Euler-Euler two-phase flow simulation of tunnel erosion beneath marine pipelines

In this study an Euler-Euler two-phase model was developed to investigate the tunnel erosion beneath a submarine pipeline exposed to unidirectional flow. Both of the fluid and sediment phases were described via the Navier-Stokes equations, i.e. the model was implemented using time-averaged continuity and momentum equations for the fluid and sediment phases and a modified k−ε turbulence closure for the fluid phase. The fluid and sediment phases were coupled by considering the drag and lift interaction forces. The model was employed to simulate the tunnel erosion around the pipeline laid on an erodible bed. Comparison between the numerical result and experimental measurement confirms that the numerical model successfully predicts the bed profile and velocity field during the tunnel erosion. It is evident that the sediments are transported as the sheet-flow mode in the tunnel erosion stage. Also the transport rate under the pipe increases rapidly at the early stage and then reduces gradually at the end of the tunnel erosion beneath pipelines.     

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.     

Instantaneous energetics sediment transport model calibration

In this note we point out a bias error that affects calibrations of ‘Bagnold-type’ energetics sediment transport models. Calibrations based on instantaneous measurements of fluid velocity and suspended sediment concentration incur an inherent increase in correlation between measured and predicted sediment transport rates because the measured fluid velocity resides on both sides of the calibration equation. Random, fully uncorrelated velocity and suspended load time series tests comparing the energetics model with a similar model which divides both sides of the equation by the velocity, showed that having velocity on both sides increased the R² correlation coefficient from its expected near zero value to 0.45. This “false correlation” can be as high as 0.55 when there is a high mean concentration relative to the concentration variance and there are small mean velocities. In contrast, when there is relatively high variability in concentration in the presence of large mean velocities (e.g. suspension events of coarse grains under waves in the surf zone with an alongshore current), the “false correlation” reduced to 0.35. Comparisons with data from two swash experiments and a surf zone study showed a similar increase in “false correlation”. Associated with the “false correlation” was a 4-fold overestimate of the calibration coefficient used to tune the sediment transport model under simulated noisy field measurement conditions.     

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.     

Swash overtopping and sediment overwash on a truncated beach

New experimental laboratory data are presented on swash overtopping and sediment overwash on a truncated beach, approximating the conditions at the crest of a beach berm or inter-tidal ridge-runnel. The experiments provide a measure of the uprush sediment transport rate in the swash zone that is unaffected by the difficulties inherent in deploying instrumentation or sediment trapping techniques at laboratory scale. Overtopping flow volumes are compared with an analytical solution for swash flows as well as a simple numerical model, both of which are restricted to individual swash events. The analytical solution underestimates the overtopping volume by an order of magnitude while the model provides good overall agreement with the data and the reason for this difference is discussed. Modelled flow velocities are input to simple sediment transport formulae appropriate to the swash zone in order to predict the overwash sediment transport rates. Calculations performed with traditional expressions for the wave friction factor tend to underestimate the measured transport. Additional sediment transport calculations using standard total load equations are used to derive an optimum constant wave friction factor of f_w = 0.024. This is in good agreement with a broad range of published field and laboratory data. However, the influence of long waves and irregular wave run-up on the overtopping and overwash remains to be assessed. The good agreement between modelled and measured sediment transport rates suggests that the model provides accurate predictions of the uprush sediment transport rates in the swash zone, which has application in predicting the growth and height of beach berms.     

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.     

Impact of lugworms (Arenicola marina) on mobilization and transport of fine particles and organic matter in marine sediments

We investigated the impact of sediment reworking fauna and hydrodynamics on mobilization and transport of organic matter and fine particles in marine sediments. Experiments were conducted in an annular flume using lugworms (Arenicola marina) as model organisms. The impact of lugworms on sediment characteristics and particle transport was followed through time in sediments experimentally enriched with fine particles (< 63 μm) and organic matter. Parallel experiments were run at low and high water current velocity (11 and 25 cm s^− 1) to evaluate the importance of sediment erosion at the sediment–water interface. There was no impact of fauna on sediment composition and particle transport at current velocity below the sediment erosion threshold. At current velocity above the erosion threshold, sediment reworking by lugworms resulted in dramatic particle transport (12 kg dry matter m^− 2) to an adjacent particle trap within 56 days. The transported matter was enriched 6–8 times in fine particles and organic matter when compared to the initial sediment. This study suggests that sediment reworking fauna is an important controlling factor for the particle composition of marine sediments. A. marina mediated sediment reworking greatly increases the sediment volume exposed to hydrodynamic forcing at the sediment–water interface, and through sediment resuspension control the content of fine particles and organic matter in the entire reworked sediment layer (> 20 cm depth).     

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.     

Measurement and modelling of the influence of grain size and pressure gradient on swash uprush sediment transport

The paper examines the dependency between total sediment transport, q, and grain size, D (i.e. q ∝ D^p) under dam break generated swash flows. Experiments were performed in a dam break flume over a sloping mobile sand bed with median grain sizes ranging from 0.22 mm to 2.65 mm. The total sediment transport was measured by truncating the flume bed and collecting the sediment transported over the edge. The experiments were designed to exclude pre-generated turbulence and pre-suspended sediment so as to focus solely on the swash flow. The magnitude and nature of the grain size dependency (i.e. p value) were inferred for different flow parameters; the initial dam depth, d_o, the integrated depth averaged velocity cubed, ∫ u³dt, and against the predicted transport potential, q_p, using the Meyer-Peter Muller (MPM) transport model and variations of that model. The data show that negative dependencies (p < 0) are obtained for d_o and q_p, whilst positive dependencies (p > 0) are obtained for ∫ u³dt. This indicates that a given d_o and q_p transport less sediment as grain size increases, whereas transport increases with grain size for a given ∫ u³dt. The p value is found to be narrowly ranged, 0.5 ≤ p ≤ − 0.5. On average, the incorporation of a pressure gradient term via the piezometric head into the MPM formulation reduces q_p by 4% (fine sand) to 18% (coarse sand). The measured total transport for fine and coarse sands is best predicted using MPM and MPM + dp*/dx respectively. However, the inferred optimum transport coefficient in the MPM formulation is about 30, much higher than the standard coefficient in a steady flow and this is not due to the presence of the pre-suspended sediment. The optimum transport coefficient indicates some sensitivity to grain size, suggesting that some transport processes remain unaccounted for in the model.     

风暴过程中潮滩悬沙浓度和悬沙输运的变化及其动力机制——以长江三角洲南汇潮滩为例

悬沙浓度是淤泥质海岸重要的环境指标。为探讨潮滩悬沙浓度和悬沙输运对风暴事件的响应过程及其动力机制,于2014年9月"凤凰"台风过境前、中、后在长江三角洲南汇潮滩进行了现场观测,获得同步高分辨率的水深、波高、近底流速和浊度剖面时间序列(9个潮周期)。结果表明,风暴中平均和最大波高、波-流联合底床剪切应力、悬沙浓度和悬沙输运率可比平静天气高数倍;风暴期间高潮位低流速阶段悬沙沉降导致近底发育数十厘米厚的浮泥层(悬沙浓度大于10 g/L)。研究认为风暴事件中淤泥质海岸悬沙浓度和悬沙输运的剧烈变化其根本动力机制是风暴把巨大能量传递给近岸水体,进而显著增大波-流联合底床剪切应力,导致细颗粒泥沙再悬浮。     

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.     

Modeling beach profile evolution at centennial to millennial scales

The proposed model allows the satisfactory reproduction of the changes in the profile geometry in each time step depending on the sediment budgets in a given morphodynamic system. The applied modification to the general Bruun rule governing the conservation of mass must account for the effect of the sediment transport, which is described in terms of the erosion and accretion rates (Er and and Ac, respectively). The scale of the erosion is a function of the total annual wave energy flux reaching the beach. The accretion is governed by the Er, on the one hand, and by the sediment budget in the morphodynamic system, on the other hand. The equilibrium profile obtained for the case of a balanced sediment budget (Er = Ac) shows good agreement with the observed profiles. A deficit or surplus in the sediment budget results in the shoreline??s retreat or advance accompanied by either a decrease or increase in the slope of the bottom profile. The model accounts for different types of shoreline responses to changes in the sea level (the Bruun rule, the development of a coastal barrier, and abrasion). Sediment budget imbalances can be a factor in the profile??s evolution due to changes in the sea level, while the combination of both factors will produce a variety of behaviors of the shoreline, as was shown by our calculations. The model was verified using historical data on the behavior of the Central Holland coast and the Abkhazian coast during the Late Holocene. It was shown that the model satisfactory reproduces the progradation of coastal barriers. An example of a relatively short-term forecast (over a 100-year period) is given.     

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.     

Longshore sediment transport on non-planar beaches

For a concave-up $\text{2}\text{3}$ power Bruun beach profile, the following two energetics-based sediment transport models are developed: (1) a Bagnold-type model and (2) a combined wave-current stress model. The stress model is calibrated with the Bagnold model using observed transport rates on planar beaches. The sediment transport profiles for the two models are in agreement within the surf zone for the planar beach case; but the stress model is also applied seaward of the breaker line where the Bagnold model is not. A mean swash transport of sand is predicted by the Bagnold model for a $\text{1}\text{2}$ power least-squares approximation to total depth including setup/setdown on a Bruun beach profile. The total longshore transport of sand is determined for each transport model as a function of the turbulent lateral mixing strength. The total sand transport is found to be less on a concave-up beach profile than for the corresponding planar beach case.     

A sheetflow sediment transport model for skewed-asymmetric waves combined with strong opposite currents

Prototype scale physical model tests were conducted to investigate the sheetflow sediment transport of uniform sand under different skewed-asymmetric oscillatory flows with and without the presence of relatively strong currents in the opposite direction against wave propagation. Experiments show that in most cases with fine sands, the “cancelling effect” which balances the on-/off-shore net transport under pure asymmetric/skewed oscillatory flows and results a moderate net transport was developed for combined skewed-asymmetric shaped oscillations. However, under certain conditions (T > 5 s) with coarse sands, the onshore sediment transport was enhanced for combined skewed-asymmetric flows. Additionally, the new experimental data under collinear oscillatory flows and strong currents show that offshore net transport rates increase with decreasing velocity skewness and acceleration skewness. Sediment movement behaviors were investigated through analysis of experimental data obtained from the image analysis technique and attempts were made to estimate and formulate the sheetflow layer thickness. Accordingly, sediment transport under oscillatory sheetflow conditions was studied and successfully explained by comparing the bed shear stress and the phase lag parameter at each half cycle. Consequently, these parameters were incorporated in an improved Dibajinia and Watanabe's type sediment transport model. The formula is calibrated against a comprehensive experimental data (331 in total). Good agreement obtained between predictions and measurements shows that the new formula is fulfilled for practical purposes.