Distribution of eddy scales for wave current combined flow

This paper illustrates the modulation of the eddy scale distribution due to superimposition of surface wave on only current flow. Time series data of three-dimensional velocity components were measured in a laboratory flume by a three-dimensional (3D) 16-MHz micro-acoustic Doppler velocimeter (Micro-ADV). The velocity time series of only current case and waves following the current were analysed to obtain the phase-averaged mean velocities, turbulent intensities, and Reynolds stress. The probability density function of phase-averaged stream-wise and vertical velocity fluctuations showed bimodal oscillations towards the free surface for higher frequency surface waves. It was revealed that surface waves along the current effectively decrease the intermittency of turbulence of the only current flow. Surface wave changed the intermittent structure of only current flow by modulation of the energy cascade mechanism of the only current flow by introduction of wave induced length scales. Also the scale of the finer dissipative eddies were prominently enhanced by the increase in surface wave frequency. Wavelet analysis of time series of velocity signals provided information on the eddy scale and their frequency of occurrence. It was found that the large eddies are carried by the crest regions of the progressive wave while the small scale eddies are carried by the trough regions.     

Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves

This is the first of three papers on the modelling of various types of surf zone phenomena. In this first paper, part I, the model is presented and its basic features are studied for the case of regular waves. The model is based on two-dimensional equations of the Boussinesq type and it features improved linear dispersion characteristics, possibility of wave breaking, and a moving boundary at the shoreline. The moving shoreline is treated numerically by replacing the solid beach by a permeable beach characterized by an extremely small porosity. Run-up of nonbreaking waves is verified against the analytical solution for nonlinear shallow water waves. The inclusion of wave breaking is based on the surface roller concept for spilling breakers using a geometrical determination of the instantaneous roller thickness at each point and modelling the effect of wave breaking by an additional convective momentum term. This is a function of the local wave celerity, which is determined interactively. The model is applied to cross-shore motions of regular waves including various types of breaking on plane sloping beaches and over submerged bars. Model results comprise time series of surface elevations and the spatial variation of phase-averaged quantities such as the wave height, the crest and trough elevations, the mean water level, and the depth-averaged undertow. Comparisons with physical experiments are presented. The phaseaveraged balance of the individual terms in the momentum and energy equation is determined by time-integration and quantities such as the cross-sectional roller area, the radiation stress, the energy flux and the energy dissipation are studied and discussed with reference to conventional phase-averaged wave models. The companion papers present cross-shore motions of breaking irregular waves, swash oscillations and surf beats (part II) and nearshore circulations induced by breaking of unidirectional and multidirectional waves (part III).     

Numerical Simulation of Spatial Lag Between Wave Breaking Point and Location of Maximum Wave-Induced Current

A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point.The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direction.The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress.An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy.The wave driver model is a phase-averaged wave model based on the wave action balance equation.Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach are used to evaluate the model's performance.The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.     

Investigation and Discussion on the Beach Morphodynamic Response Under Storm Events Based on A Three-Dimensional Numerical Model

A well-established 3D phase-averaged beach morphodynamic model was applied to investigate the morphodynamics of a typical artificial beach,and a series of discussions were made on the surfzone hydro-sedimentological processes under calm and storm events.Model results revealed that the nearshore wave-induced current presents a significant 3D structure under stormy waves,where the undertow and longshore currents exist simultaneously,forming a spirallike circulation system in the surfzone.Continuous longshore sediment transport would shorten the sediment supply in the cross-shore direction,subsequently suppress the formation of sandbars,showing that a typical recovery profile under calm waves does not necessarily develop,but with a competing process of onshore drift,undertow and longshore currents.Sediment transport rate during storms reaches several hundreds of times as those under calm waves,and two storm events contribute approximately 60%to the beach erosion.Sediment transport pattern under calm waves is mainly bed load,but as the fine sands underneath begin to expose,the contribution of suspended load becomes significant.     

Assessment of TELEMAC system performances,a hydrodynamic case study of Anglet,France

The wave propagation and flow modules of the TELEMAC system have been applied to the Adour River mouth and the adjacent beaches of Anglet (France). The wave propagation has been simulated using the phase-averaged model TOMAWAC. In addition, the phase-resolving REFDIF S model has been also used, as the diffraction of wind waves, which is not taken into account in TOMAWAC, can occur in the vicinity of the River mouth. Next, the hydrodynamics has been simulated using the two-dimensional depth-averaged flow TELEMAC 2D model.     

Modelling of waves and currents around submerged breakwaters

Recent experimental data collected during the DELOS project are used to validate two approaches for simulating waves and currents in the vicinity of submerged breakwaters.The first approach is a phase-averaged method in which a wave model is used to simulate wave transformation and calculate radiation stresses, while a flow model (2-dimensional depth averaged or quasi-3D) is used to calculate the resulting wave driven currents. The second approach is a phase resolving method in which a high order 2DH-Boussinesq-type model is used to calculate the waves and flow.The models predict wave heights that are comparable to measurements if the wave breaking sub-model is properly tuned for dissipation over the submerged breakwater. It is shown that the simulated flow pattern using both approaches is qualitatively similar to that observed in the experiments. Furthermore, the phase-resolving model shows good agreement between measured and simulated instantaneous surface elevations in wave flume tests.     

A phase-averaged Boussinesq model with effective description of carrier wave group and associated long wave evolution

From the phase-resolving improved Boussinesq equations (Beji and Nadaoka, Ocean Engineering 23 (1996) 691), a phase-averaged Boussinesq model for water waves is derived by more effectively describing carrier wave groups and accompanying long wave evolution with less CPU time. Linear shoaling characteristics of carrier wave equations are investigated and found to agree exactly with the analytical expression obtained from the constancy of energy flux for the improved Boussinesq equations themselves, showing that the present model equations are the results of a consistent derivation procedure regarding energy considerations. Numerical simulations of the derived equations for the single wave group and narrow-banded random waves show the validity of the present model and its high performance, especially on the CPU time.     

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.     

Numerical Modeling of the Undertow Structure and Sandbar Migration in the Surfzone

A process-based 3D numerical model for surfzone hydrodynamics and beach evolution was established. Comparisons between the experimental data and model results proved that the model could effectively describe the hydrodynamics, sediment transport feature and sandbar migration process in the surfzone with satisfactory precision. A series of numerical simulations on the wave breaking and shoaling up to a barred beach were carried out based on the model system. Analyzed from the model results, the wave-induced current system in the surfzone consists of two major processes, which are the phase-averaged undertow caused by wave breaking and the net drift caused by both of the nonlinear wave motion and surface roller effect. When storm waves come to the barred beach, the strong offshore undertow along the beach suppresses the onshore net drift, making the initial sandbar migrate to the seaside. Under the condition of calm wave environment, both the undertow and net drift flow to the shoreline at the offshore side of the sandbar, and then push the initial sandbar to the shoreline. The consideration of surface roller has significant impact on the modeling results of the sandbar migration. As the roller transfer rate increases, the sandbar moves onshore especially under the storm wave condition.     

Bed load transport under irregular waves plus current from Monte Carlo simulations of parameterized models with application to ripple migration rates observed in the field

The bed load transport rate under random waves plus current has been predicted for a large range of wave–current conditions. A parameterized model valid for regular waves plus current has been used in Monte Carlo simulations, assuming the wave amplitudes to be Rayleigh distributed. The mean value, standard deviation and numerical estimates of the probability density function of the bed load transport rate are presented for a wide range of wave–current conditions. It appears that overall the effect of the current is dominating the bed load transport rate. Moreover, a significant scatter of the bed load transport rate under random waves plus current is found. Such a scatter is also found in field measurements by Amos et al. [J. Coast. Res. 15 (1999) 1]. Predicted ripple migration rates in the bed load regime have been compared with those obtained from field measurements by Amos et al. [J. Coast. Res. 15 (1999) 1], taking the bed load transport rate to be proportional to the ripple migration rate times the ripple height. Overall, the predictions capture the qualitative as well as the quantitative behaviour of the ripple migration rates in a wide range of wave–current conditions; the ripple migration rates, and thereby the bed load, are predicted within the correct order of magnitude for a wide range of wave–current conditions.     

Modeling of propagation and transformation of transient nonlinear waves on a current

A novel theoretical approach is applied to predict the propagation and transformation of transient nonlinear waves on a current. The problem was solved by applying an eigenfunction expansion method and the derived semi-analytical solution was employed to study the transformation of wave profile and the evolution of wave spectrum arising from the nonlinear interactions of wave components in a wave train which may lead to the formation of very large waves. The results show that the propagation of wave trains is significantly affected by a current. A relatively small current may substantially affect wave train components and the wave train shape. This is observed for both opposing and following current. The results demonstrate that the application of the nonlinear model has a substantial effect on the shape of a wave spectrum. A train of originally linear and very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short distance from an initial position. The discrepancies between the wave trains predicted by applying the linear and nonlinear models increase with the increasing wavelength and become significant in shallow water even for waves with low steepness. Laboratory experiments were conducted in a wave flume to verify theoretical results. The free-surface elevations recorded by a system of wave gauges are compared with the results provided by the nonlinear model. Additional verification was achieved by applying a Fourier analysis and comparing wave amplitude spectra obtained from theoretical results with experimental data. A reasonable agreement between theoretical results and experimental data is observed for both amplitudes and phases. The model predicts fairly well multi-peak spectra, including wave spectra with significant nonlinear wave components.     

Evolution of waves and currents over a submerged laboratory shoal

The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal.     

Bed load transport on the shoreface by currents and waves

Tide-driven bed load transport is an important portion of the net annual sediment transport rate in many shoreface and shelf environments. However, bed load transport under waves cannot be measured in the field and bed load transport by currents without waves is barely measurable, even in spring tidal conditions. There is, consequently, a strong lack of field data and validated models. The present field site was on the shoreface and inner shelf at 2 to 8.5 km offshore the central Dutch coast (far outside the surfzone), where tidal currents flow parallel to the coast. Bed load transports were carefully measured with a calibrated sampler in spring tidal conditions without waves at a water depth of 13–18 m with fine and medium sands. The near-bed flow was measured over nearly a year and used for integration to annual transport rates. An empirical bed load model was derived, which predicts bed load transports that are a factor of > 5 smaller than predicted by existing models. However, they agree with laboratory data of sand and gravel transport in currents near incipient motion. The damped transport rates may have been caused by cohesion of sediment or turbulence damping due to mud or biological activity. The annual bed load transport rate was calculated using a probability density function (pdf) derived from the near-bed current and orbital velocity data which represented the current and wave climate well when compared to 30 years of data from a nearby wave station. The effect of wave stirring was included in the transport calculations. The net bed load transport rate is a few m²/year. This is much less than predicted in an earlier model study, which is partly due to different bed load models but also due to the difference in velocity pdf. The annual transport rate is very sensitive to the probability of the largest current velocities.     

Truss Spar平台在波流联合作用下运动响应预报方法比较

基于细长体水动力模型比较了Truss Spar平台在波流联合作用下运动响应预报的三种方法。分别采用波流耦合、速度叠加及力叠加计算Truss Spar平台在波流联合作用下的水动力载荷,根据流场水质点运动规律和Truss Spar外部形状特点,分段高效计算水动力载荷。利用Runge-Kutta-Fehlberg方法求解刚体非线性运动方程得Truss Spar在波流场中的运动响应。研究结果表明力叠加法所预报的Truss Spar纵荡和纵摇运动明显大于其他两种方法的相应运动响应预报结果,而波流耦合法与速度叠加法所预报的纵荡与纵摇运动响应幅值相当,三种方法所预报的垂荡运动响应的大小取决于具体波流参数。     

A Bingham-plastic model for fluid mud transport under waves and currents

Simplified equations of fluid mud motion, which is described as Bingham-Plastic model under waves and currents, are presented by order analysis. The simplified equations are non-linear ordinary differential equations which are solved by hybrid numerical-analytical technique. As the computational cost is very low, the effects of wave current parameters and fluid mud properties on the transportation velocity of the fluid mud are studied systematically. It is found that the fluid mud can move toward one direction even if the shear stress acting on the fluid mud bed is much smaller than the fluid mud yield stress under the condition of wave and current coexistence. Experiments of the fluid mud motion under current with fluctuation water surface are carried out. The fluid mud transportation velocity predicted by the presented mathematical model can roughly match that measured in experiments.     

Non-linear propagation of unidirectional wave fields over varying topography

The present study aims at investigating the non-linear triad interaction process affecting shoaling surface gravity wave fields. The triad interaction phenomenon being enhanced towards the shore, the domain of study is extended up to the surf zone. Three 1D non-linear wave models (one phase-resolving and two phase-averaged spectral models) have been implemented and compared to laboratory experiments performed in a wave flume. This set of models includes two existing models and a new one which has been developed in the frame of this work. The models include a breaking dissipation term based on the parametrical model of Battjes and Janssen [Battjes, J.A., Janssen, P.A.E.M., 1978. Energy loss and set-up due to breaking of random waves. Proc. 16th Int. Conf. Coastal Eng. (ASCE), Vol. 1, pp. 569–587.]. The investigations concern the evolution of variance spectra, spectral significant wave height and mean period over a barred bathymetric profile. In addition, the performances of the different models are analysed by computing the spectral source term for triad interactions. We found that all models are able to reproduce the main features of non-linear mechanisms affecting a wave field in the near-shore zone. The phase-resolving model gives the most accurate results for non-breaking situations. It correctly reproduces the non-linear coupling effect in decreasing water depths due to wave–wave interactions, as well as the harmonic release after a bar. However, the model is computationally time-consuming. The CPU time is considerably reduced using phase-averaged models. They give satisfactorily results on harmonic generation. However, they do not reproduce the release of harmonics as water depth increases. In breaking conditions, the variance spectra undergo significant changes under the combined effects of non-linear energy transfers and dissipation. The depth-induced wave breaking model included in the equations provides a good estimate of the energy decay in the surf zone.     

Induced-current effects on microwave backscatter

Microwave measurements have been made with a coherent radar in a wind-wave tank to determine the effect of induced current on backscatter. Perturbations were introduced into the wave structure by inducing a current in the water that flowed either with or against the wind. The effect of current on radar cross section was slight; the effect on the Doppler was much more pronounced. It was found that the wave components responsible for radar backscatter are predominantly free waves (that is, waves which travel at the dispersion velocity) rather than waves which are parasitic (or locked) to the dominant waves.     

结合椭圆型缓坡方程模拟近岸波流场

波浪向近岸传播的过程中,由波浪破碎效应所产生的近岸波流场是近岸海域关键的水动力学因素之一.结合近岸波浪场的椭圆型缓坡方程和近岸波流场数学模型对近岸波浪场及由斜向入射波浪破碎后所形成的近岸波流场进行了数值模拟.计算中考虑到波浪向近岸传播中由于波浪的折射、绕射、反射等效应使局部复杂区域波向不易确定,采用结合椭圆型缓坡方程所给出的波浪辐射应力公式来计算波浪产生的辐射应力,在此基础上耦合椭圆型缓坡方程和近岸波流场数学模型对近岸波流场进行数值模拟,从而使模型综合考虑了波浪的折射、绕射、反射等效应且避免了对波向角的直接求解,可以应用于相对较复杂区域的近岸波流场模拟.     

Michell and Hogner models of far-field ship waves

The far-field waves, and the related far-field wave drag, predicted by the Michell or Hogner theories are considered. These two classical theories are found to predict nearly identical transverse waves for all practical cases. However, the Michell and Hogner models predict divergent waves—dominant at high Froude numbers—that can differ significantly. Differences between the far-field waves predicted by the Michell and Hogner models are much smaller for catamarans, for which lateral interferences between the twin hulls overwhelm lateral interferences between the port and starboard sides of the hulls, than for monohull ships. Moreover, differences between the divergent waves predicted by the Michell and Hogner theories are larger for higher Froude numbers, bigger beam/length ratios, smaller draft/length ratios, or larger separation distances between the twin hulls of a catamaran.     

Intercomparison of wave-driven current models

Seven numerical models which simulate waves and currents in the surf-zone are tested for the case of a reduced-scale detached breakwater subjected to the action of regular waves with normal incidence. The computed wave heights, water levels and velocities are compared with measurements collected in an experimental wave basin. The wave height decay in the surf-zone is predicted reasonably well. Set-up and currents appear to be less well predicted. This intercomparison exercise shows that radiation stresses are systematically overestimated by formulations used in the models, mean bottom shear stresses are not always co-linear with the mean bottom velocity vector in shallow water, and turbulence modelling in the surf-zone requires a sophisticated