High-resolution field measurements and numerical modelling of intra-wave sediment suspension on plane beds under shoaling waves

Intra-wave sediment suspension is examined using high-resolution field measurements and numerical hydrodynamic and sediment models within 120 mm of a plane seabed under natural asymmetric waves. The detailed measurements of suspended sediment concentration (at 5 mm vertical resolution and at 4 Hz) showed two or three entrainment bursts around peak flow under the wave crest and another at flow reversal during the decelerating phase. At flow reversal, the mixing length was found to be approximately double the value attained at peak flow under the crest. To examine the cause of multiple suspension peaks and increased diffusion at flow reversal, a numerical “side-view” hydrodynamic model was developed to reproduce near-bed wave-induced orbital currents. Predicted currents at the bed and above the wave boundary layer were oppositely directed around flow reversal and this effect became more pronounced with increasing wave asymmetry. When the predicted orbital currents and an enhanced eddy diffusivity during periods of oppositely directed flows were applied in a Lagrangian numerical sediment transport model, unprecedented and extremely close predictions of the measured instantaneous concentrations were obtained. The numerical models were simplified to incorporate only the essential parameters and, by simulating at short time scales, empirical time-averaged parameterisations were not required. Key factors in the sediment model were fall velocities of the full grain size distribution, diffusion, separation of entrainment from settlement, and non-constant, but vertically uniform, eddy diffusivity. Over the plane bed, sediment convection by wave orbital vertical currents was found to have no significant influence on the results.     

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     

A Simple Eddy Viscosity Model of Rough Turbulent Wave Boundary Layer

- A one-layer time-invariant eddy viscosity model is specified to develop a mathematical model for describing the essential features of the turbulent wave boundary layer over a rough bed. The functional form of the eddy viscosity is evaluated based on computational results from a two-equation turbulence model in which the eddy viscosity varies with time and space. The present eddy viscosity model simplifies much of the mathematical complexity in many existing models. Predictions from the present model have been compared with a wide range of experimental data. It is found that the eddy viscosity model adopted in the present study is physically reasonable.     

Energy balance of wind waves as a function of the bottom friction formulation

Four different expressions for wave energy dissipation by bottom friction are intercompared. For this purpose, the SWAN wave model and the wave data set of Lake George (Australia) are used. Three formulations are already present in SWAN (ver. 40.01): the JONSWAP expression, the drag law friction model of Collins and the eddy–viscosity model of Madsen. The eddy–viscosity model of Weber was incorporated into the SWAN code. Using Collins' and Weber's expressions, the depth- and fetch-limited wave growth laws obtained in the nearly idealized situation of Lake George can be reproduced. The wave model has shown the best performance using the formulation of Weber. This formula has some advantages over the other formulations. The expression is based on theoretical and physical principles. The wave height and the peak frequency obtained from the SWAN runs using Weber's bottom friction expression are more consistent with the measurements. The formula of Weber should therefore be preferred when modelling waves in very shallow water.     

Process-based model for nearshore hydrodynamics, sediment transport and morphological evolution in the surf and swash zones

Hydrodynamics and sediment transport in the nearshore zone were modeled numerically taking into account turbulent unsteady flow. The flow field was computed using the Reynolds Averaged Navier–Stokes equations with a k–ε turbulence closure model, while the free surface was tracked using the Volume-Of-Fluid technique. This hydrodynamical model was supplemented with a cross-shore sediment transport formula to calculate profile changes and sediment transport in the surf and swash zones. Based on the numerical solutions, flow characteristics and the effects of breaking waves on sediment transport were studied. The main characteristic of breaking waves, i.e. the instantaneous sediment transport rate, was investigated numerically, as was the spatial distribution of time-averaged sediment transport rates for different grain sizes. The analysis included an evaluation of different values of the wave friction factor and an empirical constant characterizing the uprush and backwash. It was found that the uprush induces a larger instantaneous transport rate than the backwash, indicating that the uprush is more important for sediment transport than the backwash. The results of the present model are in reasonable agreement with other numerical and physical models of nearshore hydrodynamics. The model was found to predict well cross-shore sediment transport and thus it provides a tool for predicting beach morphology change.     

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.     

Acoustic imaging of cohesive sediment resuspension and re-entrainment in the Changjiang Estuary, East China Sea

 Vertical profiles of instantaneous cohesive suspension concentration, obtained from an acoustic suspended sediment monitor in the Changjiang Estuary, indicate that near-bed high-concentration suspensions consist of upper and lower high-concentration suspensions, separated by a natural breakpoint at ca. 2 g l^-1. Acoustic images revealed near-bed high-frequency resuspension events of a few seconds, which contribute mainly to the formation of the lower near-bed high-concentration suspension. Upper and lower lutoclines are also indicative of re-entrainment of lower and upper high concentration suspension, respectively. Near-bed high-frequency resuspension is caused by turbulence, while re-entrainment is probably attributable to internal wave activity. Received: 26 April 1996 / Revision received: 23 July 1996     

Nonuniform sediment transport under non-breaking waves and currents

Empirical formulas have been developed to calculate the fractional bed-load and suspended-load transport rates and near-bed suspended-load concentration under non-breaking waves and currents for coastal applications. The formulas relate the bed-load transport rate to the grain shear stress, the suspended-load transport rate to the energy of the flow system, and the near-bed suspended-load concentration to the bed-load transport rate, velocity and layer thickness. Adequate methods are adopted to determine the bed shear stress due to coexisted waves and currents. The hiding and exposure mechanism in nonuniform bed material is considered through a correction factor that is related to the hiding and exposure probabilities and in turn the size composition of bed material. The developed formulas have been tested using a large database of single-sized sediment transport and several sets of multiple-sized sediment transport data collected from literature, and compared with several existing formulas. The developed formulas can provide reasonably good predictions for the test cases.     

Analysis of dune erosion processes in large-scale flume experiments

Large-scale physical model tests were conducted with different wave periods to examine the physical processes driving dune erosion. The model tests have been carried out in a flume (2DV) with a sandy dune exposed to extreme surge and wave conditions [Van Gent, M.R.A., Van Thiel de Vries, J.S.M., Coeveld, E.M., De Vroeg, J.H. and Van de Graaff, J., 2008. Large-scale dune erosion tests to study the effect of wave periods. Coastal Engineering. doi:10.1016/j.coastaleng.2008.04.003.]. Detailed measurements in time and space of water pressure, flow velocities and sediment concentrations were performed in the near shore area. The data revealed that both short- and long waves are important to inner surf hydrodynamics. Depth averaged flows are directed offshore and increase towards the shore line. The corresponding mean sediment concentrations rise sharply towards the dune face (up to 50 g/l near the bed). The strong increase in the mean sediment concentration towards the dune face correlates well with the maximum wave surface slope which in turn is coupled to both the pressure gradient and the near-bed wave-breaking induced turbulence. Analysis shows that the pressure gradient is only partially coupled to the flow acceleration suggesting that the latter cannot always be used as a proxy for the first. Weak correlation is obtained with the near-bed flows related to the bed shear stress. Tests with a larger wave period resulted in a larger dune erosion volume. During these tests more wave energy (combined incident and infragravity waves) reached the dune face, but more importantly, this wave energy is dissipated by fewer waves resulting in more intense wave breakers and steeper wave fronts. It is therefore expected that the wave-breaking induced near-bed turbulence increases resulting in significantly higher (O(100%)) mean sediment concentrations. In addition the mean flow velocities are comparable, yielding a substantially larger offshore directed sediment transport capacity. This increase in offshore directed transport is only partially compensated by a concurrent increase in the wave related onshore transport capacity associated with intrawave processes, resulting in a net increase in the dune erosion rate.     

On the local equilibrium of winds and wind-waves in relation to surface drag

Local equilibrium of winds and wind-waves is discussed as a basis for research of the drag coefficient of the water surface as well as for the spectral growth of wind-waves. This hypothesis assumes, in a narrow sense, that statistical properties are determined from four physical quantities, which represent winds and wind-waves: the friction velocityu _*, the gravitational accelerationg, the powerE of the surface displacement, and the peak frequency _p of a wind-wave spectrum. Then one has only one nondimensionalcontrol parameter, which may be either the wave age or wave nonlinearity (slope) of dominant waves. In a wide-sense, one can take into account viscosity and surface tension in terms of one more additional parameter by virtue of the virtual invariance of those material constants; that parameter describes the scale ratio between dominant waves and the short waves for which viscosity or surface tension is important. A unified expression for the roughness height according to this hypothesis turns out to include Charnock's and Toba's formulas as special cases. On the basis of a preliminary analysis of the experimental data, a new empirical formula is proposed.     

含变涡动系数的超浅海风暴潮模型

超浅海风暴潮模型提出后[2],对渤海风潮,作为超浅海问题,进行了数值研究[1]。其结果的分析和观测资料的比较都表明了该模型有一定的应用价值;故,对超浅海风暴潮模型作进一步的探讨是有一定意义的。尤其因为我国是一个多浅水域和多风暴潮的国家,这种研究就具有更重要的意义。     

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.     

A new formula for the total longshore sediment transport rate

A new predictive formula for the total longshore sediment transport (LST) rate was developed from principles of sediment transport physics assuming that breaking waves mobilize the sediment, which is subsequently moved by a mean current. Six high-quality data sets on hydrodynamics and sediment transport collected during both field and laboratory conditions were employed to evaluate the predictive capability of the new formula. The main parameter of the formula (a transport coefficient), which represents the efficiency of the waves in keeping sand grains in suspension, was expressed through a Dean number based on dimensional analysis. The new formula yields predictions that lie within a factor of 0.5 to 2 of the measured values for 62% of the data points, which is higher than other commonly employed formulas for the LST rate such as the CERC equation or the formulas developed by Inman–Bagnold and Kamphuis, respectively. The new formula is well suited for practical applications in coastal areas, as well as for numerical modeling of sediment transport and shoreline change in the nearshore.     

基于FLOW-3D的三维数值波流水槽的构建及应用研究

为获得具有自由液面的三维波流水槽,基于FLOW-3D有限差分程序,选用RNG?-?紊流模型,基于线性波速度入口法造波,采用VOF方法对自由液面进行追踪。构建具有自由液面的三维波流联合作用数值水槽,对比压力出流边界与Sammerfeld辐射边界发现,在波流水槽内采用压力出流边界能够保持流体体积守恒,波形稳定;加入的孔隙结构,不仅能保证良好的消波效果,而且流体能够顺利通过,对消除反射波影响效果良好;与实验结果对比发现,垂向时均流速与实验数据拟合较好。波流场中桩柱前形成明显下潜水流及漩涡,是形成局部冲刷主要原因。本文所构建的波流数值模型波形稳定、具有良好的波流特性,能较好反应波浪与水流之间的相互作用,可进一步模拟波流场与结构物之间的相互作用或波流作用下泥沙冲刷等研究。     

Large Eddy Simulation for Wave Breaking in the Surf Zone

In this paper, (he large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads lo the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale mode! is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this pape     

Predictability of wave-induced net sediment transport using the conventional 1DV RANS diffusion model

Based on a large database of laboratory experiments, the predictability of the conventional one-dimensional vertical Reynolds-averaged Navier–Stokes (RANS) diffusion model is systematically investigated with respect to wave-induced net sediment transport. The predicted net sediment transport rates are compared with the measured data of 176 physical experiments in wave flumes and oscillating water tunnels, covering a wide range of wave conditions (surface, skewed, and asymmetric waves with and without currents), sediment conditions (fine, medium, and coarse sands with median grain diameters ranging from 0.13 to 0.97 mm) and bed forms (flat beds and rippled beds), corresponding to various sediment dynamic regions in the near-shore area. Comparisons show that the majority (73 %) of predictions on a flat bed are within a factor 2 of the measurements. The model behaves much better for medium/coarse sand than for fine sand. The model generally underpredicts the transport rates beneath asymmetric waves and overpredicts the fine sand transport beneath skewed waves. Nevertheless, the model behaves well in reproducing the transport rates under surface waves. A detailed discussion and a quantitative measure of the overall model performance are made. The poor model predictability for fine sand cases is mainly due to the underestimation of unsteady phase-lag effect. It is revealed that the model predictability can be significantly improved by implementing alternative bedload formulas and incorporating more physical processes (mobile-bed roughness, hindered settling, and turbulence damping).     

Eddy viscosities and velocities in combined wave-current flows

The eddy viscosities for the steady and the periodic components of combined wave-current flows have been studied quantitatively from the presently available experimental data. It has been found that inside the boundary interaction layer [z < δ] the eddy viscosity ε_c for the steady flow is increased in the presence of waves while outside the boundary interaction layer [z >δ] it is affected little by the wave motion, and that the eddy viscosity ε_w for the wave motion in the boundary layer is independent of the current strength U^*. On the other hand, a new eddy viscosity model is presented to give a good prediction of the velocity distributions of the waves and currents in comparison with experimental data.     

Sheet flow and suspension of sand in oscillatory boundary layers

after revisionTime-dependent measurements of flow velocities and sediment concentrations were conducted in a large oscillating water tunnel. The measurements were aimed at the flow and sediment dynamics in and above an oscillatory boundary layer in plane bed and sheet-flow conditions. Two asymmetric waves and one sinusoidal wave were imposed using quartz sand with D₅₀ = 0.21 mm. A new electro-resistance probe with a large resolving power was developed for the measurement of the large sediment concentrations in the sheet-flow layer. The measurements revealed a three layer transport system consisting of a pick-up/deposition layer, an upper sheet flow layer and a suspension layer.In the asymmetric wave cases the total net transport was directed “onshore” and was mainly concentrated in the thin sheet flow layer (< 0.5 cm) at the bed. A small net sediment flux was directed “offhore” in the upper suspension layer. The measured flow velocities, sediment concentrations and sedimenl fluxes showed a good qualitative agreement with the results of a (numerical) 1DV boundary-layer flow and transport model. Although the model did not describe all the observed processes in the sheet-flow and suspension layer, the computational results showed a reasonable agreement with measured net transport rates in a wide range of asymmetric wave conditions.     

A comparison of weakly and fully non-linear models of the shoaling of a solitary internal wave

This study investigates the behaviour of internal solitary waves crossing a continental slope in the presence of a seasonal thermocline. Comparisons are made between a fully non-linear computational fluid dynamics (CFD) model, and weakly non-linear theory. Previous observations suggested that the amplitudes of solitary waves are capped as they pass across the continental slope, which may be due to laminar dynamics, or due to the effect of turbulence. Across the continental slope, CFD and second order variable depth KdV (vEKdV) predictions agree well with observations of a limited change in solitary wave amplitude. First order variable depth KdV theory overpredicts the final amplitude significantly. In terms of the wave shape, the CFD modeled wave changes from a KdV shape in deep water towards an EkdV solution in shallow water, as observations suggest. The phase speed of the CFD and vEKdV waves are similar to that observed in waters of 400–500 m deep, but are slightly lower than observed in 140 m depth. CFD predictions using a standard k, turbulence model showed that turbulence had little effect on the amplitude. These preliminary results indicate that in this situation wave capping is due to laminar, large amplitude solitary wave dynamics and is independent of turbulent mixing.