Two-dimensional,two-phase granular sediment transport model with applications to scouring downstream of an apron

We present a two-dimensional, two-phase model for non-cohesive sediment transport. This model solves concentration-weighted averaged equations of motion for both fluid and sediment phases. The model accounts for the interphase momentum transfer by considering drag forces. A collisional theory is used to compute the sediment stresses, while a two-equation (k–ε) fluid turbulence closure is implemented. A benchmark sediment transport problem concerning the scouring downstream of an apron is carried out as an example and numerical results agree with existing experimental data.     

Numerical modelling of suspended sediment fluxes in estuarine waters

A two-dimensional finite difference numerical model, capable of predicting depth-averaged tidal flow fields in coastal and estuarine waters, has been extended to include tide-induced non-cohesive sediment transport processes. The partial differential equations governing the conservation of mass, momentum and suspended sediment in an incompressible turbulent flow are included in a depth-integrated form in the model. For the representation of the processes of erosion and deposition of sediment from the bed an empirically based source-sink term was refined, based on the results of three mobile bed flume studies. The model has been tested by simulating tidal flows and suspended sediment fluxes in two estuaries, with particular application to the Humber estuary in the U.K. The model was calibrated and found to produce an encouraging degree of agreement between the numerical predictions and corresponding field measurements for this estuary. Furthermore, the predicted gross deposition and erosion features of the estuary were found to be in close agreement with interpretations from Eulerian tidal residual predictions.     

Numerical simulation of a partially buried pipeline in a permeable seabed subject to combined oscillatory flow and steady current

Hydrodynamic forces exerting on a pipeline partially buried in a permeable seabed subjected to combined oscillatory flow and steady current are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k−ω turbulent model closure are solved to simulate the flow around the pipeline. The Laplace equation is solved to calculate the pore pressure below the seabed with the simulated seabed hydrodynamic pressure as boundary conditions. The numerical model is validated against the experimental data of a fully exposed pipeline resting on a plane boundary under various flow conditions. Then the flow with different embedment depths, steady current ratios and KC numbers is simulated. The amplitude of seepage velocity is much smaller than the amplitude of free stream velocity as expected. The normalized Morison inertia, drag and lift coefficients based on the corresponding force coefficients of a fully exposed pipeline are investigated. The normalized Morison force coefficients reduce almost linearly with the increase of embedment depth and that the KC only has minor effect on the normalized Morison coefficients. It is also found that the permeable seabed condition causes a slight increase on the inline force and has a little effect on the lift force, compared with corresponding conditions in an impermeable bed.     

轴线倾斜海底管道冲刷速率试验研究

通过物理模型试验研究水流作用下轴线倾斜海底管道的三维局部冲刷问题。利用超声波探头监测管道下部冲刷沿管轴线方向的扩展过程,分析海底管道三维局部冲刷的动态发展机理。由模型沙的冲蚀试验,建立沙床面剪切应力与泥沙表观侵蚀速率之间的关系式,并引入经验公式对沙床面剪切应力放大系数、泥沙表观侵蚀速率以及远场床面剪切应力之间的关系进行表达。由倾斜管道模型试验,在分析冲刷扩展位置随时间变化数据的基础上,结合上述经验公式以及沙床面剪切应力放大系数与管道埋深的关系,建立轴线倾斜海底管道冲刷扩展速率的预测公式。     

A numerical model for onset of scour below offshore pipelines

A numerical model is developed to predict the onset of local scour below offshore pipelines in steady currents and waves. The scour is assumed to start when the pressure gradient underneath the pipeline exceeds the floatation gradient of the sediments. In this model, the water flow field above the bed is determined by solving the two-dimensional (2-D) Reynolds-averaged Navier–Stokes equations with a k-ω turbulence closure. The seepage flow below the seabed is calculated by solving the Darcy's law (Laplace's equation) with known pressure distribution along the common boundaries of the flow domains-seabed. The numerical method used for both the turbulent flow around the pipeline and Darcy's flow in the seabed is a fractional finite element method. The average pressure gradient along the buried pipe surface is employed in the evaluation of onset condition with a calibration coefficient. The numerical model is validated against experimental data available in literature. A unified onset condition for steady currents and waves is proposed. Influences of flow parameters, including water depth, embedment depth, boundary layer thickness, Reynolds number (Re) and Keuleagan–Carpenter (KC) number, on the pressure drop coefficient over the pipeline are studied systematically.     

Prediction of berm geometry using a set of laboratory tests combined with teaching–learning-based optimization and artificial bee colony algorithms

Understanding sediment movement in coastal areas is crucial in planning the stability of coastal structures, the recovery of coastal areas, and the formation of new coast. Accretion or erosion profiles form as a result of sediment movement. The characteristics of these profiles depend on the bed slope, wave conditions, and sediment properties. Here, experimental studies were performed in a wave flume with regular waves, considering different values for the wave height (H₀), wave period (T), bed slope (m), and mean sediment diameter (d₅₀). Accretion profiles developed in these experiments, and the geometric parameters of the resulting berms were determined. Teaching–learning-based optimization (TLBO) and artificial bee colony (ABC) algorithms were applied to regression functions of the data from the physical model. Dimensional and dimensionless equations were found for each parameter. These equations were compared to data from the physical model, to determine the best equation for each parameter and to evaluate the performances of the TLBO and ABC algorithms in the estimation of the berm parameters. Compared to the ABC algorithm, the TLBO algorithm provided better accuracy in estimating the berm parameters. Overall, the equations successfully determined the berm parameters.     

Effective Nikuradse Roughness on the Mobile Plan Bed

Nikuradse roughness (ks) is very important in the sediment transport prediction because it is related to the evaluations of the velocity distribution, shear stress and erosion depth. Dimensionless Nikuradse roughness (ks/D, where D is the sediment diameter) is usually given 1–2.5 on the immobile plan bed or at low shear stress. But it behaves differently on the mobile plan bed at high shear stress with much sediment picked up to movement when the Shields parameter (Θ) is larger than 0.8–1.0. The effective Nikuradse roughness on the mobile plan bed was derived indirectly from the erosion depth correlated to the mobile plan bed thickness considering the mass conservation in the present study. The proposed erosion depth confirmed the relation to the Shields parameters with an extra factor consisting of suspended sediment and its damping to turbulence. The decrement of the erosion depth caused by the increment of the sediment diameter at large shear stress was obtained, which was usually absent in classical empirical formulas based on the bedload theory. Good agreement with experiments was achieved by the present prediction of the Nikuradse roughness, erosion depth and sediment transport rate. Discussion was mainly focused on the prediction improvement caused by considering the impact of suspended sediment and its damping to turbulence.     

Prediction of offshore bar-shape parameters resulted by cross-shore sediment transport using neural network

In order to understand the features of coastal zone and to utilize the coastal areas, it is necessary to determine the sediment movement and the resulting transport. Waves, topographic features, and material properties are known as the most important factors affecting the sediment movement and coastal profiles. In this study, by taking into consideration of wave height and period (H₀, T), bed slope (m) and sediment diameter (d₅₀), cross-shore sediment movement was studied in a physical model and various bar-shape parameters of the resultant erosion type profile were determined. Using 80 experimental data which are obtained from physical model studies, a neural network (NN) has been calibrated to predict bar-shape parameters of beach profiles. A sensitivity analysis was firstly carried out to decide data of training and test sets. Four different models, in which the rates of their training and testing set data were 80% and 20%, 70% and 30%, 60% and 40%, 50% and 50% were constituted and their performances were compared. It was determined that the model, in which the rate of its training and testing set data was 80% and 20%, respectively, has the best results. Therefore, a total of 64 experimental data were used as training set and the remainders of the experimental data were used as a testing set for the model. The performance of the NN model was compared with the regression equations developed in a previous study and the equations cited in literature indicating better performance over the equations.     

Numerical modeling of flow and scour below a pipeline in currents: Part II. Scour simulation

A vertical two-dimensional (2D) numerical model for time dependent local scour below offshore pipelines subject to unidirectional steady flow is developed. The governing equations for the flow and sediment transport are solved by using finite difference method in a general curvilinear coordinate system. The performance of two turbulence models, the standard k–ɛ model and Smagorinsky subgrid scale (SGS) model, on modeling time dependent scour processes is examined. Both suspended load and bed load are considered in the scour model. The suspended-load model is verified against two channel sediment transport cases. The change of bed level is calculated from the continuity equation of total sediment transport. A new time marching scheme and a sand slide scheme are proposed for the scour calculation. It is found that the proposed time marching scheme and sand slide model work well for both clear-water and live-bed scour situations and the standard k–ɛ turbulence closure is more preferable than the SGS model in the 2D scour model developed in this study.     

近岸波浪和波生流环境中泥沙输运的数值模拟

Owing to lack of observational data and accurate definition,it is difficult to distinguish the Kuroshio intrusion water from the Pacific Ocean into the South China Sea(SCS).By using a passive tracer to identify the Kuroshio water based on an observation-validated three-dimensional numerical model MITgcm,the spatio-temporal variation of the Kuroshio intrusion water into the SCS has been investigated.Our result shows the Kuroshio intrusion is of distinct seasonal variation in both horizontal and vertical directions.In winter,the intruding Kuroshio water reaches the farthest,almost occupying the area from 18°N to 23°N and 114°E to 121°E,with a small branch flowing towards the Taiwan Strait.The intrusion region of the Kuroshio water decreases with depth gradually.However,in summer,the Kuroshio water is confined to the east of 118°E without any branch reaching the Taiwan Strait;meanwhile the intrusion region of the Kuroshio water increases from the surface to the depth about 205 m,then it decreases with depth.The estimated annual mean of Kuroshio Intrusion Transport(KIT) via the Luzon Strait is westward to the SCS in an amount of –3.86×106 m3/s,which is larger than the annual mean of Luzon Strait Transport(LST) of –3.15×106 m3/s.The KIT above 250 m accounts for 60%–80% of the LST throughout the entire water column.By analyzing interannual variation of the Kuroshio intrusion from the year 2003 to 2012,we find that the Kuroshio branch flowing into the Taiwan Strait is the weaker in winter of La Ni?a years than those in El Ni?o and normal years,which may be attributed to the wind stress curl off the southeast China then.Furthermore,the KIT correlates the Ni?o 3.4 index from 2003 to 2012 with a correlation coefficient of 0.41,which is lower than that of the LST with the Ni?o 3.4 index,i.e.,0.78.     

潮流波浪联合输沙及海床冲淤演变的理论体系与其数学模拟

根据近岸带及河口区潮流、波浪、湍流各自物理尺度的不同,从Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和质量传输方程出发,利用Ｒｅｙｎｏｌｄｓ分解的方法,建立了模拟波浪 流联合输沙及海床冲淤演变的理论体系,给出了潮流作用下近岸波浪传播方程、波浪作用下潮流运动方程并通过利用波流合成底部切应力、底层湍流脉动随机特性,得出了波流联合作用下不平衡沙计算中泥沙起悬与沉降量的确定方法。本文模型应用于“广西合浦围垦工程潮流波浪     

Biological influences on morphology and bed composition of an intertidal flat

Biological activity is known to influence sediment strength at bed–water interfaces. However, its precise effect on geomorphology and on bed composition is not known. This paper proposes a parameterization of sediment destabilizing and stabilizing organisms on three parameters that describe the erosion and mixing processes of the sediment bed, namely the critical bed shear stress, the erosion coefficient and the bioturbation coefficient. This parameterization is included in a 3D sand–mud morphodynamic model to form the sand–mud–bio model. The performance of the sand–mud–bio model is demonstrated by testing it on the Paulinapolder intertidal flat in the Western Scheldt estuary of The Netherlands. Model results show that biological influences on sediment strength result in significant morphological change and bed composition variations. Destabilizing organisms always cause a significant decrease in mud content in the bed and an increase of erosion. On the other hand, stabilizing organisms can, but do not necessarily, cause an increase of mud content and additional sedimentation.     

Numerical analysis of the impact forces exerted by submarine landslides on pipelines

Submarine pipelines that transport crude oil and natural gas are often in a complex marine geological environment and may become unstable and fail upon impact by submarine landslides. Previous research has mostly focused on the impact forces exerted by submarine landslides on suspended pipelines, but the impact of submarine landslides on pipelines laid on the seafloor at various impact angles, θ, have been relatively infrequently discussed, and the effects of suspended height, H, on the impact forces exerted by submarine landslides on pipelines have not been thoroughly investigated. In this study, based on the Herschel–Bulkley model, the impact forces exerted by a submarine landslide on laid-on or suspended pipelines at various impact angles θ were simulated using the computational fluid dynamics (CFD) approach. Equations for calculating the axial and normal drag coefficients of a submarine pipeline were proposed. The CFD numerical simulation results were rearranged based on the soil mechanics approach. By comparing the parameters, an essentially corresponding relationship was found between the soil mechanics and CFD approaches when the equations were used to calculate the impact forces exerted by a submarine landslide on a pipeline. In addition, a semi-analytical expression for the failure envelope was provided. Furthermore, the effects of H on the forces on a pipeline were discussed, and an equation for calculating the acting forces on a pipeline along the flow direction of a submarine landslide that comprehensively accounts for the effects of θ and H was proposed. The lift force was discussed preliminarily and the results provide a basis for further investigation. The achievement of this study is applicable for selecting locations of submarine pipeline routes and for designing submarine pipelines.     

Experimental Study of Hydrodynamic and Self-Buried Behavior of Submarine Pipeline with Perpendicular Spoilers

The spoiler is a kind of device to disturb current and promote burying.At present,all submarine pipeline spoilers at home and abroad are parallel spoilers,that is,the plane of the spoiler is parallel to the vertical plane of the pipeline axis.According to the results of indoor experiments,when the pipeline with the forward spoiler is installed perpendicular to the direction of water flow,the spoiler will accelerate the seabed erosion and cause the pipeline to endure downward pressure,which will eventually cause the pipeline self-buried to form a protection.However,when the pipeline direction is consistent with the flow direction,the self-buried behavior and protective effect is vanished.By aiming at the defect that the forward spoiler cannot be self-buried when the direction of the pipeline and the flow are basically parallel,the spoiler burying aid device perpendicular to the pipeline axis has been innovatively developed,and the hydrodynamic changes and sediment erosion characteristics near the pipeline after the installation of the device were studied based on the experiment.Results reveal that although the perpendicular spoiler cannot generate downforce,it can greatly increase the turbulent kinetic energy of the flow and the rate of sediment erosion.The larger the angle between the pipeline axis and the spoiler plane is,the larger the increase in turbulent energy will be.The increase in turbulent energy near the bed surface can reach up about 70%when the angle is 90°,while serious sediment erosion mainly occurs along both sides of the pipeline with a distance of about 2?4 times the pipe diameter.In the future,we can further explore the influence of the perpendicular spoiler size and installation position on the pipeline downforce and the effect of burying promotion.At the same time,field tests on the perpendicular spoiler burying aid device currently developed will conduct to observe the actual effect of perpendicular spoiler promoting pipeline scouring and burying,and improve submarine pipeline safety protection technology.     

Numerical simulation of time-dependent beach and dune erosion

A computational procedure is developed for predicting the time-dependent, two-dimensional beach and dune erosion during severe storms due to elevated water levels and waves. The model employs the equation of sediment continuity and a dynamic equation governing the cross-shore sediment transport due to a disequilibrium of wave energy dissipation levels. These equations are solved numerically by an implicit, double-sweep procedure to determine the change in position of elevation contours in the profile. Given sufficient time, the profile will evolve to a form where the depth, h, in the surf zone is related to the distance seaward of the waterline by the relationship: $\text{h = Ax}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$, which is consistent with many natural profiles and in which A depends on sediment characteristics.The model is verified qualitatively and quantitatively through application to several idealized cases and through a preliminary simulation of erosion during Hurricane Eloise. In general, the time scales for shoreline response were found to be quite long relative to natural storm systems and erosion in the early response stages was found to be sensitive to storm surge height, but much less sensitive to wave height. The model response characteristics for simulation of erosion due to time-varying storm conditions show a lag between the maximum storm surge elevation and maximum erosion with the maximum erosion rate occurring at the time of the peak surge. For the simulated erosion due to Hurricane Eloise, reasonable agreement was found between the post-hurricane dune profiles and those calculated. However, the eroded volumes were in better agreement than the profile forms as the steepening of the natural dune profiles was not reproduced in the model.     

Formula for predicting bedload transport rate in oscillatory sheet flows

At high bed shear stress sheet flows often occur in coastal waters in which high-concentration bedload sediments are transported in a thin layer near the bed. This paper firstly constructs a theoretical model (partial differential equations, PDEs) for the intense transport of non-cohesive bedload sediments by unidirectional currents and then seeks a special solution to the PDEs to determine the thickness of the bedload particle–water mixture, which could serve as the “reference height” that is often invoked in numerical computation and simulation of suspended sediment transport in turbulent flows. Moreover, a modified formula is presented to determine the “reference concentration”. Using a “uch” approach the present study derives a 1D formula for predicting bedload transport rate in sheet flows driven by asymmetric waves, with the help of a novel formula for evaluating wave friction factor. The new bedload formula can generically take into account slope angle (positive and negative), wash load concentration in the driving water flow and other factors that affect bedload transport rate. It compares well with measured data in a large-scale wave flume [Dohmen-Janssen, C.M., Hanes, D.M., 2002. Sheet flow dynamics under monochromatic non-breaking waves. Journal of Geophysical Research, 107(C10), 1301–1321], a large-scale oscillatory water tunnel [ Hassan, W.N., Ribberink, J.S., 2005. Transport processes of uniform and mixed sands in oscillatory sheet flow. Coastal Engineering, 52, 745–770] and in a swash zone of natural beach [Masselink, G., Hughes, M.G., 1998. Field investigation of sediment transport in the swash zone. Continental Shelf Research, 18, 1179–1199].     

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.