Formula for predicting bedload transport rate in oscillatory sheet flows

The method of Wang [Wang, Y.-H., 2007. Formula for predicting bedload transport rate in oscillatory sheet flow. Coastal Engineering 54, 594–601] to predict the wave friction factor is discussed. At the threshold of sediment entrainment the proposed equation produces a wide scatter of data points when plotted against an equation based on the Shields parameter. It is shown that a better correlation coefficient can be obtained by calculating the critical wave friction factor directly from the wave period, as well as the sediment and water properties.     

The inception of sheet flow in oscillatory flow

A simple model is developed to study the inception of sheet flow in oscillatory flow based on the available experimental data. The inception of sheet flow in oscillatory flow is well defined by the simple model: A/d=KA²ω/ν+B, where A is the semi-excursion of wave orbital motion near the bed, d is the grain size, ω is the angular frequency, ν is the kinematic viscosity of water, and K and B are the coefficients and dependent on sediment properties only. The inception velocity of sheet flow derived from the model is shown to be the function of grain size d, oscillatory period T and specific sediment density s. For a given sediment, the inception velocity is found to increase sharply initially with T and then approach a constant at T>6.0 s. The present model is quite simple and gives good agreement with the available experimental data.     

The dimensions of sand ripples in full-scale oscillatory flows

New large-scale experiments have been carried out in two oscillatory flow tunnels to study ripple regime sand suspension and net sand transport processes in full-scale oscillatory flows. The paper focuses on ripple dimensions and the new data are combined with existing data to make a large dataset of ripple heights and lengths for flows with field-scale amplitudes and periods. A feature of the new experiments is a focus on the effect of flow irregularity. The combined dataset is analysed to examine the range of hydraulic conditions under which oscillatory flow ripples occur, to examine the effects of flow irregularity and ripple three-dimensionality on ripple dimensions and to test and improve existing methods for predicting ripple dimensions.The following are the main conclusions. (1) The highest velocities in a flow time-series play an important role in determining the type of bedform occurring in oscillatory flow. Bedform regime is well characterised by mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth peak velocities in the case of irregular flow. (2) For field-scale flows, sand size is the primary factor determining whether equilibrium ripples will be 2D or 3D. 2D ripples occur when the sand D₅₀ ≥ 0.30 mm and 3D ripples occur when D₅₀ ≤ 0.22 mm (except when the flow orbital diameter is low). (3) Ripple type (2D or 3D) is the same for regular and irregular flows and ripple dimensions produced by equivalent regular and irregular flows follow a similar functional dependence on mobility number, with mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth velocities in the case of irregular flow. For much of the ripple regime, ripple dimensions have weak dependency on mobility number and ripple dimensions are similar for regular and irregular flows with the same flow orbital amplitude. However, differences in ripples produced by equivalent regular and irregular flows become significant at the high mobility end of the ripple regime. (4) Ripple dimensions predicted using the Wiberg and Harris formulae are in poor agreement with measured ripple dimensions from the large-scale experiments. Predictions based on the Mogridge et al. and the Nielsen formulae show better overall agreement with the data but also show systematic differences in cases of 3D ripples and ripples generated by irregular flows. (5) Based on the combined large-scale data, modifications to the Nielsen ripple dimension equations are proposed for the heights and lengths of 2D ripples. The same equations apply to regular and irregular flows, but with mobility number appropriately defined. 3D ripples are generally smaller than 2D ripples and estimates of 3D ripple height and length may be obtained by applying multipliers of 0.55 and 0.73 respectively to the 2D formulae. The proposed modified Nielsen formulae provide an improved fit to the large-scale data, accounting for flow irregularity and ripple three-dimensionality.     

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.     

Measurements of sheet flow transport in acceleration-skewed oscillatory flow and comparison with practical formulations

Near-bed oscillatory flows with acceleration skewness are characteristic of steep and breaking waves in shallow water. In order to isolate the effects of acceleration skewness on sheet flow sand transport, new experiments are carried out in the Aberdeen Oscillatory Flow Tunnel. The experiments have produced a dataset of net transport rates for full-scale oscillatory flows with varying degrees of acceleration skewness and three sand sizes. The new data confirm previous research that net transport in acceleration-skewed flow is non-zero, is always in the direction of the largest acceleration and increases with increasing acceleration skewness. Large transport rates for the fine sand conditions suggest that phase lag effects play an important role in augmenting positive net transport. A comparison of the new experimental data with a number of practical sand transport formulations that incorporate acceleration skewness shows that none of the formulations performs well in predicting the measured net transport rates for both the fine and the coarser sands. The new experimental data can be used to further develop practical sand transport formulations to better account for acceleration skewness.     

A two-phase numerical model for sediment transport prediction under oscillatory sheet flows

To predict sediment transport under oscillatory sheet flow condition, especially for fine sand, is still a challenging research subject in coastal engineering. This paper describes a newly-developed numerical model based on two-phase theory with the use of a one-equation turbulence closure, and its applications in predicting fine sediment suspension in near-prototype oscillatory sheet flow conditions. Model results were compared with comprehensive laboratory measurements of flow velocity and sediment concentration under both symmetrical and asymmetrical oscillatory sheet flows from a large-scale water tunnel. Good agreements between the model results and measurements were achieved and the results demonstrated that the model is capable of reproducing detailed characteristics of sediment entrainment process in the sheet flow regime. The comparisons also revealed the fact that the concentration peaks at flow reversal is associated with the strong vertical sediment transport flux in the pickup layer, which has been widely observed in many laboratory experiments. The effects of flow reversal events on total sediment transport were also discussed.     

Combined tidal and wind driven flows and bedload transport over a flat bottom

The combined tidal and wind driven flow and resulting sediment transport in the ocean over a flat bottom at intermediate water depth has been investigated, using a simple one dimensional two-equation turbulence closure model. This model has been verified against field measurements of a tidal flow in the Celtic Sea. The tidal velocity ellipses and the time series of the horizontal velocity components at given elevations above the bottom are well predicted through the water column although there are some deviations between the predicted and measured velocities near the bottom due to the uncertainty of the bottom roughness. For the combined tidal and wind driven flows the velocity profiles, turbulent kinetic energy profiles and surface particle trajectories are predicted for weak and strong winds. Furthermore, the bottom shear stress and the resulting bedload transport have been predicted; the parts of the particle trajectories in the close vicinity of the bottom where the bedload transport exists are displayed. Finally, the direction and magnitude of the surface drift, the depth-averaged mean velocity and the mean bedload transport are given, and the effect of the bottom roughness on the sea surface drift is investigated.     

Variability of wave-induced ripple migration in wave-flume experiments and its implications for sediment transport

A thorough discussion of results from laboratory experiments with regular waves sheds light on the gap that lies between the sediment transport associated with ripple migration and the performance of a standard bedload transport formula in terms of bed shear concept. It is found that the extent of deviations of the bedload transport formula by Ribberink (1998) from the measured rate of sediment transport associated with ripple migration becomes systematically apparent under conditions of increasing settling time factor Ω_s (= η/(w₀T); η is the ripple height, w₀ the settling velocity and T the wave period). Re-examination of previous two field studies demonstrates a further reinforcement for phase-lag argument addressed in this paper.     

振荡流层移输沙条件下悬沙层泥沙扩散系数垂向分布特征研究

层移输沙是海岸带泥沙运动的主要形式之一,其垂向悬沙浓度分布规律的研究一直是海岸工程关心的重点。一般情况下,经典的纯扩散模型被用来描述和解释悬沙浓度的试验数据,该模型认为周期平均悬沙浓度主要由参考浓度、泥沙沉速和泥沙扩散系数确定。泥沙扩散系数可以由泥沙沉速和悬沙浓度的垂向梯度反演得到。既往研究大多直接给出泥沙扩散系数的结果,对于不同反演计算方法间结果差别的研究较少。本研究汇总了已有振荡流层移输沙试验数据,采用曲线拟合方法和直接差分方法计算了相应的泥沙扩散系数,研究表明两种方法得到的计算结果在垂向位置z 0.15 m处差异不大,随着垂向位置的升高,差分方法的计算结果略微大于拟合方法。考虑到拟合方法可以得到连续的泥沙扩散系数垂向分布,本研究推荐使用幂函数形式的曲线拟合方法求解悬移泥沙扩散系数。基于此,对比分析了层移输沙悬沙层泥沙扩散系数随泥沙粒径、振荡流周期、均方根流速和振荡流类型等物理参数的变化规律。在纯振荡流层移输沙条件下,泥沙扩散系数随泥沙粒径的增大而增大,而振荡流周期和均方根流速几乎不影响泥沙扩散系数。在振荡流和定常流共同作用下,泥沙扩散系数受振荡流周期和定常流流速的影响,泥沙扩散系数随着振荡流周期的增大或定常流流速的减小而增大。     

Modelling of sand transport under wave-generated sheet flows with a RANS diffusion model

A 1DV-RANS diffusion model is used to study sand transport processes in oscillatory flat-bed/sheet flow conditions. The central aim is the verification of the model with laboratory data and to identify processes controlling the magnitude and direction (‘onshore’/‘offshore’) of the net time-averaged sand transport. The model is verified with a large series of measured net sand transport rates, as collected in different wave tunnels for a range of wave-current conditions and grain sizes. Although not all sheet flow details are represented in the 1DV-model, it is shown that the model is able to give a correct representation of the observed trends in the data with respect to the influence of the velocity, wave period and grain diameter. Also detailed mean sediment flux profiles in the sheet flow layer are well reproduced by the model, including the direction change from ‘onshore’ to ‘offshore’ due to a difference in grain size from 0.34 mm (medium sand) to 0.13 mm (fine sand). A model sensitivity study with a selected series of net transport data shows that the stirring height of the suspended sediment ε_s/w_s strongly controls the magnitude and direction of the net sediment transport. Inclusion of both hindered settling and density stratification appears to be necessary to correctly represent the sand fluxes for waves alone and for waves + a superimposed current. The best agreement with a large dataset of net transport measurements is obtained with the 1DV-RANS model in its original settings using a Prandtl–Schmidt number σ_ρ = 0.5.     

非对称歪斜波引起的片流输沙数值研究

本文用了一个可考虑相位差作用和波浪边界层非对称性的瞬态理论模型和一个两相紊流模型共同研究非对称歪斜波引起的片流输沙现象。为了解速度偏度和加速度偏度对输沙通量和输沙率的贡献,两相流模型为理论模型提供了必要的相位超前、瞬时侵蚀深度和边界层的发展过程。理论模型研究显示了由速度偏度和加速度偏度引起的向岸阶段和离岸阶段的泥沙运动非对称性,解释了净输沙的产生原因。在以往的非对称歪斜波片流输沙研究中,净输沙的产生主要被归结于相位差作用。本文的研究则表明了非对称的边界层发展所产生的净流量和动床面效应在净输沙产生过程中的比相位差作用更为重要。     

Fundamental study for morphodynamic modelling: Sand mounds in oscillatory flows

Experiments on sand mounds in oscillatory flow, undertaken in controlled, large-scale laboratory conditions, have produced well-defined data sets for model comparison. Three bathymetries with different levels of submergence, including a surface-piercing case, were tested. The maximum slope was about 1:5.5. Sediment transport is due to bed load with ripple formation. The principal time-dependent bulk parameters are the vertical distance of the centre of gravity above the base and the volume of the mound. A semi-implicit finite-volume depth-averaged hydrodynamic model is used to drive morphodynamics, using van Rijn's sediment flux model generalized to take account of bed slope, and some justification is given for depth-averaged modeling in these conditions. Starting the model runs with the conditions at the end of the first cycle avoided initial atypical physical behaviour. In general good predictions were obtained with an angle of repose reduced from the standard value of about 30° for stationary beds to 15°. For these situations, morphodynamics was largely unaffected by a hydrodynamic roughness height in the range 2.5D₅₀ to 51D₅₀, with larger values accounting for ripple roughness. The reduced angle of repose may be physically expected with mobile beds but this specific value is only expected to be suited to this form of bed motion. In one case an exaggerated ripple formed near the top of the mound reducing agreement with experiment. For the submerged case with normal ripple structure excellent predictions were obtained. For the initially surface-piercing mound, the time of submergence was better predicted with a 30° angle of repose, presumably due to the prominent influence of the near stationary bed near the wet/dry interface, although long term predictions were better predicted with 15°. The occurrence of vortex shedding in the first cycle modeled was in agreement with experimental observation.     

沙质海岸沿岸输沙率计算方法研究进展

准确预测波浪作用下沿岸输沙率是沙质海岸研究领域的重要科学问题。根据数十年来国内外沿岸输沙率公式的研究进展,按研究方法对各项成果进行分类,并兼顾时间逻辑,回顾了各研究方法的发展历程及其代表性成果。对各项成果的理论基础、考虑因素、资料来源等方面进行了探讨,并采用现场原型沙、室内原型沙和室内轻质沙等实测资料,对国内外常用公式的预测准确性进行了检验。结果表明,孙林云公式与各项实测资料的吻合程度最高,在众多沿岸输沙率公式中具有明显的先进性。在此基础上,对未来可进一步深化研究的方向作出了展望。     

21世纪格陵兰冰川融化速率对海平面变化的影响

本文利用大洋环流模式POP研究RCP4.5情景下21世纪格陵兰冰川不同的融化速率对全球及区域海平面变化的影响。结果显示:当格陵兰冰川的融化速率以每年1%增加时,全球大部分海域的动力和比容海平面变化基本不变,主要是由于格陵兰冰川在低速融化时并不会导致大西洋经向翻转流减弱。当格陵兰冰川的融化速率以每年3%和每年7%增加时,动力海平面在北大西洋副极地、大西洋热带、南大西洋副热带和北冰洋海域呈现出显著的上升趋势,这是因为格陵兰冰川快速融化导致大量的淡水输入附近海域,造成该上层海洋层化加强和深对流减弱,导致大西洋经向翻转流显著减弱;与此同时,热比容海平面在北冰洋、格陵兰岛南部海域和大西洋副热带海域显著下降,而在热带大西洋和湾流海域明显上升;此时盐比容海平面的变化与热比容海平面是反相的,这是由于大量的低温低盐水的输入,造成北大西洋副极地海域变冷变淡、大西洋经向翻转流和热盐环流显著减弱,引起了太平洋向北冰洋的热通量和淡水通量减少,导致了北冰洋海水变冷变淡,同时热带大西洋滞留了更多的高温高盐水,随着湾流被带到北大西洋,北大西洋副极地海域低温低盐的海水,被风生环流输运到副热带海域。     

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.