The motion of cobbles in the swash zone on an impermeable slope

The purpose of this communication is to present the results of a series of laboratory experiments aimed at better understanding the dynamics of the motion of large bottom particles (cobbles) in a swash zone. In this region, a thin sheet of water that results from the collapse of a turbulent bore, runs up the beach and can induce the transport of relatively large solid objects in the on-shore direction. The aims of the study were to: (i) mimic this process in laboratory experiments and identify the associated physical processes involved; and (ii) to develop a suitable theoretical model to describe the motion of cobbles. The experiments employed a solid impermeable bottom and were conducted in a long tank of rectangular cross-section. An impulsive hydraulic bore, produced by a dam-break mechanism at one end of the tank, was used to simulate the water motion in the swash zone. Solid objects of simple discoid shape were used to model the cobbles. The results of the laboratory observations were compared with model predictions. In the range of external parameters used for the experiments (size and density of cobbles, propagation velocity and height of the water front, slope and friction at the bottom), a reasonable agreement between the measured and calculated values of the cobble displacement as a function of time was obtained.     

Morphodynamics and cobbles behavior in and near the surf zone

The evolution of an initially flat sandy slope and the dynamics of large objects (cobbles/mines) emplaced on it are studied in a laboratory wave tank under simulated surf conditions. Upon initiation of wave forcing, the initially flat beach undergoes bedform changes before reaching a quasi-steady morphology characterized by a system of sand ripples along the slope and a large bar near the break point. Although the incoming wave characteristics are held fixed, the bottom morphology never reaches a strict steady state, but rather slowly changes due to the migration of ripples and bar transformation. When the wave characteristics are changed, the bedform adjusts to a new quasi-steady state after a suitable adjustment time. Studies conducted by placing model cobbles/mines on the evolving sandy bottom subjected to wave forcing show four distinct scenarios: (i) periodic cobble oscillations with zero mean displacement and small scour around the cobbles, (ii) mean onshore motion of relatively light cobbles, (iii) periodic burial of relatively heavy cobbles when their sizes are comparable to those of sand ripples, and (iv) the burial of relatively large cobbles under the bar, when the bar migrates due to changes of incoming waves. Quantitative data on the characteristics and dynamics of the bedform, including ripple-formation front propagating down the slope, ripple growth and drift, and flow around ripples, are presented. Physical explanations are provided for the observations.     

Numerical modeling of crenulate bay shapes

A numerical model is developed to compute the shoreline planform in a crenulate bay beach. The new model combines polar and Cartesian coordinates and can be used effectively to compute a hooked zone shoreline in the lee of upcoast headland. The model is calibrated using laboratory data with an incident wave angle ranging from 25° to 60°. The results of calibration and verification suggest that the ratio of the sediment transport parameters by wave and longshore current in this model is close to unity, and the computed shoreline planforms for the hooked and unhooked zones are in good agreement with the ones measured, especially when a bay is close to static equilibrium. In addition, the bay shape calculated by the present model is similar to that given by the well-known empirical parabolic equation for a bay in static equilibrium. The process of bay shape development from a straight beach to a static equilibrium bay is studied using laboratory experiments and the present numerical model. The temporal variations in the computed longshore sediment transport at different locations within a bay beach are analyzed. From this the decrease in the sediment transport becomes apparent while a bay beach changes its shape from straight toward a state of equilibrium. Based on this experience, it may be concluded that the present numerical model can produce a temporal change in the shoreline planform of a crenulate bay beach from a transition state to static equilibrium subject to seasonal wave action.     

Surface waves and bottom sediment response

Abstract

Field measurements of bottom oscillations and wave characteristics have been made in a study of the interaction of fine‐grained sediments and surface waves. A wave staff, pressure sensor, and accelerometer were used in East Bay, Louisiana, an area that has a fine‐grained clay bottom. The accelerometer contained three solid‐state accelerometers mounted at right angles. The instrument was placed about 0.3 m below the mudline. The results of the study indicate that bottom motions under wave action show well‐defined periodic features. The bottom sediments appear to be undergoing an elastic response to bottom pressures, such that the bottom is depressed under a surface wave crest. Under the range of bottom pressures measured, bottom displacement varied linearly with bottom pressure. Measured bottom pressures were up to 35% larger than predicted by linear wave theory. The effect of a movable bottom on wave pressure is considered. The energy lost from the surface wave to the bottom in forcing the bottom response is shown to be significant and larger than the energy lost to bottom friction.     

浪、潮、风暴潮联合作用下的底应力效应

运用建立的二维非线性浪,潮和风暴耦全模式分析了波流相互作用下的底应力及其对耦合波浪场和流场的影响。由渤海的两次强寒潮过程的数值实验表明,在波流相互作用下,底应力明显增大,增大的底应力对波浪场影响甚微,但将明显改变水位和流速的大小,这种影响在近岸浅水区更加显著。     

On the evolution and run-up of breaking solitary waves on a mild sloping beach

This paper presents new laboratory experiments carried out in a supertank (300 m × 5 m × 5.2 m) of breaking solitary waves evolution on a 1:60 plane beach. The measured data are employed to re-examine existing formulae that include breaking criterion, amplitude evolution and run-up height. The properties of shoreline motion, underwater particle velocity and scale effect on run-up height are briefly discussed. Based on our analyses, it is evidently found that there exist five zones during a wave amplitude evolution course on the present mild slope. A simple formula which is capable of predicting maximum run-up height for a breaking solitary wave on a uniform beach with a wide range of beach slope (1:15–1:60) is also proposed. The calculated results from the present model agree favorably with available laboratory data, indicating that our method is compatible with other predictive models.     

海滩修复工程影响下的低能海岸波浪能量时空分布特征研究

本研究基于第三代海浪模式SWAN(Simulating Wave Nearshore),对茅尾海及其邻近海域波浪场进行了为期la的数值模拟,利用实测资料验证了该模型的可靠性.根据模型计算结果分析了茅尾海海域波浪要素的时空分布特征,在此基础上进一步探讨了波浪能量的输入耗散过程以及海滩修复对波浪能量空间分布的影响.研究发现...     

A NUMERICAL STUDY OF THE TIDE AND TIDAL CURRENT IN BEIBU GULF

The systems of diurnal tidal wave (K1) and semi-diurnal tidal wave (M2) in the Beibu Gulf are studied with numerical method. Also discussed in this paper are the influences of the Qiongzhou Strait, the bottom friction term, the horizontal turbulent friction term and the inertial (acceleration) term in dynamic equations on the tidal system. The calculated results show that there is an independent left-handed tidal system in the diurnal tidal wave of the gulf, the amphidromic point being roughly located at Taigeli Island; that the semi-diurnal wave constitutes no tidal system, generating a small tidal range in the region near Feizhulong Islands; and that the influence of the tidal wave from the strait on the tidal system of the K1 is not evident, but its effect on the system of the M2 component tide is quite obvious. The bottom friction term, the horizontal turbulent friction term, and the inertial term have effects upon the tidal system in the gulf.     

Parabolic Approximation of the Weakly Nonlinear Mild Slope Equation with Bottom Friction

This paper presents a refined parabolic approximation model of the mild slope equation to simu-late the combination of water wave refraction and diffraction in the large coastal region.The bottom frictionand weakly nonlinear term are included in the model.The difference equation is established with the Crank-Nicolson scheme.The numerical test shows that some numerical prediction results will be inaccurate in com-plicated topography without considering weak nonlinearity;the bottom friction will make wave height damp-ing and it can not be neglected for calculation of wave field in large areas.     

Modeling the erosion of cohesive clay coasts

A model was developed to study the erosion of cohesive clay coasts in macro- to non-tidal environments. The model shares some of the characteristics of previous models, including the erosion of bare clay surfaces by wave generated bottom shear stresses, and of mobile, sediment-covered surfaces by abrasion. It differs from previous models, however, in several important ways. The morphodynamics of beaches with clay foundations, under different wave conditions, are based on a previously developed model for beaches on rocky shore platforms. Sediment thickness along a beach profile is calculated at regular intervals and compared with the maximum thickness that could be moved at that location under prevailing wave conditions. Wave friction factors are determined, where necessary, according to the occurrence and morphology of ripples on the bottom. In addition to abrasion and the effect of wave induced shear stresses on the clay bottom, erosion by stresses generated by wave impact at the bluff foot and on the intertidal platform is calculated using an expression derived from hard rock coastal models. Tides are represented by their computed tidal duration values, the amount of time each year that the water level falls within each 0.1 m vertical interval. Water depths are modified by wave setup and set-down conditions. Several preliminary model runs were made. The profiles were concave in the submarine zone and roughly linear in the intertidal zone. Equilibrium profiles developed which were maintained as they migrated landwards.     

Numerical Simulation of Wave Field at the Kemena River Mouth in Kalimantan Island

-By use of the parabolic equation of numerical simulation of wave which is suitable forlarge-angle propagation and Crank-Nicolson differential method,the wave field at the Kemema Rivermouth has been studied for analysis of sediment movement in the area.In order to reflect wave energy lossaccurately,the Bretchneider-Reid formula is quoted and the friction coefficient in the formula is discussedin this paper.The calculation results indicate that the wave becomes a little damped at the mouth ofKemena River influenced by the topography and bottom friction,and the wave at the east beach is higherthan that at the west beach,because the east beach extends out.     

The impact of various methods of wave transfers from deep water to nearshore when determining extreme beach erosion

Several levels of increasing complexity of transferring wave information from offshore to nearshore have been studied to quantify their influence on extreme beach erosion estimates. Beach profiles which have been monitored since 1976 were used to estimate extreme beach erosion and compared to predictions. Examination of the wave propagation assumptions revolves around two types of offshore to nearshore transfer: excluding or including wave breaking and bottom friction. A second complication is whether still water level variations (ocean tide plus storm surge) are included.The inclusion of various combinations of wave propagation processes other than shoaling and refraction in the wave transfer function changes on the extreme erosion distribution tail through lowering estimates above one year return period. This brings the predicted tails closer to the observations, but does not capture the upper limit of storm demand implied by the extensive beach profile data set. Including wave breaking has a marked effect on probabilistic estimates of beach erosion. The inclusion of bottom friction is less significant. The inclusion of still water level variability in the wave transfer calculation had minimal impact on results for the case study site, where waves were transferred from offshore to water at 20 m depth. These changes were put into perspective by comparing them to changes resulting from limiting beach erosion by adjusting the statistical distributions of peak wave height and storm duration to have maximum limits. We conclude that the proposed improvements on wave transformation methods are as significant as limiting wave erosion potential and worth including.     

STWAVE simulation of Hurricane Ike: Model results and comparison to data

Hurricane Ike (2008), with its associated storm surge, caused extensive damage across parts of the northwestern Gulf Coast when it made landfall in the late hours of September 12, 2008 along the upper Texas coast at the upper end of Category 2 intensity. An extensive instrumentation effort allowed the collection of both nearshore and inland wave and water level data as Hurricane Ike passed the Louisiana coast and made landfall in Texas. This article presents the results of a validation effort for the STWAVE model and the bottom friction coefficients applied in the model with comparisons to the Hurricane Ike measured wave data. Examination of STWAVE model results as contour plots and time series of wave height and period; wave spectra at selected time steps and scatter plots of simulated versus modeled wave results allow evaluation of the model performance. STWAVE model results indicate good agreement with the measured nearshore wave data for an open water Manning ‘n’ bottom friction coefficient equal to 0.03 s/m^0.33. STWAVE model results indicate good agreement with the measured inshore wave data with Manning ‘n’ bottom friction coefficients equal to values derived from land classification data and applied in the ADCIRC model.     

Experimental and numerical study of the effect of variable bathymetry on the slow-drift wave response of floating bodies

An experimental campaign is reported on the slow-drift motion of a rectangular barge moored at different positions along an inclined beach, at waterdepths ranging from 54 cm to 21 cm, and submitted to irregular beam seas. The beach is achieved by inclining the 24 m long false bottom of the tank at a slope of 5%, from a depth of 1.05 m. The slow-drift component of the measured sway motion is first compared with state-of-the-art calculations based on Newman’s approximation. At 54 cm depth a good agreement is obtained between calculations and measurements. At 21 cm depth the Newman calculations exceed the measured values. When the flat bottom setdown contribution is added up, the calculated values become 2 to 3 times larger than the measured ones. A second-order model is proposed to predict the shoaling of a bichromatic sea-state propagating in varying water-depth. This model is validated through comparisons with an extension of Schäffer’s model for a straight beach [Schäffer HA. Infragravity waves induced by short-wave groups. J Fluid Mech 1993;247:551-88] and with a fully nonlinear Boussinesq model. It appears that the long wave amplitude is much less than predicted by the flat bottom model, and that its phase difference with the short wave envelope also deviates from the flat bottom model prediction. As a result of this phase shift the actual second-order wave loads can be lower than predicted by Newman’s approximation alone. Application of the shoaling model to the barge tests yields a notably better agreement between numerical and experimental values of its slow-drift sway motion.     

Modified mild slope equation and open boundary conditions

A numerical model to compute wave field is developed. It is based on the Berkhoff diffraction-refraction equation, in which an energy dissipation term is added, to take into account the breaking and the bottom friction phenomena. The energy dissipation function, by breaking and by bottom friction, is introduced in the Berkhoff equation to obtain a new equation of propagation.The resolution is done with the hybrid finite element method, where lagrangians elements are used.     

Modelling shallow water wave generation and transformation in an intertidal estuary

An experiment is described in which wave growth was measured in Manukau Harbour, a New Zealand estuary with relatively large fetches and extensive intertidal flats. Wave spectra were obtained from pressure sensors and current meters placed at six sites across the estuary. The SWAN third-generation spectral model was then used to simulate wave transformation during a part of the study period during which consistent south-westerly winds blew along the instrument transect. The simulations incorporated refraction by currents using output from a circulation model of the estuary. Measured wave variance spectra were compared with the model results, and the contributions of the various processes represented by source terms within the model were compared. It was found that, along with whitecapping, bed friction and exponential growth from wind input, four-wave nonlinear interactions played a dominant role. Some limitations were noted in the discrete interaction approximation which the SWAN model uses to compute the four-wave nonlinear interaction term.     

Mathematical analysis of long-wave breaking on open channels with bottom friction

In this paper we study the breaking of long waves propagating along an open channel with linear friction on the bottom. The equations governing the wave propagation consist of a pair of first-order nonlinear hyperbolic partial differential equations (PDEs). We first transformed the PDEs into a pair of ordinary differential equations (ODEs) along the characteristic directions by means of a pair of Riemann invariants. By analyzing the ODEs, we found that the breaking of waves can be identified by the singularity of the derivative of the Riemann invariants. Thus, we derived an analytical solution for the derivative of the Riemann invariants. Then, a breaking criterion and an analytical formula for the estimation of breaking time were developed and validated through numerical experiments. It is also shown in the paper that the present model includes the previous model neglecting bottom friction as a special case.     

岬间海滩泥沙输运趋势与剖面分形研究

根据1999年7月实测的粤东岬间海滩沉积与地形变化资料,采用沉积物输运概率模式(McLaren模型)对海滩沿岸泥沙运移趋势进行探讨。结果表明,在常波况条件下海滩沿岸泥沙向偏南方向运移,在高能条件下可能出现与常波况条件下相反运动的趋势。进一步利用分形分布模型研究了海滩剖面的分形性质,提出了岬间海滩剖面地形变化的短期分形预测模型。     

近海海洋对热带风暴线性响应的底坡度和底摩擦效应

一个简单的二维线性模式用于考查近海海洋对过境热带风暴的动力响应过程中的底坡度和底摩擦效应。选择了自东向西和向西后转向的两个模式风暴路径。数值试验结果表明，海底坡度与风暴引起的水位波动、风暴中心后部的尾流以及路径右侧后方面的涡旋密切相关。而底摩察是阻尼风暴潮和风暴流持续增长的重要因子。结果还表明，近海对风暴的强响应偏向于风暴轨迹的右侧，这与Ｃｈａｎｇ和Ａｎｔｈｅｓ（１９７８）对深海响应的研究结论是一