Experimental Study of Wave Breaking on Gentle Slope

—An experimental study of regular wave and irregular wave breaking is performed on a gentleslope of 1:200.In the experiment,asymmetry of wave profile is analyzed to determine its effect on wavebreaker indices and to explain the difference between Goda and Nelson about the breaker indices of regu-lar waves on very mild slopes.The study shows that the breaker index of irregular waves is under less influ-ence of bottom slope i,relative water depth d/L_0 and the asymmetry of wave profile than that of regularwaves.The breaker index of regular waves from Goda may be used in the case of irregular waves, whilethe coefficient A should be 0.15.The ratio of irregular wavelength to the length calculated by linear wavetheory is 0.74.Analysis is also made on the waveheight damping coefficient of regular waves after break-ing and on the breaking probability of large irregular waves.     

An experimental investigation of plunging breaker boundary layers in the transformation zone

Experimental investigation is made on the boundary layers of the transformation zone (i.e. the region between the last symmetrical wave profile depth and the breaking point) of plunging breakers propagating on a smooth beach with 1/12 uniform slope. Using a laser anemometer, the particle velocities are measured at four verticals along the transformation zone for three different steepnesses of waves within the plunging breaker range. The boundary layer flow in the transformation zone is found mostly of turbulent character and vertical distribution of particle velocities does not seem to conform to the classical law of the wall distribution given for steady-flow boundary layers. The results show that free-stream particle velocities, in the boundary layer of the breaker under the crest phase, increase considerably as the wave progresses towards the breaking point. The boundary layer thickness, defined as the velocity-affected region, remains constant throughout the transformation zone but it decreases with increasing deep-water wave steepness for the particular beach slope tested.     

卷破波作用下沙质岸滩剖面形态判别式初探

通过波浪水槽实验,开展不同类型波浪作用下的沙质岸滩演化规律研究工作。本次实验研究不考虑比尺,采用1:10与1:20组成的复合沙质斜坡对岸滩进行概化,选取规则波和椭圆余弦波两种典型波浪作用,对波浪的传播、变形和破碎、上爬、回落过程以及波浪作用前后沙质岸滩床面地形进行了观测,探讨波浪作用下沙质岸滩剖面演化规律。本文实验工况中,规则波作用下,岸滩剖面呈现出沙坝剖面和滩肩剖面,椭圆余弦波作用下的岸滩剖面均呈滩肩形态,发现岸滩剖面形态不仅与波浪作用类型、强度、周期等因素相关,还与波浪破碎的强度等因素有关。通过对实验过程中现象的进行观察和分析,引入了卷破波水舌冲击角的概念。对波浪卷破破碎后形成的水流挟沙运动与岸滩剖面形态的关系进行定性分析,对水舌冲击角与Irribarren参数之间的关系进行定量分析,基于Irribarren参数与岸滩剖面形态的关系初步建立了波浪作用下沙质岸滩剖面形态判别关系式。通过本文实验结果和前人实验结果对趋势线进行拟合,求得其判别系数,判别式能够较好地划分淤积型岸滩、侵蚀型岸滩及过渡型岸滩三种岸滩形态。     

海底山脊作用下内孤立波破碎研究

基于实验室水槽实验,研究了内孤立波在海底山脊地形存在下的破碎过程.实验设置了两层流体的分层环境,定量地控制了上下层水体厚度及密度,使用不同高度的高斯地形模拟实际的海山作用,讨论了不同高度地形作用下内孤立波破碎过程的异同.实验结果表明,内孤立波的破碎过程中由于逆压梯度的存在,在地形处发生边界层分离,产生了底边界层反向射流...     

Dynamics of surf-zone turbulence in a strong plunging breaker

The characteristics of turbulence created by a plunging breaker on a 1 on 35 plane slope have been studied experimentally in a two-dimensional wave tank. The experiments involved detailed measurements of fluid velocities below trough level and water surface elevations in the surf zone using a fibre-optic laser-Doppler anemometer and a capacitance wave gage. The dynamical role of turbulence is examined making use of the transport equation for turbulent kinetic energy (the k-equation). The results show that turbulence under a plunging breaker is dominated by large-scale motions and has certain unique features that are associated with its wave condition. It was found that the nature of turbulence transport in the inner surf zone depends on a particular wave condition and it is not similar for different types of breakers. Turbulent kinetic energy is transported landward under a plunging breaker and dissipated within one wave cycle. This is different from spilling breakers where turbulent kinetic energy is transported seaward and the dissipation rate is much slower. The analysis of the k-equation shows that advective and diffusive transport of turbulence play a major role in the distribution of turbulence under a plunging breaker, while production and dissipation are not in local equilibrium but are of the same order of magnitude. Based on certain approximate analytical approaches and experimental measurements it is shown that turbulence production and viscous dissipation below trough level amount to only a small portion of the wave energy loss caused by wave breaking. It is suggested that the onshore sediment transport produced by swell waves may be tied in a direct way to the unique characteristics of turbulent flows in these waves.     

Numerical study on vertical structures of undertow inside and outside the surf zone

Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and t...     

Seabed shear stresses under irregular waves plus current from Monte Carlo simulations of parameterized models

Shear stresses on a rough seabed under irregular waves plus current are calculated. Parameterized models valid for regular waves plus current have been used in Monte Carlo simulations, assuming the wave amplitudes to be Rayleigh-distributed. Numerical estimates of the probability distribution functions are presented. For waves only, the shear stress maxima follow a Weibull distribution, while for waves plus current, both the maximum and time-averaged shear stresses are well represented by a three-parameter Weibull distribution. The behaviour of the maximum shear stresses under a wide range of wave-current conditions has been investigated, and it appears that under certain conditions, the current has a significant influence on the maximum shear stresses. Results of comparison between predictions and measurements of the maximum bottom shear stresses from laboratory and field experiments are presented.     

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 wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.     

Kinematics of overturning solitary waves and their relations to breaker types

Numerical simulations using a full-nonlinear BIM (Boundary Integral Method) potential-theory wave model are carried out to study the internal velocity and acceleration fields of an solitary wave overturning on a reef with vertical face (submerged breakwater) and their relation to breaker type. The simulations make it clear that the jet size normalized by the incident wave height is uniquely governed by the crown height of the reef, while the jet shape is similar and independent of the size. Further, they reveal that the overall internal kinematics of overturning waves is clearly related to the jet size. As the jet size increases and the breaker type changes from spilling to plunging, the kinematics thus become increasingly different from those of steady waves. Water particles with the greatest velocities or accelerations within the wave converge towards the jet. After the breaking, both of the velocities and accelerations almost simultaneously reach extreme values near locations beneath the jet. Some of the extreme values are closely related to the breaker type and can be uniquely determined by substituting the breaker type index into the regression equations suggested here.     

Experimental study of three-dimensional breaking wave kinematics

Particle image velocimetry has been used to examine three-dimensional breaking wave kinematics. Two cases of wave breaking were studied. In the first case, the wave field contains a single frequency with a uniform angular spreading within a given range {{ — , .}}. The wave field of the second case consists of a number of frequencies with a uniform angular spreading applied to each frequency. In both cases, the waves are designed such that the wave energy is focused at a given point. The degree of angular spreading has been found to have great effects on the breaking characteristics and kinematics. Two types of breaker were observed, the first being plunging and the second being spilling. Increasing the angular spreading had the effect of making the velocities within the extreme waves larger. The ratio of the crest velocity to the breaking wave speed was approximately unity under both single and multiple frequency conditions, regardless of the angular spreading.     

规则波在缓坡上变形与破碎数值分析

通过在二维数值水槽内用边界元法直接求解Laplace方程,对规则波在缓坡上的变形及破碎进行了数值计算。分析了不同底坡及采用不同底摩阻系数时规则波的破碎特征,并对规则波破碎的极限坡度进行了研究。重点分析了规则波破碎时海底坡度、底摩阻系数及波形不对称性对破碎指标的影响。     

Large Eddy Simulation for Plunge Breaker and Sediment Suspension

Breaking waves are a powerful agent for generating turbulence that plays an important role in many fluid dynamical processes, particularly in the mixing of materials. Breaking waves can dislodge sediment and throw it into suspension, which will then be carried by wave-induced steady current and tidal flow. In order to investigate sediment suspension by breaking waves, a numerical model based on large-eddy-simulation (LES) is developed. This numerical model can be used to simulate wave breaking and sediment suspension. The model consists of a free-surface model using the surface marker method combined with a two-dimensional model that solves the flow equations. The turbulence and the turbulent diffusion are described by a large-eddy-simulation (LES) method where the large turbulence features are simulated by solving the flow equations, and a subgrid model represents the small-scale turbulence that is not resolved by the flow model. A dynamic eddy viscosity subgrid scale stress model has been used for the     

Seabed shear stress and bedload transport due to asymmetric and skewed waves

A simple conceptual formulation to compute seabed shear stress due to asymmetric and skewed waves is presented. This formulation generalizes the sinusoidal wave case and uses a variable friction factor to describe the physics of the boundary layer and to parameterize the effects of wave shape. Predictions of bed shear stresses agree with numerical computations using a standard boundary layer model with a k–ε turbulence closure. The bed shear stress formulation is combined with a Meyer-Peter and Müller-type formula to predict sheet flow bedload transport under asymmetric and skewed waves for a horizontal or sloping bed. The predictions agree with oscillatory water tunnel measurements from the literature.     

Measurement and modeling of bed shear stress under solitary waves

Direct measurements of bed shear stresses (using a shear cell apparatus) generated by non-breaking solitary waves are presented. The measurements were carried out over a smooth bed in laminar and transitional flow regimes (~ 10⁴ < R_e < ~ 10⁵). Measurements were carried out where the wave height to water depth (h/d) ratio varied between 0.12 and 0.68; maximum near bed velocity varied between 0.16 m/s and 0.51 m/s and the maximum total shear stress (sum of skin shear stress and Froude–Krylov force) varied between 0.386 Pa and 2.06 Pa. The total stress is important in determining the stability of submarine sediment and in sheet flow regimes. Analytical modeling was carried out to predict total and skin shear stresses using convolution integration methods forced with the free stream velocity and incorporating a range of eddy viscosity models. Wave friction factors were estimated from skin shear stress at different instances over the wave (viz., time of maximum positive total shear stress, maximum skin shear stress and at the time of maximum velocity) using both the maximum velocity and the instantaneous velocity at that phase of the wave cycle. Similarly, force coefficients obtained from total stress were estimated at time of maximum positive and negative total stress and at maximum velocity. Maximum positive total shear stress was approximately 1.5 times larger than minimum negative total stress. Modeled and measured positive bed shear stresses are well correlated using the best convolution model, but the model underestimates the data by about 4%. Friction factors are dependent on the choice of normalizing using the maximum velocity, as is conventional, or the instantaneous velocity. These differ because the stress is not in phase with the velocity in general. Friction factors are consistent with previous data for monochromatic waves, and vary inversely with the square-root of the Reynolds number. The total shear stress leads the free stream fluid velocity by approximately 50°, whereas the skin friction shear stress leads by about 30°, which is similar to that reported by earlier researchers.     

An investigation of breaker heights, shapes and pressures

The shape of breaking waves has a significant effect on wave impact pressures on vertical sea walls. In order to refine the results of previous researchers, a systematic study of breaker shapes and wave impact pressures on a vertical wall using a newly developed experimental technique, sequential flash photography, was conducted at Queen's University of Belfast. Assumptions, like the existence of a vertical flip-through jet or a parallel face impact, could not be confirmed. The maximum pressure was found to occur for plunging breakers and at Still Water Level (SWL), although high pressures can also occur for other breaker types above or below SWL.     

珊瑚礁地形上破碎波高试验研究

破碎波高是珊瑚礁地形上波浪演化的重要参数之一,对工程安全和海岸变形具有重要影响。通过二维波浪水槽,对珊瑚礁地形上破碎波高进行试验研究,分析破碎波高随波陡、礁坪水深以及礁前斜坡坡度的变化。研究表明,相对破碎波高随相对礁坪水深的增大而增大,随入射波陡的增大而减小,但礁前斜坡坡度对相对破碎波高的影响并不明显。通过引入相对礁坪水深,将经典的破碎波高计算公式拓展至珊瑚礁地形上破碎波高的计算。该公式计算值与前人的试验值进行对比验证,吻合较好。研究成果可为工程实践和数值模拟提供参考与借鉴。     

Research on Measurement of Bed Shear Stress Under Wave?Current Interaction

The movement of sediment in estuary and on coast is directly restricted by the bed shear stress. Therefore, the research on the basic problem of sediment movement by the bed shear stress is an important way to research the theory of sediment movement. However, there is not a measuring and computing method to measure the bed shear stress under a complicated dynamic effect like wave and current. This paper describes the measurement and test research on the bed shear stress in a long launder of direct current by the new instrument named thermal shearometer based on micro-nanotechnology. As shown by the research results, the thermal shearometer has a high response frequency and strong stability. The measured results can reflect the basic change of the bed shear stress under wave and wave?current effect, and confirm that the method of measuring bed shear stress under wave?current effect with thermal shearometer is feasible. Meanwhile, a preliminary method to compute the shear stress compounded by wave?current is put forward according to the tested and measured results, and then a reference for further study on the basic theory of sediment movement under a complicated dynamic effect is provided.