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.     

Effect of bed roughness on turbulent boundary layer and net sediment transport under asymmetric waves

This paper presents an investigation of the roughness effects in the turbulent boundary layer for asymmetric waves by using the baseline (BSL) k–ω model. This model is validated by a set of the experimental data with different wave non-linearity index, N_i (namely, N_i = 0.67, N_i = 0.60 and N_i = 0.58). It is further used to simulate asymmetric wave velocity flows with several values of the roughness parameter (a_m/k_s) which increase gradually, namely from a_m/k_s = 35 to a_m/k_s = 963. The effect of the roughness tends to increase the turbulent kinetic energy and to decrease the mean velocity distribution in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the turbulent kinetic energy and the mean velocity distribution is relatively unaffected. A new simple calculation method of bottom shear stress based on incorporating velocity and acceleration terms is proposed and applied into the calculation of the rate of bed-load transport induced by asymmetric waves. And further, the effect of bed roughness on the bottom shear stress and bed-load sediment transport under asymmetric waves is examined with the turbulent model, the newly proposed method, and the existing calculation method. It is found that the higher roughness elements increase the magnitude of bottom shear stress along a wave cycle and consequently, the potential net sediment transport rate. Moreover, the wave non-linearity also shows a big impact on the bottom shear stress and the net sediment transport.     

The influence of scale,slope and channel geometry on the flow dynamics of submarine channels

Submarine channels are major morphological features of the sea floor and are important in the transport of sediment to the deep ocean. Although much is known concerning the large-scale distribution of sediment within and surrounding submarine channels, there is little understanding of the fluid dynamic processes that control this sedimentation. Direct measurement of flow velocities and concentrations has proved to be extremely difficult within submarine channels, with the resultant paucity of direct observations making physical laboratory modelling a critical technique for examining the processes that operate in, and control, submarine channel development.Recent experimental and numerical studies have proposed a new model of secondary circulation within submarine channel bends, characterised by a reversal in the orientation of the secondary circulation cell relative to that found in meandering rivers. This new paradigm for submarine channels thus predicts basal flow from the inside to the outside of the bend at a bend apex, with an upper return flow directed towards the inner bend. The reversal in orientation of the secondary flow cell has been linked to the vertical distribution of downstream velocity and associated changes in centrifugal and pressure gradient forces. However, previous work has additionally proposed that shearing of the within-channel flow by overbank flow may also generate secondary flow reversal.This study assesses the applicability of the proposed submarine bend flow model against a range of key channel parameters. We demonstrate that the sense of secondary circulation is the same for all experimental conditions, strongly supporting the new model of secondary flow in submarine channels. Furthermore, investigation of overbank shear induced secondary circulation confirms for the first time that this mechanism can occur, and identifies the channel styles most likely to exhibit this effect. Such shear-induced circulation is, however, shown to be a secondary mechanism, with the vertical distribution of downstream velocity the principal mechanism. In certain channel configurations, the two mechanisms may act to augment one another.     

Laboratory observation of boundary layer flow under spilling breakers in surf zone using particle image velocimetry

A boundary layer flow under spilling breakers in a laboratory surf zone with a smooth bottom is investigated using a high resolution particle image velocimetry (PIV) technique. By cross-correlating the images, oscillatory velocity profiles within a viscous boundary layer of O(1) mm in thickness are resolved over ten points. Using PIV measurements taken for an earlier study and the present study, flow properties in the wave bottom boundary layer (WBBL) over the laboratory surf zone are obtained, including the mean velocities, turbulence intensity, Reynolds stresses, and intermittency of coherent events. The data are then used to estimate the boundary layer thickness, phase variation, and bottom shear stress. It is found that while the time averaged mass transport inside the WBBL is onshore in the outer surf zone, it changes to offshore in the inner surf zone. The zero Eulerian mass transport occurs at h/h_b ≈ 0.92 in the outer surf zone. The maximum overshoot of the streamwise velocity and boundary layer thickness are not constant across the surf zone. The bottom shear stress is mainly contributed by the viscous stress through mean velocity gradient while the Reynolds stress is small and negligible. The turbulence level is higher in the inner surf zone than that in the outer surf zone, although only a slight increase of turbulent intensity is observed inside the WBBL from the outer surf zone to the inner surf zone. The variation of phase inside and outside the WBBL was examined through the spatial velocity distribution. It is found the phase lead is not constant and its value is significantly smaller than previous thought. By analyzing instantaneous velocity and vorticity fields, a remarkable number of intermittent turbulent eddies are observed to penetrate into the WBBL in the inner surf zone. The size of the observed large eddies is about 0.11 to 0.16 times the local water depth. Its energy spectra follow the − 5/3 slope in the inertial subrange and decay exponentially in the dissipation subrange.     

Three-dimensional hydrodynamic model, study cases for quarter annular and idealized ship channel problems

An extended version of the three-dimensional hydrodynamic model, ADCIRC 3D-DSS, was utilized to simulate both horizontal and vertical flows in a (quarter) annular harbor (QATP and ATP) and rectangular basin with an idealized ship channel (RBSC). Comparison of horizontal and vertical solutions to the analytical solution and results of other researchers are in good agreement. The vertical velocity solution is highly sensitive to the horizontal velocity solutions. The presence of the sidewall boundary may also affect the vertical solutions. Around the sloping bank of RBSC channel with one-third gradient, the vertical velocity becomes important. The maximum vertical velocity approaches ±50% of the sediment fall velocity of fine sand.     

Transport processes of uniform and mixed sands in oscillatory sheet flow

New experiments were carried out in the Large Oscillating Water Tunnel of WL|Delft Hydraulics (scale 1:1) using asymmetric 2nd-order Stokes waves. The main aim was to gain a better understanding of size-selective sediment transport processes under oscillatory plane-bed/sheet-flow conditions. The new data show that for uniform sand sizes between 0.2 < D < 1.0 mm, measured net transport rates are hardly affected by the grain size and are proportional to the third-order velocity moment. However for finer grains (D = 0.13 mm) net sand transport rates change from the ‘onshore’ direction into the ‘offshore’ direction in the high velocity range. A new measuring technique for sediment concentrations, based on the measurement of electro-resistance (see [McLean, S.R., Ribberink, J.S., Dohmen-Janssen, C.M. and Hassan, W.N.M., 2001. Sediment transport measurements within the sheet flow layer under waves and currents. J. Waterw., Port, Coast., Ocean Eng., ISSN 0733-950X]), was developed further for the improved measurement of sediment dynamics inside the sheet-flow layer. This technique enabled the measurements of particle velocities during the complete wave cycle. It is observed that for long period waves (T = 12.0 s), time-dependent concentrations inside the sheet-flow layer are nearly in phase with the time-dependent flow velocities. As the wave period decreases, the sediment entrainment from the bed as well as the deposition process back to the bed lags behind the wave motion more and more. The new data show that size-gradation has almost no effect on the net total transport rates, provided the grain sizes of the sand mixture are in the range of 0.2 < D < 1.0 mm. However, if very fine grains (D = 0.13 mm) are present in the mixture, net total transport rates of graded sand are generally reduced in comparison with uniform sand with the same D₅₀. The transport rates of individual size fractions of a mixture are strongly influenced by the presence of other fractions in a mixture. Fine particles in sand mixtures are relatively less transported than in that uniform sand case, while the opposite occurs for coarse fractions in a mixture. The relative contribution of the coarse grains to the net total transport is therefore larger than would be expected based on their volume proportion in the original sand mixture. This partial transport behaviour is opposite to what is generally observed in uni-directional (e.g. river) flows. This is caused by vertical sorting of grain sizes in the upper bed layer and in the sheet flow and suspension layers. Kinematic sorting is believed to be responsible for the development of a coarse surface layer on top of a relatively fine sub-layer, providing in this way a relatively large flow exposure for the coarser sizes. Furthermore fine grains are suspended more easily than coarse grains to higher elevations in the flow where they are subject to increasing phase-lag effects (settling lags). The latter also leads to reduced net transport rates of these finer sizes.     

Turbulence-induced steady streaming in an oscillating boundary layer: On the reliability of turbulence closure models

The accuracy of several closure models of the Reynolds-Averaged Navier–Stokes Equations in predicting the characteristics of an oscillating turbulent wall boundary layer is analyzed. The analysis involves four low Reynolds number k − ε models and a k − ω model and it is carried out by comparing the model results both with experimental data and with data obtained by a Direct Numerical Simulation (DNS) of the Navier–Stokes equations. The boundary layer is generated by a spatially constant time-oscillating pressure gradient given by the sum of two harmonic components characterized by angular frequencies Ω^∗ and 2Ω^∗ respectively, which generates a steady streaming because of the asymmetry of turbulence intensity during the cycle. Thus the results are relevant to the boundary layer at the bottom of nonlinear sea waves. The attention is therefore focused on the accuracy of the models in reproducing the period averaged profiles of the hydrodynamic characteristics of the steady streaming. The instantaneous quantities, such as time development of the wall shear stress, profiles of the streamwise velocity, Reynolds stresses and turbulent kinetic energy are also considered and analyzed. The results shows that a model can be judged better or worse than other models depending on the specific flow characteristic under investigation. However, an approach has been adopted which allowed to rank the models according to their accuracy in predicting the values of the hydrodynamic quantities involved in the present study.     

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.     

Phase-lag effects in sheet flow transport

The inception of the sheet flow regime as well as the effects of the phase lag when the sheet flow regime is established were investigated for oscillatory flows and combined steady and oscillatory flows. A new criterion for the inception of sheet flow is proposed based on around 300 oscillatory flow cases from experiments. This criterion was introduced in the Camenen and Larson [Camenen, B., Larson, M., 2005. A bedload sediment transport formula for the nearshore. Estuarine, Coastal and Shelf Science 63, 249–260.] bed load formula in order to take into account phase-lag effects in the sheet flow regime. The modification of the Camenen and Larson formula significantly improves the overall agreement with data and yields a correct behavior in relation to some of the main governing parameters, which are the median grain size d₅₀, the orbital wave velocity U_w, and the wave period T_w. The calibration of the new formula was based on more than 200 experimental data values on the net sediment transport rate for a full wave cycle. A conceptual model was also proposed to estimate the ratio between sediment transport rate with and without phase lag, (r_pl = q_s,net / q_s,net,ϕ=0). This simple model provides accurate results and may be used together with any quasi-steady model for bed load transport.     

Experimental investigations on developments of velocity field near above a sandy bed during regular wave-induced fluidized responses

Regular waves were applied in a laboratory flume to investigate the evolutions of the velocity fields near above a fine sandy bed (d₅₀=0.073 mm) during fluidized responses. Measurements of 2D velocity components and suspended sediment concentration (SSC) at 1 cm above the bed in addition to water surface displacements and sub-soil pore pressures were carried out with an acoustic Doppler velocimeter and an optical probe. The results have shown similar three typical soil responses including one unfluidized and two fluidized responses to previous report in other fine-grained soil beds. In the post- and pre-fluidized stages of a resonantly fluidized response, amplitudes of horizontal velocity component can be decreased by a maxima value of 50% while vertical components can be amplified up to 5 times larger. The developments of near-bed velocity field become less significant in consecutive non-resonantly fluidized responses. Particularly, the evolutions of the velocity field are closely dependent on the deepening of fluidized surface soil layers d_f and the characteristics of soil fluidization responses. The amplified vertical velocity components are clearly contradictory to the dissipated overloading waves near above a fluidized bed but are critical to much drastic sediment suspensions by interactions between overloading waves and fluidized bed soils.     

Field studies of velocity,salinity and suspended solids concentration in a shallow tidal channel near tidal flap gates

The design and operation of mathematical models of solute mixing and sediment transport in estuaries rely heavily on the provision of good-quality field data. We present some observations of salinity, suspended sediment concentration and velocity at one of the tidal limits of a semi-enclosed tidal lagoon in Southern England (Pagham Harbour, West Sussex, UK) where the natural processes of tidal incursion and solute mixing have been heavily modified as a result of the construction of sea walls dating back to the 18th Century. These observations, made immediately downstream of two parallel tidal flap gates by conductivity-temperature-depth (CTD) profiler, and also using bed-mounted sensor frames to measure velocity at 2 fixed depths, have yielded a set of results covering 11 tidal cycles over the period 2002–04. It is clear from the results obtained that over a typical tidal cycle, the greatest vertical salinity gradients occur in the 1–2 h immediately after the onset of the flood tide, and that subsequently, energetic mixing acts to rapidly break down this stratification. Under moderate-to-high fresh water flows (>0.5 m³/s), the break-down in vertical salinity gradient is more gradual, while under low fresh water flows (<0.2 m³/s), the vertical salinity gradient is generally less pronounced. Estimates of Richardson number during the early flood-tide period reveal values that vary rapidly between <1 and about 20, with lower values occurring after around 1.5–2 h after low water. Observations of suspended sediment concentration vary widely even for similar tidal and fresh water flow conditions, revealing the possible influence of wind speed, the storage effects of the water in the lagoon downstream of the observation site, and the complexity of the hydrodynamics downstream of tidal flap gates. The data also show that most of the sediment transport is landward, and occurs during flood tides, with estimated total tidal landward flood tide flux of fine sediment of the order of 50–120 kg under low fresh water flow conditions. These observations, which reinforce the results presented in Warner et al. (2004) and elsewhere, can help to provide information about the appropriate techniques for managing sediments and pollutants, including nutrients from sewage effluent waters, in estuaries where hydraulic flap gates are used to control the entry of fresh water over the tidal cycle.     

The effect of standing biomass on flow velocity and turbulence in Spartina alterniflora canopies

Plant-flow interactions on the surface of tidal wetlands result in flow characteristics that are profoundly different from non-vegetated flows. Reductions in mean flow velocity and turbulence, especially the vertical components, limit vertical mixing and may impact a wide range of processes including geochemical exchanges at the sediment water interface, larval recruitment and dispersion, and sediment deposition and retention. The goal of this paper is to quantify horizontal and vertical components of velocity, turbulence intensity and total turbulent kinetic energy in Spartina alterniflora canopies in southeastern North Carolina and to relate flow characteristics to particulate transport on the marsh surface. Another aim of this paper is to assess the extent to which the distribution of standing biomass affects mean flow and turbulence by comparing S. alterniflora data to other canopy types and through a series of canopy manipulations which altered canopy height and stem densities.The results of this study indicate that flow velocity, turbulence intensity, and total turbulent kinetic energy (TKE) are significantly reduced within the vegetated canopy and that this reduction is inversely related to the amount of biomass present in the water column. Within the canopy, approximately 50% of the initial mean velocity and TKE is reduced within 5 m of the canopy edge. Within the canopy, mean velocity and TKE_horiz usually exceeded vertical velocity or TKE_vert and the vertical components of flow were attenuated more strongly than the horizontal. These results suggest that within the vegetation, turbulence contributes more to lateral advection than to vertical mixing. As a result, total suspended solid concentrations were shown to decrease logarithmically with distance from the canopy edge and to decrease at a faster rate in more densely vegetated regions of the canopy (i.e. lower TKE_vert) as compared to areas of sparser vegetation (i.e. higher TKE_vert).     

Megacusps on rip channel bathymetry: Observations and modeling

The formation of beach megacusps along the shoreline of southern Monterey Bay, CA, is investigated using time-averaged video and simulated with XBeach, a recently developed coastal sediment transport model. Investigations focus on the hydrodynamic role played by the bay's ever-present rip channels. A review of four years of video and wave data from Sand City, CA, indicates that megacusps most often form shoreward of rip channels under larger waves (significant wave height (H_s) = 1.5–2.0 m). However, they also occasionally appear shoreward of shoals when waves are smaller (H_s ~ 1 m) and the mean water level is higher on the beach. After calibration to the Sand City site, XBeach is shown to hindcast measured shoreline change moderately well (skill = 0.41) but to overpredict the erosion of the swash region and beach face. Simulations with small to moderate waves (H_s = 0.5–1.2 m) suggest, similar to field data, that megacusps will form shoreward of either rip channels or shoals, depending on mean daily water level and pre-existing beach shape. A frequency-based analysis of sediment transport forcing is performed, decomposing transport processes to the mean, infragravity, and very-low-frequency (VLF) contributions for two highlighted cases. Results indicate that the mean flow plays the dominant role in both types of megacusp formation, but that VLF oscillations in sediment concentration and advective flow are also significant.     

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.     

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.     

Characteristics of turbulent boundary layers over a rough bed under saw-tooth waves and its application to sediment transport

A large number of studies have been done dealing with sinusoidal wave boundary layers in the past. However, ocean waves often have a strong asymmetric shape especially in shallow water, and net of sediment movement occurs. It is envisaged that bottom shear stress and sediment transport behaviors influenced by the effect of asymmetry are different from those in sinusoidal waves. Characteristics of the turbulent boundary layer under breaking waves (saw-tooth) are investigated and described through both laboratory and numerical experiments. A new calculation method for bottom shear stress based on velocity and acceleration terms, theoretical phase difference, φ and the acceleration coefficient, a_c expressing the wave skew-ness effect for saw-tooth waves is proposed. The acceleration coefficient was determined empirically from both experimental and baseline k–ω model results. The new calculation has shown better agreement with the experimental data along a wave cycle for all saw-tooth wave cases compared by other existing methods. It was further applied into sediment transport rate calculation induced by skew waves. Sediment transport rate was formulated by using the existing sheet flow sediment transport rate data under skew waves by Watanabe and Sato [Watanabe, A. and Sato, S., 2004. A sheet-flow transport rate formula for asymmetric, forward-leaning waves and currents. Proc. of 29th ICCE, ASCE, pp. 1703–1714.]. Moreover, the characteristics of the net sediment transport were also examined and a good agreement between the proposed method and experimental data has been found.     

波浪-海流-微地形耦合的沉积动力模式建立及应用

沙纹微地形普遍存在于海底,沙纹的消长能改变底部应力进而影响泥沙的运移。以往研究较多侧重于波致沙纹,并已应用于波浪模式的底摩擦计算,而较少考虑波流联合效应产生的沙纹,也未将其应用于综合的水动力模式和沉积物输运模式。本文在POM水动力模式中嵌入新南威尔士大学泥沙模式,通过耦合波流共同作用的微地形模型与波流相互作用底边界层模型,发展了波浪-海流-微地形（沙纹）耦合的沉积动力模式。本文将该模式应用于澳大利亚Jervis湾,针对波主导和波流联合主导沙纹两种类型,分别进行了沙纹发展状态、几何形态的分布及悬浮泥沙的模拟。结果表明:波致沙纹比波流联合作用的沙波具有更大的波高和波长,因此当波主导时沙纹对悬浮泥沙起着关键作用。通过考虑随沙纹变化的粗糙度,相比于以往模式设置均一的粗糙度,该模型能对悬浮物浓度的骤升过程进行更精细的预测。     

长江口南港底部边界层特征的观测与分析

对长江口2002年和2003年共4个潮周期的数据进行了分析,通过流速对数剖面公式计算边界层参数,并对各个潮周期内的边界层参数的变化规律进行了分析,同时也对悬沙输送可能对垂向水流结构以及边界层参数造成的影响进行了探讨。结果表明,悬沙的时间分布特征对温度、盐度、水体密度的分布格局有重要影响,主要表现在水体的Rf值普遍较高,分层稳定。此外,悬沙也可影响边界层参数,从而对水流结构产生影响。由于水体的层化作用,使层间的摩擦阻力增大,相当于在垂向上产生不同内边界层,因而影响了流速在垂向上的变化。