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.     

Evaluation of scale effects in hydraulic models by analysis of laminar and turbulent flows

The paper presents an analysis of laminar and turbulent flow in porous stone material in order to evaluate the order of magnitude of scale effects in hydraulic models. Hydraulic model tests, such as for example breakwater model tests, are normally carried out at such small scales that the flow through the various layers of the breakwater is not completely turbulent. For this reason scale effects occur. A well-known method to compensate for the scale effects is to use larger stones than calculated by Froude's model law in certain regions of the model. The paper presents formulae for the calculation of the compensated stone sizes based on earlier work by Engelund. Further an evaluation of the energy dissipation in hydraulic models is made in order to determine the scale effect due to “laminar” flow.     

Practical sand transport formula for non-breaking waves and currents

Many existing practical sand transport formulae for the coastal marine environment are restricted to a limited range of hydrodynamic and sand conditions. This paper presents a new practical formula for net sand transport induced by non-breaking waves and currents. The formula is especially developed for cross-shore sand transport under wave-dominated conditions and is based on the semi-unsteady, half wave-cycle concept, with bed shear stress as the main forcing parameter. Unsteady phase-lag effects between velocities and concentrations, which are especially important for rippled bed and fine sand sheet-flow conditions, are accounted for through parameterisations. Recently-recognised effects on the net transport rate related to flow acceleration skewness and progressive surface waves are also included. To account for the latter, the formula includes the effects of boundary layer streaming and advection effects which occur under real waves, but not in oscillatory tunnel flows. The formula is developed using a database of 226 net transport rate measurements from large-scale oscillatory flow tunnels and a large wave flume, covering a wide range of full-scale flow conditions and uniform and graded sands with median diameter ranging from 0.13 mm to 0.54 mm. Good overall agreement is obtained between observed and predicted net transport rates with 78% of the predictions falling within a factor 2 of the measurements. For several distinctly different conditions, the behaviour of the net transport with increasing flow strength agrees well with observations, indicating that the most important transport processes in both the rippled bed and sheet flow regime are well captured by the formula. However, for some flow conditions good quantitative agreement could only be obtained by introducing separate calibration parameters. The new formula has been validated against independent net transport rate data for oscillatory flow conditions and steady flow conditions.     

Sand transport under combined current and wave conditions: A semi-unsteady,practical model

For the general purposes of morphodynamic computations in coastal zones, simple formula-based models are usually employed to evaluate sediment transport. Sediment transport rates are computed as a function of the bottom shear stress or the near bed flow velocity and it is generally assumed that the sediment particles react immediately to changes in flow conditions. It has been recognized, through recent laboratory experiments in both rippled and plane bed sheet flow conditions that sediment reacts to the flow in a complex manner, involving non-steady processes resulting from memory and settling/entrainment delay effects. These processes may be important in the cross-shore direction, where sediment transport is mainly caused by the oscillatory motions induced by surface short gravity waves.The aim of the present work is to develop a semi-unsteady, practical model, to predict the total (bed load and suspended load) sediment transport rates in wave or combined wave-current flow conditions that are characteristic of the coastal zone. The unsteady effects are reproduced indirectly by taking into account the delayed settling of sediment particles. The net sediment transport rates are computed from the total bottom shear stress and the model takes into account the velocity and acceleration asymmetries of the waves as they propagate towards the shore.A comparison has been carried out between the computed net sediment transport rates with a large data set of experimental results for different flow conditions (wave-current flows, purely oscillatory flow, skewed waves and steady currents) in different regimes (plane bed and rippled bed) with fine, medium and coarse uniform sand. The numerical results obtained are reasonably accurate within a factor of 2. Based on this analysis, the limits and validity of the present formulation are discussed.     

Flow and bed shear stresses in scour protections around a pile in a current

Transport of bed sediment inside and beneath the scour protection may cause deformation and sinking of the scour protection for pile foundations. This may reduce the stability of the mono pile and change the natural frequency of the dynamic response of an offshore wind turbine installed on it in an unfavourable manner. Using physical models and 3D computational fluid dynamic (CFD) numerical simulations, the velocity and bed shear stresses are investigated in complex scour protections around mono piles in steady current. In the physical model the scour protections consisted of an upper cover layer with uniformly distributed coarse stones and a lower filter layer with finer stones. For the numerical simulations, the Flow-3D software was used. The scour protection layers were simulated with different numerical approaches, namely regularly arranged spheres, porous media, or their combinations (hybrid models). Numerical simulations with one or four layers of cover stones without filter layer were first computed. Three additional simulations were then made for a scour protection with a cover layer and a single filter layer. Finally, a simulation of a full scale foundation and scour protection was made with porous media approach.Based on the physical and numerical results, a method to determine the critical stones size to prevent motion of the base sediment is established and compared to a full scale case with sinking of scour protection (Horns Rev I Offshore Wind Farm, Denmark). It is also found that the CFD simulations are capable of calculating the flow velocities when the scour protection is represented by regular arranged spheres, while the turbulence in general is underestimated. The velocity can also be calculated using porous media flow approach, but the accuracy is not as good as for spheres. The deviation is more severe for more complex scour protections. In general, computational models provide valuable information for the prediction and design of scour protections for offshore wind farms.     

Sand ripples generated by regular oscillatory flow

The prediction of ripple geometry is a necessary precursor to the prediction of sand transport under waves for ripple regime conditions. The paper begins with a comparison of four existing methods for predicting the geometry of sand ripples generated by oscillatory flow. The comparison points to substantial differences between ripple dimensions predicted by the methods, especially for field-scale conditions. Ripple geometry experiments carried out in a large oscillatory flow tunnel are then described. The experiments involved a range of sand sizes and sinusoidal and asymmetric flows with periods and velocities typical of field conditions. Comparison of measured and predicted ripple geometries leads to the recommendation that the method of Mogridge, Davies and Willis be used to predict ripple geometry for field-scale oscillatory flows. The Nielsen method yields good predictions of ripple length, but the rapid fall-off in ripple steepness predicted by the Nielsen method at high mobility number is not supported by the measurements. The lengths and heights of symmetric ripples produced by sinusoidal flows are found to be similar to the lengths and heights of asymmetric ripples produced by “equivalent” asymmetric flows. Three-dimensional ripples occur with fine sand in long-period flows typical of field conditions. The dimensions of these ripples cannot be predicted using methods developed for two-dimensional ripples. Previously suggested criteria for predicting the occurrence of three-dimensional ripples fail when tested against a wide range of flow and sand conditions. The occurrence of three-dimensional ripples and the effects of ripple and flow history on ripple geometry require further research.     

Intense near-bed sediment motions in waves and currents

In the past few years, two-phase models have been developed to describe the detail behaviour of fluid/sediment interactions and transport under the sheet flow conditions. Due to the complexity of the governing equations and uncertainties in the formulations of various stress terms, few complete solutions of these equations are known and the validations are thus far limited to only a few experimental data. In this paper, the numerical predictions of the behaviour of sheet flows using an improved version of an earlier two-phase flow model [Coastal Eng. 36(2) (1999) 87] are described. Although the general structure of the model was retained, a number of improvements had been made to give better account the underlying physics of the flow in areas very close to the stationary bed. All key flow parameters have been predicted and analysed in order to gain insight into the processes. Calculated time-dependent as well as time-averaged concentrations are compared with experimental data from purely oscillatory flows and oscillatory flow plus a current. Good qualitative agreements between predictions and measurements were achieved for the time-dependent concentrations while the time-averaged concentrations are quantitatively accurate as well.     

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。     

Database of full-scale laboratory experiments on wave-driven sand transport processes

A new database of laboratory experiments involving sand transport processes over horizontal, mobile sand beds under full-scale non-breaking wave and non-breaking wave-plus-current conditions is described. The database contains details of the flow and bed conditions, information on which quantities were measured and the value of the measured net sand transport rate for 298 experiments conducted in 7 large-scale laboratory facilities. Analysis of the coverage of the experiments and the measured net sand transport rates identified the following gaps in the range of test conditions and/or the type of measurements: (i) graded sand experiments, (ii) wave-plus-current experiments and (iii) intra-wave velocity and concentration measurements in the ripple regime. Furthermore, it highlights two areas requiring further research: (i) the differences in sand transport processes and sand transport rates between real waves and tunnel flows with nominally similar near-bed oscillatory flow conditions and (ii) the effects of acceleration skewness on transport rates. The database is a useful resource for the development and validation of sand transport models for coastal applications.     

Analytical solution of oscillating inviscid flow over oblate spheroids with spheres and flat disks as special cases

The hydrodynamic forces acting on an oblate spheroid placed in an oscillating free stream are obtained for the special case of inviscid flow. The flow is assumed incompressible and axisymmetric and the free stream oscillations are harmonic. The flow direction is always along the spheroid's axis of symmetry. Analytical expressions are obtained for the potential and stream functions as well as the surface pressure distribution and the hydrodynamic force coefficient. The analysis is based on the solution of the unsteady equations of motion and continuity in oblate spheroidal coordinate system. The parameters involved are the major to minor axes ratio and the Strouhal number. The solutions for the two limiting cases of oscillating flows over disks and spheres can be easily obtained from the presented analytical solution.     

Threshold of Sediment Movement in Different Wave Boundary Layers

A review of former studies on the onset of sediment movement under wave action reveals that the Shields criterion obtained in unidirectional steady flow can also be applicable to oscillatory unsteady flow when the boundary layer is the same. In this paper, through comparison of different boundary layers in wave and steady flow conditions, a new criterion is presented which can be used to predict the threshold of sediment movement under wave action. The criterion curve shows good agreement with the experimental data.     

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 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.     

Initial grain motion under oscillatory flow: A comparison of some threshold criteria

Experimental data are described on the threshold of transport of quartz, ilmenite, and cassiterite grains under oscillatory flow in a flume and the results are compared to those of other investigators. The results show that for a given particle size, critical shear stress (τ_crit) increases with increasing wave period and that τ_crit increases with both grain size and grain density. These data are compared with prediction equations.     

Modelling the optical properties of suspended particulate matter of coral reef environments using the finite difference time domain (FDTD) method

The optical scattering properties of non-spherical calcium carbonate particles were modelled using the finite difference time domain (FDTD) method. This algorithm is computationally expensive but an implementation running on a standard computer’s graphics processing unit (GPU) provided up to 40 times speed increase and made feasible several thousand model runs for particles up to size parameter 33 (4 μm for a wavelength of 376 nm in water). The model evaluates all coefficients of the single-particle Mueller matrix and, when applied to spheres in this size range, compares closely to Mie theory. The modelled unpolarised and polarised angular irradiance scattering from elongate calcium carbonate spicules displayed many differences from that of spheres of equivalent volume. Scattering features were observed that are not immediately obvious consequences of spicule geometry. The extinction efficiency of these particles is also less than that of spheres of equivalent volume. These results suggest both potential consequences of the non-sphericity of particles on instrument calibration and radiative transfer modelling, and opportunities for information extraction by polarimetry.     

选择性起动条件下砾石沉积物转动角的实验室测量

沉积物颗粒与下覆颗粒间转动角是制约沉积物颗粒起动的一个重要因素。本文样品采集于1987年。作者通过一系列实验探明了沉积物转动角同颗粒形状、相对粒径比以及迭瓦状构造等因素之间的相互关系。在均匀粒径条件下,球状砾石转动角的测量数值同理论数值相吻合,但随粒径的减小而增大。这一结果同前人利用球状砂粒进行实验所获得的结果相一致。利用球状、椭球状及棱角状砾石进行的实验表明,沉积物转动角φ随相对粒径的增大而减小,随颗粒扁平度及颗粒棱角度的增大而增大。扁平砾石的迭瓦状构造将导致转动角的增大,其增大值约等于砾石的迭瓦角。若其它因素相同,沉积物起动的难度自球状、椭球状、棱角状及迭瓦状构造而依次增强。这些结果将有助于对颗粒粒径、形状、构造同沉积物搬运临界状态以及沉积物选择性起动之间的相互关系进行定量分析。     

Initial grain motion under oscillatory flow: A comparison of some threshold criteria

Experimental data are described on the threshold of transport of quartz, ilmenite, and cassiterite grains under oscillatory flow in a flume and the results are compared to those of other investigators. The results show that for a given particle size, critical shear stress (τ_crit) increases with increasing wave period and that τ_crit increases with both grain size and grain density. These data are compared with prediction equations.