Nearshore Circulation Driven by Focused/Defocused Waves

An offshore shoal or bar refracts ocean surface waves and causes wave focusing/defocusing on the adjacent beach. Wave focal patterns characterized by alongshore variations in wave height, wave angle, and breaking location induce alongshore non-uniformities of wave setup and nearshore circulation, e.g., rip currents and alongshore currents, in the surfzone. A simplified analytic model for nearshore circulation generated by focused/defocused waves on a planar beach is developed and theoretical solutions are obtained using transport stream function and perturbations in alongshore distributions of wave height and wave angle at the breaker line. The analytic model suggests that alongshore currents are strongly affected by a pair of counter-rotating vortices generated shoreward of the wave focal zone. The vortices are persistent, and their strengths depend on the amplitudes of alongshore variations in wave height and wave angle. The alongshore gradient in wave height tends to intensify the vortices while the convergence of wave angle tends to weaken the vortices. Divergent flows associated with the vortices in the surfzone are intense, strengthening alongshore currents in the downstream of the wave focal zone and weakening alongshore currents or causing flows reversal in the upstream. Alongshore currents are modulated by rip currents associated with the wave focusing/defocusing patterns.

Experimental study of small scale siphon breaker to verify Siphon Breaker Simulation Program (SBSP)

This study was conducted with the design of a small scale siphon breaker using the Siphon Breaker Simulation Program (SBSP). The feasibility of SBSP was researched in a small scale experimental facility. C factor, Chisholm B coefficient, and simulation results of the Undershooting Height (UH) were obtained by the SBSP. The major parts of the experimental facility are an upper tank, a lower tank, a downcomer, and a Siphon Breaker Line (SBL). The experiment variables are LOCA sizes of 30 and 38 mm and SBL sizes of 2/8, 3/8, and 4/8 in. The overall analysis of the air sweep-out mode was conducted by observing the differential pressure, flow patterns in the downcomer, and the UH. In addition, the reasons for the deviation of the UH prediction were analyzed in terms of the C factor-Chisholm B coefficient relation. We observed partial and zero sweep-out modes from the experimental results with SBL 3/8 and 4/8 in. In these experiments, the UH prediction results by the SBSP showed an average error of approximately 16 mm, which deviates by 2.5% compared with the height of the upper tank. Therefore, the SBSP predicts the experimental results well. Contrarily, full, partial and zero sweep-out modes were observed for the SBL 2/8 in. experiment. The UH for this experiment was predicted with a maximum error of approximately 48%. Consequently, the experimental results fairly agree with the SBSP model predictions for C factor range of 100,000–420,000. However, the disagreement becomes larger as the C factor increases and since the UH is too big in a high C factor range, in which full sweep-out mode occurs, the high C factor range (over 420,000) should be avoided during the siphon breaker designing stage. Finally, the SBSP could be considered as a reasonable simulation software for designing various scale siphon breakers.

Field and numerical modelling studies for an efficient placement of roof bolts as breaker line support

Depending upon the site conditions, field studies of roof bolt-based breaker line support (RBBLS) found that its positions need to vary from 0.5 to 2m out-bye side from the goaf edge for a better performance. This variation is done to adjust the extent of spalling/loosening of sides of the surrounding natural supports. As per the studied site conditions of different mechanised depillaring operations, a detailed parametric investigation is conducted on the simulated models to estimate rock load height (RLH) for a given site conditions. Results of the static (elastic) simulation study are used for an estimation length of a bolt in the RBBLS. But the field measurements found that the bolts were subjected to dynamic loading during caving of the roof strata. Accordingly, the support resistance of the RBBLS is estimated considering the dynamic effect of caving, derived from the field measurements. On the basis of these investigations, empirical formulations are attempted among the relevant geo-mining parameters for the design of a RBBLS.

Rock Mechanics Considerations for Roof Bolt-Based Breaker Line Design

Application of roof bolts to support in developed galleries during underground coal mining is a common practice. Mechanised depillaring (MD) applies these roof bolts to support the galleries at the goaf edge also. Goaf edge of a depillaring panel inherits a number of openings, which provides least resistance path for the caving roof strata to encroach the working areas. Influence of strata caving, inside the goaf, make it difficult to apply conventional roof bolt support norms in these openings at the goaf edge. Basic rock mechanics considerations find that the mining induced stress development improves the efficacy of roof bolt at the goaf edge. Application of, relatively, high density of bolts as roof bolts-based breaker line support (RBBLS) in the existing openings at the goaf edge to arrest the goaf encroachment is found to be working satisfactorily only if the surrounding natural supports are stable. The stability of a natural support, in and around the goaf edge, is found to be diluted due to side spalling/loosening caused by the mining induced stress. Different field experiences found that a high value of the stress causes side spalling/loosening in natural supports, standing in and around the goaf edge. Under the existing geo-mining conditions of some of the recent MD operations in Indian coalfields, the extent of spalling varied from 0.5 m to 2 m only. Considering an acceptable dimension of the rib/snook for these site conditions, the position of RBBLS is shifted out-bye from the goaf line as per the extent of spalling, which performed satisfactorily in the field. Presenting basic working principles of a RBBLS at the goaf edge; this paper discusses different field experiences for a suitable positioning of the RBBLS at the goaf edge.

The Role of Infragravity Waves in Near-Bed Cross-Shore Sediment Flux in the Breaker Zone

Results from a series of field experiments, conducted to investigate the influence of infragravity waves (from wave groups), ripple type and location relative to the breaker line on cross-shore suspended sediment flux close to the sea bed in nearshore environments, are presented. The field data were collected from Cable Beach (Broome) and Mullaloo Beach in Western Australia and Chilaw in Sri Lanka. These beaches experience different incident wave, tidal and morphological conditions, with Cable Beach having a 10-m spring tidal range, whilst the other two beaches have tidal ranges <1.0 m. Measurements included simultaneous records of surface elevation, two-dimensional horizontal current velocities and suspended sediment concentrations, together with half-hourly observations of the seabed topography. Although most of the data sets were obtained just outside of the surf zone, a few results from inside of the surf zone were also included. A significant correlation between wave groups and suspended sediment concentration was found at all of the measurement sites, either with or without bed ripples. The direction and magnitude of cross-shore suspended sediment flux varied with location with respect to the breaker line; however, other parameters, such as bed ripples and velocity skewness, could have influenced this result. In Broome, where the measurement location with respect to the breaker line varied with the tidal cycle, the cross-shore sediment flux due to swell waves was shoreward inside and just outside of the surf zone and seaward farther offshore of the breaker line. Further, sediment flux due to swell waves was onshore when the seabed was flat and offshore over post-vortex ripples. Sediment flux due to swell waves was onshore when the normalised velocity skewness towards the shore was high (positive); the flux was offshore when the skewness was lower, but positive, suggesting the influence of other parameters, such as ripples and grain size. The net cross-shore sediment flux was onshore when the Dean number was less than 1.67 and offshore when the Dean number was greater than 1.67. Nevertheless, the Dean number did not account for the influence of ripples or velocity skewness. The cross-shore sediment flux at the infragravity frequency was mainly offshore outside of the surf zone, whereas it varied between onshore and offshore inside of the surf zone.

Lagrangian description of gravity-capillary waves propagating on a sloping bottom

An asymptotic solution that describes a small amplitude gravity-capillary wave propagating on the surface of a gentle sloping beach is derived in the Lagrangian coordinates. The analytical solution in Lagrangian form satisfies the zero pressure at the free surface. In the Lagrangian approximation, the parametric expression of water particles can be obtained directly and explicitly as a function of the wave steepness, the bottom slope and surface tension. The analytical solution for wave asymmetry parameter up to the breaker line for an arbitrary bottom slope can also be derived. The Lagrangian solution enables the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile which leads to wave breaking. Furthermore, by comparing the theoretical values of wave asymmetry with experimental results, it is found that theoretical results of the present solution are in good agreement with the experimental data. It is also found that surface tension lower the breaking wave height, lengthen the wave length and increase the breaking water depth.

Horizontal circulation and jumps in Hamiltonian wave models

Abstract. We are interested in the modelling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian dynamics of a new water wave model, incorporating both the shallow water and pure potential flow water wave models as limiting systems. It is based on a Hamiltonian reformulation of the variational principle derived by Cotter and Bokhove (2010) by using more convenient variables. Our new model has a three-dimensional velocity field consisting of the full three-dimensional potential velocity field plus extra horizontal velocity components. This implies that only the vertical vorticity component is nonzero. Variational Boussinesq models and Green–Naghdi equations, and extensions thereof, follow directly from the new Hamiltonian formulation after using simplifications of the vertical flow profile. Since the full water wave dispersion is retained in the new model, waves can break. We therefore explore a variational approach to derive jump conditions for the new model and its Boussinesq simplifications.

STEADY CURRENTS INDUCED BY SEA WAVES PROPAGATING OVER A SLOPING BOTTOM

A numerical model aimed at computing the mean velocity generated by a sea wave propagating over a sloping bottom, offshore the breaker line, is presented. The model is based on the assumption that the fluid domain can be partitioned into two boundary layers and a core region where at a first order of approximation the flow can be regarded as irrotational. The irrotational flow is computed by using a theory based on the assumption of small amplitude waves which allows both fully absorbed waves and partially reflected waves at the coastline to be considered. The distribution of the mean velocity is controlled by the ratio between the thickness of the boundary layer and the wave amplitude. When this ratio is small, the mean velocities are rather constant along the depth and a second boundary layer develops close to the bottom. In the case of fully reflected waves such boundary layer separates and the mean vorticity can be convected far from the bottom.

Evolution of the turbulence structure in the surf and swash zones

The velocity field and turbulence structure within the surf and swash zones forced by a laboratory-generated plunging breaking wave were investigated using a particle image velocimetry measurement technique. Two-dimensional velocity fields in the vertical plane from 200 consecutive monochromatic waves were measured at four cross-shore locations, shoreward of the breaker line. The phase-averaged mean flow fields indicate that a shear layer occurs when the uprush of the bore front interacts with the downwash flow. The turbulence characteristics were examined via spectral analysis. The larger-scale turbulence structure is closely associated with the breaking-wave- and the bore-generated turbulence in the surf zone; then, the large-scale turbulence energy cascades to smaller scales, as the turbulent kinetic energy (TKE) evolves from the outer surf zone to the swash zone. Smaller-scale energy injection during the latter stage of the downwash phase is associated with the bed-generated turbulence, yielding a −1 slope in the upper inertial range in the spatial spectra. Depth-integrated TKE budget components indicate that a local TKE equilibrium exists during the bore-front phases and the latter stage of the downwash phases in the outer surf zone. The TKE decay resembles the decay of grid turbulence during the latter stage of the uprush and the early stage of the downwash, as the production rate is small because of the absence of strong mean shear during this stage of the wave cycle as well as the relatively short time available for the growth of the bed boundary layer.

Hydrodynamics of a headland-bay beach—Nearshore current circulation

This paper is devoted to the analysis of the hydrodynamic equilibrium of a headland or semi-elliptic shaped beach. It is shown that the state of equilibrium depends not only on the in- and outgoing sediment but also on the accommodation of the sediment within the embayment. The shape and relative depth of shoals, or settling zones, also directly affect the wave and current patterns inside the bay, within which the resultant breaker line almost stops wave-induced currents at some locations, whereas the magnitude of current increases at other locations. Several numerical tests are analytically conducted in a semi-elliptic beach with two symmetrical shoals of varying relative depth where circulatory current systems are detected and analyzed. Numerical modelling for wave climate and wave-induced current estimation is also presented in order to corroborate results and provide a tool for complicated and/or physical domains. The results lead to a redefinition of the concept of equilibrium for headland-bay beaches taking into account not only the net sediment transport but also the role of the formation and disappearance of settling zones, as well as sediment interchanges between the beach and shoals.

Modelling the impact on coastal morphology of the water management in transboundary river basins

Purpose – To study the impact of River Nestos (North Greece) dams construction on coastal morphology.Design/methodology/approach – In order to study the evolution of the coastal morphology in the area, an “one‐line shoreline change model” was developed (PELNCON). The model's input comprises the field characteristics, the wave characteristics at the breaker line and a “source” term for the sediment supply rate by River Nestos. The model calculates the shoreline change over a given period of time. The annually transported sediment quantity by the river is estimated using filed measurements and other models' results for various sites along the Greek part of the hydrologic basin of Nestos (Nestos is a transboundary river extending along Greece and Bulgaria).Findings – The “PELNCON” results demonstrate a serious erosion threat for the coastal area due to the sediment budget deficit of about 1.8 × 106 m3/year.Research limitations/implications – The developed model is subject to common structural weaknesses of c...

Discussion of “A simple method to determine breaker height and depth for different deepwater wave height/length ratios and sea floor slopes”, by J.P. Le Roux [Coastal Engineering 54 (2007) 271–277

In the recent paper by J.P. Le Roux [Coastal Engineering 54 (2007) 271–277], the author provides a simplified approach to calculating the depth, length, and height of waves at the onset of depth-induced breaking (i.e. at the breaker line). However, the proposed methodology and the comparisons to other methods suffer from a large number of inconsistencies and basic calculation errors. In addition, there are a number of erroneous physical interpretations and many of the conclusions are based on erroneous data. The remaining conclusions are either not new or based on circular logic, such as to render them moot. In the following, we will not attempt to point out all the errors or inconsistencies that we found, instead we focus on major points of contention.

Nearshore Wave Modeling with High-Order Boussinesq-Type Equations

The accuracy of using high-order Boussinesq-type models as compared to the typical order models is examined in this paper. The high-order model used is the two-layer model of Lynett and Liu in 2004, which captures both linear and nonlinear wave evolution up to kh≈6 . The physical situations examined all involve nearshore breaking, and an eddy-viscosity type breaking model is adopted for the two-layer model. One-horizontal dimension setups are the focus of this paper. It is shown that high-order models show significant benefit very near to the breaker line. For regular incident waves, the overshoaling seen in the one-layer (“fully nonlinear” extended Boussinesq) model is due to rapid increase of energy in the fifth and higher harmonics. These high-order nonlinear components are captured well in the two-layer model. The two-layer model also exhibits a noticeable accuracy increase for cnoidal waves breaking on a slope. For regular wave evolution over a bar, the high-order models are in good agreement with ex...

Jetski-based plankton towing as a new method of sampling larval fishes in shallow marine habitats

I tested jetski-based plankton towing as a new method of sampling larval fishes in a shallow marine environment in warm temperate South Africa. Larval fishes were collected by towing a stainless-steel ring net behind a three-man jetski. The sampling technique was designed and tested to overcome problematic sampling of shallow sandy beach surf zones and the adjacent, shallow nearshore immediately seaward of the surf zone (behind the breaker line) with the same type of equipment. The composition, density, stage of development, estuary association, and length frequency of larval fish catches obtained by the new sampling method in the surf zone and in the adjacent shallow nearshore were compared. The success of the technique was evaluated by determining the extent of replication of known trends observed in other surf studies in the same climatic region of South Africa using either a seine or pushnet. Preflexion and postflexion larval fishes were collected. Larvae of the family Sparidae dominated the catches. Trends in catch composition, estuary association, and length frequency of the larvae were similar to those found in other studies of warm temperate South African surf zones. Density of larvae varied depending on the type of equipment used, although these results are tentative given the subjectivity of calculation of the water volume sampled and the extent of nursery use by larvae in the habitats sampled in each study. Increased towing times are recommended. Jetski-based plankton towing is a useful alternative technique for sampling larval fishes in shallow habitats and can easily be applied in surf zones, shallow nearshore areas, and estuaries. The technique greatly increases sampling agility in previously problematic sampling areas.

Theoretical analysis of surface waves shoaling and breaking on a sloping bottom. Part 2: Nonlinear waves

This is the second of two papers on the theoretical analysis of surface wave propagating on sloping bottoms. In the first paper, the linear solution for velocity potential was derived as a function of bottom slope α to the third order. In this paper, Part 2, we use the two-parameter perturbation method to develop a new mathematical derivation to describe nonlinear periodic gravity surface waves propagating over sloping bottoms. In the Eulerian coordinate system, the velocity potential is obtained as a function of the nonlinear ordering parameter ε and the bottom slope α perturbed to the fourth order ( ε m α n , m + n = 4). A time-decoupled solution is derived and the condition of the conservation of mass flux is examined in detail for the first time. Then, the solution is used to estimate the mean return current for waves progressing over the sloping bottom. The analytical solution for wave asymmetry and set-down valid up to the breaker line for an arbitrary bottom slope can also be obtained. Besides, the direct influence of nonlinearity and bottom slope upon the wave number and a new second-order dispersion relation is also derived. This nonlinear analytical solution is verified by reducing to the classical Stokes fourth-order solution of progressive waves in both the limit of deep water and of constant depth. Furthermore, by comparing the theoretical values of wave asymmetry and set-down with the experimental data, it is found that theoretical results of the present solution are in good agreement with the experimental data.