Acoustic measurements of the velocity field beneath shoaling and breaking waves

An acoustic current meter attached to a servo-hydraulic surface-following device was used to obtain near-surface velocity measurements beneath breaking and near breaking surface gravity waves shoaling on a 1:40 beach. The data are compared to velocities predicted by two adaptations of linear theory: superposition and stretching. For unbroken and near breaking waves, the predictions are in close agreement with the measurements. For breaking and broken waves, near surface crest velocity measurements are influenced by air entrainment; trough velocities are relatively well predicted. The problems associated with the acoustic measurement of near-surface velocities are highlighted.     

Void fraction measurements and scale effects in breaking waves in freshwater and seawater

This paper follows from the work of Blenkinsopp and Chaplin (2007) and describes detailed measurements of the time-varying distribution of void fractions generated by breaking waves in freshwater, artificial seawater and natural seawater under laboratory conditions, along with flow visualisation of the entrainment process. The measurements were made with highly sensitive optical fibre phase detection probes and the results demonstrate that although an additional population of fine (d < 0.3 mm) bubbles existed in the seawater cases, the total volume and distribution of entrained air, and the spatial and temporal evolution of the bubble plumes were very similar in all three water types. The influence of water type may be relatively insignificant, but a numerical bubble tracking model shows that the effect of scale is an important consideration when modelling the post-entrainment evolution of breaker-entrained bubble plumes. Consequently the results suggest that while the use of freshwater in laboratory models of oceanic processes can be considered valid in most situations, the effect of scale may impact interpretation of the results.     

Large eddy simulation of breaking waves

A numerical model is used to simulate wave breaking, the large scale water motions and turbulence induced by the breaking process. The model consists of a free surface model using the surface markers method combined with a three-dimensional model that solves the flow equations. The turbulence is described by large eddy simulation where the larger turbulent features are simulated by solving the flow equations, and the small scale turbulence that is not resolved by the flow model is represented by a sub-grid model. A simple Smagorinsky sub-grid model has been used for the present simulations. The incoming waves are specified by a flux boundary condition. The waves are approaching in the shore-normal direction and are breaking on a plane, constant slope beach. The first few wave periods are simulated by a two-dimensional model in the vertical plane normal to the beach line. The model describes the steepening and the overturning of the wave. At a given instant, the model domain is extended to three dimensions, and the two-dimensional flow field develops spontaneously three-dimensional flow features with turbulent eddies. After a few wave periods, stationary (periodic) conditions are achieved. The surface is still specified to be uniform in the transverse (alongshore) direction, and it is only the flow field that is three-dimensional.The turbulent structures are investigated under different breaker types, spilling, weak plungers and strong plungers. The model is able to reproduce complicated flow phenomena such as obliquely descending eddies. The turbulent kinetic energy is found by averaging over the transverse direction. In spilling breakers, the turbulence is generated in a series of eddies in the shear layer under the surface roller. After the passage of the roller the turbulence spreads downwards. In the strong plunging breaker, the turbulence originates to a large degree from the topologically generated vorticity. The turbulence generated at the plunge point is almost immediately distributed over the entire water depth by large organised vortices. Away from the bed, the length scale of the turbulence (the characteristic size of the eddies resolved by the model) is similar in the horizontal and the vertical direction. It is found to be of the order one half of the water depth.     

Laboratory study of deep-water breaking waves

In an attempt to elucidate the mechanics of deep-water wave breaking, a variety of breaking waves, including spilling and plunging waves, of different length scales and geometries was studied. The waves were generated through wave-wave interactions using wave packets with constant-steepness components, constant-amplitude components, and also components following the Pierson-Moskowitz distribution. Wave steepening prior to breaking were found to cause an increase in the high frequency spectral slope of the wave spectrum. The slopes were correlated to the type of breaking and the intensity of the breaking. The energy loss through breaking varied with the spectral characteristics of the wave packet. On the other hand, it was also noted that, irrespective of the wave packet, the losses were from the higher frequency end of the first harmonics.     

Video DCIV measurements of mass and momentum fluxes and kinetic energies in laboratory waves breaking over a bar

The experimental investigation of water waves breaking over a barred beach in a glass walled flume is presented. The time series of the water levels along the flume were measured using wave gauges and video imaging of the water surface, providing estimates of the mean wave-heights and water levels at various positions along the flume. The instantaneous velocity fields were measured using digital correlation image velocimetry for positions beyond the initial breaking point. The mass (/velocity) and momentum fluxes, and kinetic energies were computed from the velocity flow fields by means of phase ensemble averaging and then time averaging of relevant quantities derived from the instantaneous velocity fields. These parameters reached a maximum value some distance shorewards of the break point on the bar. The relative density of the fluid in the crest of the wave, estimated using the forward and reverse velocity fluxes, was found to be in the range from 0.4 to 0.8. Preliminary analysis of the momentum fluxes and mean water levels indicates a decreasing dynamic pressure shorewards of a peak that occurs shortly after wave breaking.     

Prediction of breaking waves with neural networks

The height of a wave at the time of its breaking, as well as the depth of water in which it breaks, are the two basic parameters that are required as input in design exercises involving wave breaking. Currently the designers obtain these values with the help of graphical procedures and empirical equations. An alternative to this in the form of a neural network is presented in this paper. The networks were trained by combining the existing deterministic relations with a random component. The trained network was validated with the help of fresh laboratory observations. The validation results confirmed usefulness of the neural network approach for this application. The predicted breaking height and water depth were more accurate than those obtained traditionally through empirical schemes. Introduction of a random component in network training was found to yield better forecasts in some validation cases.     

Velocity predictions for shoaling and breaking waves with a Boussinesq-type model

In this paper, the performance of a 1-D Boussinesq model is evaluated against laboratory data for its ability to predict surf zone velocity moments. Wave evolution over a plane beach and a complex bathymetry both extending into the surf-zone is examined for six cases. For the plane beach, these comprise two cases, a spilling and a plunging cnoidal wave. For the complex bathymetry, these comprise four cases of longer and short wavelengths (spilling and plunging breakers), with regular and irregular periodicity. The model evaluation places emphasis on parameters of the wave field that could be used for the prediction of sediment transport; orbital velocity, undertow, velocity skewness, kurtosis and asymmetry. It is found that, despite an overestimation of the depth-averaged horizontal velocity in the regular waves cases, the predicted higher order velocity moments and undertow are in good agreement with the laboratory data. A bispectral analysis demonstrates that the nonlinear transfers of energy amongst the low order harmonics are well reproduced, but energy exchanges with the higher harmonics are less well predicted. As a result, the model handles velocity moments better in the shorter wave tests than in the long wave cases where triad interactions are stronger. Of the four parameters describing wave breaking, the model behaviour is most sensitive to the critical wave front slope φ_B, especially with regard to velocity skewness and kurtosis predictions. It is also found that increasing the thickness of the surface roller for the case of plunging breakers improves the model's performance.     

Equilibrium beach profiles under breaking and non-breaking waves

Simple theoretical models to determine the equilibrium profile shape under breaking and non-breaking waves are presented. For the case of breaking waves, it is assumed that the seaward transport in the undertow is locally balanced by a net vertical sedimentation, so that no bottom changes occur at equilibrium. The parameterization of the water and sediment flux in the surf zone yields a power curve for the equilibrium profile with a power of 2/3, which is in agreement with previous field investigations on surf zone profile shapes. Three different models were developed to derive the profile shape under non-breaking waves, namely (1) a variational formulation where the wave energy dissipation in the bottom boundary layer is minimized over the part of the profile affected by non-breaking waves, (2) an integration of a small-scale sediment transport formula over a wave period where the slope conditions that yield zero net transport determine equilibrium, and (3) a conceptual formulation of mechanisms for onshore and offshore sediment transport where a balance between the mechanisms defines equilibrium conditions. All three models produced equilibrium profile shapes of power-type with the power typically in the range 0.15–0.30. Comparison with field data supported the results obtained indicating different powers for the equilibrium profile shape under breaking and non-breaking waves.     

Modeling of the eddy viscosity by breaking waves

Breaking wave induced nearsurface turbulence has important consequences for many physical and biochemical processes including water column and nutrients mixing,heat and gases exchange across air-sea interface.The energy loss from wave breaking and the bubble plume penetration depth are estimated.As a consequence,the vertical distribution of the turbulent kinetic energy(TKE),the TKE dissipation rate and the eddy viscosity induced by wave breaking are also provided.It is indicated that model results are found to be consistent with the observational evidence that most TKE generated by wave breaking is lost within a depth of a few meters near the sea surface.High turbulence level with intensities of eddy viscosity induced by breaking is nearly four orders larger than υwl(=κuwz),the value predicted for the wall layer scaling close to the surface,where uw is the friction velocity in water,κ with 0.4 is the von Kármán constant,and z is the water depth,and the strength of the eddy viscosity depends both on wind speed and sea state,and decays rapidly through the depth.This leads to the conclusion that the breaking wave induced vertical mixing is mainly limited to the near surface layer,well above the classical values expected from the similarity theory.Deeper down,however,the effects of wave breaking on the vertical mixing become less important.     

近岸破碎波水体掺气及气泡输运过程研究

为准确探讨破碎波作用下气体如何卷入以及气泡的形成与输运特性, 文章结合粒子图像测速技术(particle image velocimetry, PIV)、高速相机和气泡测量系统, 以及基于Navier-Stokes方程的三维数值模型对气泡形成及其运动过程进行研究。研究结果表明: 文章建立的数值模型能合理地捕捉到破碎波作用下气体的卷入及其输运过程; 波浪的破碎会形成较大的气腔, 其破裂过程又将产生大量的气体微团; 气泡会增加水体的紊动, 造成水体与空气交界面附近形成大量的漩涡以及水体的飞溅; 气泡的破裂会消耗大量的水体能量, 同时发现较大的紊动动能与气泡的生成有关, 且气泡数随平均紊动动能的增加呈线性增长关系。     

Reflection and breaking of internal waves on a sloping beach

The reflection and breaking of internal waves on a sloping beach were studied in a small wavetank filled with water and petroleum. The dependence of the reflection coefficient of the internal waves on wave steepness and on beach slope is found to be very similar to that of surface waves. The reflection coefficient is small for the very gentle slope, increases rapidly as the slope increases, and becomes almost constant for the steep slope. The reflection coefficient decreases with increase of the wave steepness. Also, the transition slope at which the coefficient curve has the maximum gradient increases with increase of the wave steepness. Breaking pattern of the internal waves is classified into four types; breaking, semi-breaking, wrinkle-generating, and non-breaking. Their dependence on beach slope and wave steepness is examined. The regular sequence of the four breaking types from breaking to non-breaking is observed with decrease of wave steepness or with increase of beach slope.     

Corrected Incompressible SPH method for accurate water-surface tracking in breaking waves

A Corrected Incompressible SPH (CISPH) method is proposed for accurate tracking of water surface in breaking waves. Corrective terms are derived based on a variational approach to ensure the angular momentum preservation of Incompressible SPH (ISPH) formulations. The proposed CISPH method is applied to solve the Navier–Stokes equation for simulating the breaking and post-breaking of solitary waves on a plane slope. The enhanced precision (compared to the ISPH method) of the CISPH method is confirmed through both qualitative and quantitative comparisons with experimental data. The introduction of corrective terms significantly improves the capability and the accuracy of the ISPH method in the simulation of wave breaking and post-breaking.     

Impact pressure of breaking waves on vertical and sloping walls

Laboratory tests are conducted to measure the impact pressures of breaking waves on vertical, 5° forward, and 5, 10, 20, 30, and 45° backward sloping walls. The base structure of the wall has a foreshore slope of . Regular waves are used throughout the experiments for all wall angles. The maximum impact pressures on the wall are shown to satisfy the log-normal probability distribution. It is found from the present experiments that the impact pressures and resulting forces on sloping walls can be greater than those on a vertical wall. On the seven different walls tested, the maximum impact pressures occur most frequently slightly below the still-water level. The pattern of the impact pressure history does not change with the slope of the wall, and as the probability of maximum impact pressure decreases, the pressures around the peak pressure region of the impact pressure histories remain longer.     

一个波浪破碎散射模型的改进

为了得到与实测数据更为一致的散射模型,对KHCC03散射模型进行了改进.研究了考虑波浪破碎影响的KHCC03散射模型的适用范围.研究结果表明,KHCC03散射模型在入射角为25°～40°范围内,模型结果与实测数据吻合较好,在入射角小于25°和入射角大于40°的情况下,模型结果与实测数据差异较大.针对这一问题,对KHCC03模型进行了改进,结果表明:与原KHCC03模型相比,改进后的模型结果与实测数据吻合程度明显提高.     

A method for detecting the breaking of wind-generated waves in deep water

The breaking of wind-generated waves is an important phenomenon in the ocean, having close relation to many aspects of the ocean, such as air-sea interaction, ocean wave dynamics, oceanic remote sensing and ocean engineering. The first problem encountered in both its theoretical study and practical measurement is how to detect the breaking of waves.     

Energy dissipation in waves breaking on gentle slopes

The flow field of waves breaking on a gently sloping beach is shown to closely resemble that of hydraulic jumps. This supports the use of the hydraulic jump formulation for the breaking wave energy dissipation. A correction to this formulation, which takes into account the effects of turbulent flow, is found to explain the observed discrepancies between the classical theoretical result and the experiments satisfactorily. These findings are used to propose a simple, semi-empirical model for the wave height decay which includes the set-up. The model is generalized to a wider range of wave conditions by analyzing published data.     

Experimental study on the hydrodynamics of regular breaking waves

This paper illustrates the results of experimental research carried out in the wave flume of the Water Engineering and Chemistry Department laboratory of Bari Technical University (Italy) and based on the analysis of three different regular waves breaking on a sloping bottom. The investigation refers particularly to the surf zone, with the aim to develop two themes: the study of velocity and Reynolds shear stress distributions in the shoaling zone of a regular wave field and the study of turbulence in the breaking region, observing that these two aspects greatly influence many coastal processes, such as undertow currents, sediment transport and action on maritime structures.     

Geometrical properties of perfect breaking waves on composite breakwaters

The experimental results have so far shown that when a wave breaks on a vertical wall with an almost vertical front face at the instant of impact that is called perfect breaking or perfect impact, the greatest impact forces are produced on the wall. Therefore, the configuration of breaking waves is important in the design considerations of coastal structures. The present study is concerned with determining the geometrical properties of oscillatory waves that break perfectly on the vertical wall of composite-type breakwaters. The laboratory tests for perfect breaking waves on composite breakwaters are conducted with base slopes of 1/2, 1/4 and 1/6, and with berm widths of 0.00, 0.10, 0.20, 0.30 and 0.40 m. The shape and the dimensions of waves at the instant of perfect breaking on the wall are determined using a video camera. The experimental results for the geometrical properties of the breakers are presented non-dimensionally. Within the range of present experimental conditions, it is found that the dimensionless breaker crest height, h_b/d_w, and dimensionless breaker height, H_b/d_w, decrease; and, dimensionless breaker depth, d_w/H₀, increases with increasing relative berm width, B/D. The breaker height index, H_b/H₀, is almost unaffected by B/D. The deep-water wave steepness and the base slope of the breakwater do not seem to influence the geometrical properties of the breakers at wall systematically.