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This study presents results from laboratory experiments to investigate the wake structure in the lee side of a scaled three-bladed horizontal axis tidal stream turbine with a mono-pile support structure. Experiments are conducted for a range of approaching flow velocity and installation height of rotor. Analysis of the results shows that bed shear stress increases with the increase of approaching velocity and decrease of installation height within 2D (D is the diameter of the rotor) downstream of the rotor. The flow field within 2D downstream of the rotor is greatly influenced by the presence of nacelle and mono-pile. Low stream-wise flow velocity and large turbulence intensity level is detected along the flume center right behind the nacelle and mono-pile from 1D to 2D downstream of the rotor. Stream-wise velocity at the blade tip height lower than the nacelle increases sharply from 1D to 2D and gradually grows afterwards. Correspondingly, the turbulence intensity decreases quickly from 1D to 2D and slowly afterwards. Large bed shear stress is measured from 1D to 2D, which is closely related to turbulence induced by the mono-pile. It is also found that the presence of the mono-pile might make the flow field more ‘disc-shaped’.

Pile foundations have been widely used in offshore engineering. In this study, a three-dimensional numerical model was used to investigate the seabed response around a mono-pile under wave-current loading. Reynolds-averaged Navier-Stokes equations were used to simulate the flow field, and Biot's consolidation equations were used for simulating the response of a porous seabed. The pore water pressure within soil and the effective stress along the depth of the seabed were simulated for various current velocities, with currents traveling either along or against the wave. Results indicate that the current has a significant effect on the effective stress and the pore water pressure distributions, which increases with the current velocity, and that the current traveling against the wave increases the liquefaction depth of the porous seabed.

Solutions for dam-break flow mainly developed for rectangular channels are not applicable to prediction of the propagation of the dam-break wave in frictional triangular channels. This stud...

The instability of soil slopes is directly related to the shear parameters of the soil material and groundwater, which usually causes some uncertainty. In this study, a novel method, the e...

Aquatic vegetation can significantly affect flow structure, sediment transport, bed scour and water quality in rivers, lakes, reservoirs and open channels. In this study, the lattice Boltzmann method is applied for performing the two dimensional numerical simulation of the flow structure in a flume with rigid vegetation. A multi-relaxation time model is applied to improve the stability of the numerical scheme for flow with high Reynolds number. The vegetation induced drag force is added in lattice Boltzmann equation model with the algorithm of multi-relaxation time in order to improve the simulation accuracy. Numerical simulations are performed for a wide range of flow and vegetation conditions and are validated by comparing with the laboratory experiments. Analysis of the simulated and experimentally measured flow field shows that the numerical simulation can satisfactorily reproduce the laboratory experiments, indicating that the proposed lattice Boltzmann model has high accuracy for simulating flow-vegetation interaction in open channel.

In this paper, an analytical model that represents the streamwise velocity distribution for open channel flow with submerged flexible vegetation is studied. In the present vegetated flow modelling, the whole flow field has been separated into two layers vertically: a vegetated layer and a non-vegetated free-water layer. Within the vegetated layer, an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted. In the non-vegetated layer, a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated. Based on the studied analytical model, a sensitivity analysis has been conducted to assess the influences of the drag ( C D ) and friction ( C f ) coefficients on the flow velocity. The investigated ranges of C D and C f have also been compared to published values. The findings suggest that the C D and C f values are non-constant at different depths and vegetation densities, unlike the constant values commonly suggested in literature. This phenomenon is particularly clear for flows with flexible vegetation, which is characterised by large deflection.

Laboratory experiments are presented to investigate the effect of different piggyback pipeline configurations on the morphology of local scour under wave conditions. Scour depth and width around the pipelines under regular and irregular waves are measured and analyzed for a range of pipeline and wave conditions; such as the spacing between two pipes (G), gap between the main pipe and seabed (e), pipe diameter (D), wave height (H) and period (T). Experimental results reveal that both the scour depth and width around piggyback pipeline is much larger than those around single pipe under the same wave conditions. Scour depth increases with the increase of the Keulegan-Carpenter (KC) number and decreases with increase of G and e. When e exceeds 0.5D, scour depth tends to approach 0. When spacing G is greater than 0.4D, the destabilization from small pipe to large one is greatly reduced, resulting in scour depth around piggyback pipeline being close to that around single pipe. Similar to scour depth, scour width broadens with the increase of KC number increasing and decreases with the increase of G. Experiments also show that the effect of e on scour depth is greater than that of G under the same test conditions, while their impact on scour width is opposite. Furthermore, scour width under irregular waves is extended slightly compared with regular wave for otherwise the identical conditions.

This paper presents the results of laboratory experiments and numerical simulations to investigate the effect of different piggyback pipeline configuration on the morphology of local seabed scour subject to steady currents. Piggyback pipeline configuration investigated includes the commonly used piggyback pipeline, namely a small pipe attached on the top of large pipe and new form of piggyback pipeline proposed in this study in which a small pipe is attached to the large pipe on the upstream and downstream side, respectively. Pressure gradient, drag coefficient, lift coefficient and scour extent around pipelines are measured and analyzed for a range of pipelines and current conditions. Results show that the vortex strength downstream of the commonly used piggyback pipeline is larger than that for a single as well as the new piggyback pipeline under the same condition. This new type piggyback pipeline can effectively reduce the depth and width of the scour hole. In particular, when the ratio of the small pipe diameter over the large pipe diameter is greater than 0.3, little scour under this new type piggyback pipeline occurs for the test conditions. The bed topography downstream of the pipe has also been altered to favor the backfill.

Seabed instability around a pipeline is one of the primary concerns in offshore pipeline projects. To date, most studies focus on investigating the wave/current-induced response within a porous seabed around either a fully buried pipeline or a thoroughly exposed one. In this study, unlike previous investigations, a series of comprehensive laboratory experiments are carried out in a wave flume to investigate the wave-induced pore pressures around a partially embedded pipeline in a trench layer. Measurements show that the presence of the partially buried pipeline can significantly affect the excess pore pressure in a partially backfilled trench layer, which deviates considerably from that predicted by the theoretical approach. The morphology of the trench layer accompanied with the backfill sediments, especially the deeper trench and thicker backfill (i.e., b ≥ 1 D , e ≥ 0.5 D ), provides a certain degree of resistance to seabed instability. The amplitude of excess pore pressure around the trench layer roughly exhibits a left-right asymmetric distribution along the periphery of the pipeline, and decays sharply from the upper layer of the trench to the lower region. Deeper trench depth and thicker buried layer significantly weaken the pore-water pressures in the whole trench area, thus sheltering and protecting the submarine pipeline against the transient seabed liquefaction.

Based on the method of characteristics, in this study an analytical solution for one-dimensional shallow-water equations is developed to simulate the instantaneous dam-break flows propagati...

The existing analytical solutions of dam-break flow do not consider simultaneously the effects of wet downstream bottom and bed slope on the dam-break wave propagation. In this study, a new...

In this study, the evolution process of the swallow-tailed flip bucket water nappe entering into the plunge pool is simulated by using the standard k-ε turbulence model and the volume-of-fluid method. The effects of the upstream opening width ratio and downstream bucket angle on the flow pattern, the unit discharge distribution, and the impact pressure distribution are studied. Based on the numerical results, the inner and outer jet trajectories are proposed by using the data. Results show that the longitudinal stretching length decreases with the increase of the upstream opening width ratio and increases with the increase of the downstream bucket angle. The water nappe enters the plunge pool in a long strip shape. Thus, the unit discharge distribution of water nappe entry is consistent with the pressure distribution at the plunge pool bottom. The upstream opening width ratio and downstream bucket angle should be chosen as their intermediate values in order to have a uniform discharge distribution and to reduce the pressure peak at the plunge pool floor, which is effectively to avoid instability and destruction of plunge pool floor.

For overbank flows in meandering channels, the flow direction along a meander varies and is affected by floodplain vegetation. This study proposes a model for predicting the depth-averaged two-dimensional flow direction (depth-averaged flow angle) along a meander in smooth and vegetated meandering compound channels. Laboratory experiments were performed in smooth and vegetated channels. Measurements show that the height of the secondary current cell in the main channel is increased by dense floodplain vegetation comparing with that in a non-vegetated channel. A method of determining the height of the cell is proposed. At the middle section between the apex and exit sections, where the secondary current cell is absent, the depth-averaged flow angle is independent of the height of the cell. Beyond the middle section, a new secondary current cell is formed, and the flow angle is highly dependent on the height of the cell. The proposed model is thoroughly verified using the flume experimental and field observed data. Good agreement is obtained between predictions and measurements, indicating that the proposed model is capable of accurately predicting the depth-averaged flow angle along a meander in smooth and vegetated meandering compound channels.

When ocean waves propagate over porous seabed, they cause variations of the pore pressure within seabed, leading to the possible wave attenuation and soil liquefaction. In order to advance and improve our understanding of the process of wave-induced seabed liquefaction and its impact on wave propagation, systematical experiments are carried out in a wave flume with a soil basin filled with silt. Both the pore pressures and water surface elevations are measured simultaneously, while the seabed liquefaction is videotaped using a high-speed camera. Laboratory measurements show that the pore pressure in surface layer mainly oscillates over time, while the wave period averaged pore pressure has little change. In the deep layer, however, the wave period averaged value of the pore pressure builds up dramatically. The results show that the wave height decreases rapidly along the direction of wave propagation when seabed liquefaction occurs. Such a wave attenuation is greatly enhanced when the liquefaction depth further increases. The experiments also demonstrate that the conditions (wave height and wave period) of incident waves have significant impacts on the wave-induced pore pressures, liquefaction depth and wave attenuation in a silt bed.

Field measurements and numerical simulations demonstrate the existence of an upper saline plume in tidally dominated beaches. The effect of tides on the saltwater-freshwater mixing occurring at both the upper saline plume and lower salt wedge is well understood. However, it is poorly understood whether the tidal driven force acts equally on the mixing behaviours of above two regions and what factors control the mixing fluctuation features. In this study, variable-density, saturated-unsaturated, transient groundwater flow and solute transport numerical models are proposed and performed for saltwater-freshwater mixing subject to tidal forcing on a sloping beach. A range of tidal amplitude, fresh groundwater flux, hydraulic conductivity, beach slope and dispersivity anisotropy are simulated. Based on the time sequential salinity data, the gross mixing features are quantified by computing the spatial moments in three different aspects, namely, the centre point, length and width, and the volume (or area in a two-dimensional case). Simulated salinity distribution varies significantly at saltwater-freshwater interfaces. Mixing characteristics of the upper saline plume greatly differ from those in the salt wedge for both the transient and quasi-steady state. The mixing of the upper saline plume largely inherits the fluctuation characteristics of the sea tide in both the transverse and longitudinal directions when the quasi-steady state is reached. On the other hand, the mixing in the salt wedge is relatively steady and shows little fluctuation. The normalized mixing width and length, mixing volume and the fluctuation amplitude of the mass centre in the upper saline plume are, in general, one-magnitude-order larger than those in the salt wedge region. In the longitudinal direction, tidal amplitude, fresh groundwater flux, hydraulic conductivity and beach slope are significant control factors of fluctuation amplitude. In the transverse direction, tidal amplitude and beach slope are the main control parameters. Very small dispersivity anisotropy (e.g., α L / α T 5 ) could greatly suppress mixing fluctuation in the longitudinal direction. This work underlines the close connection between the sea tides and the upper saline plume in the aspect of mixing, thereby enhancing understanding of the interplay between tidal oscillations and mixing mechanisms in tidally dominated sloping beach systems.

Sui, T.; Zhang, C.; Zheng, J.; Guo, Y., and Xie, M., 2018. Numerical study of standing wave-induced residual response with the non-homogenous soil property. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 921–925. Coconut Creek (Florida), ISSN 0749-0208. Coastal seabed soil is usually non-homogeneous vertically. Seabed instability may take place under dynamic wave loading which may lead to the marine landslides. Most of the existing models have been limited to the soil oscillatory mechanism for a sandy seabed with relatively large permeability, which neglects the residual mechanism in a silt seabed with poor drainage condition. In this study, based on the Fully-dynamic (FD) seabed model, the numerical invesitgation for standing wave induced non-homogeneous seabed residual response is proposed. The present model is validated based on the flume tests in...

The flow in the main channel of a meandering compound channel does not occur in the ridge direction because of the effect of the upstream floodplain flows. This study proposes a model for estimating the flow direction in the depth-averaged two-dimensional domain (depth-averaged flow angles) between the entrance and the apex sections. Detailed velocity measurements were performed in the region between the meander entrance section and apex section in a large-scale meandering compound channel. The vertical size of the secondary current cell is highly related to the depth-averaged flow angle; thus, the means of the local flow angles above the secondary current cell and within the cell are separately discussed. The experimental measurements indicate that the mean local flow angle above the cell is equal to the section angle, whereas the mean local flow angle within the cell is equal to zero. The proposed model is validated using published data from five sources. Good agreement is obtained between the predictions and measurements, indicating that the proposed model can accurately estimate the depth-averaged flow direction in the meandering compound channels. Finally, the limitations and application ranges of the model are discussed.

This paper presents the results from a numerical simulation study to investigate the effect of the position angle (α) of small pipeline on the local scour and the hydrodynamic force around the piggyback pipeline in steady current conditions. Results show that the local scour depth around the piggyback pipeline increases first and then decreases with the increase of α. The scour depth and width reach the maximum values as the small pipe locates at the top of the large pipeline (i.e. α = 90°). The scour around the piggyback pipeline is accelerated when α ranges between 30° and 165°, while for α = 0°–30° and 165°–180°, the local scour around the piggyback pipeline is inhibited. Furthermore, the small pipe placed in front of the large pipe has slightly larger effect on the scour hole morphology than that when it is placed behind the large pipe. The drag force coefficient increases first and reaches the maximum value at α = 75°, and then decreases with the increase of α. Eventually the drag force coefficient approaches roughly a constant. The lift force coefficient is approximately a V-shaped with the variation of α and has the maximum value at α = 90°.

Ice cover formed on an alluvial channel can significantly alter the flow characteristics, such as the vertical distributions of streamwise velocity and shear stress, and hence the water and sediment transport process. The vertical profile of the suspended sediment concentration in the ice-covered alluvial channels with steady uniform flows is investigated in this study. To calculate the suspended sediment concentration, we are based on the Schmidt O’Brien equation and deduce an analytical model that employs an existing eddy viscosity model and a modified formula of the sediment fall velocity considering the common effects of the upper and lower boundaries. The proposed analytical model is then validated by using available experimental data reported in the literature. The predicted accuracy of the proposed model is evaluated through error statistics by comparing to previous modeled results. The relative concentration profiles of the suspended sediment are subsequently simulated by applying the validated analytical model with different characteristic parameters. Results show that the relative concentration decreases with the increase of both the ice cover roughness and the sediment fall velocity. The uniformity of the relative concentration distribution is closely related to the value of the proportionality parameter σ, revealing the physical mechanism that the more prominent the turbulent diffusion effect is, the more uniform the relative concentration profile is.

Stability and safety of offshore wind turbines with mono-pile foundations, affected by nonlinear wave effect and dynamic seabed response, are the primary concerns in offshore foundation design. In order to address these problems, the effects of wave nonlinearity on dynamic seabed response in the vicinity of mono-pile foundation is investigated using an integrated model, developed using OpenFOAM, which incorporates both wave model (waves2Foam) and Biot's poro-elastic model. The present model was validated against several laboratory experiments and promising agreements were obtained. Special attention was paid to the systematic analysis of pore water pressure as well as the momentary liquefaction in the proximity of mono-pile induced by nonlinear wave effects. Various embedded depths of mono-pile relevant for practical engineering design were studied in order to attain the insights into nonlinear wave effect around and underneath the mono-pile foundation. By comparing time-series of water surface elevation, inline force, and wave-induced pore water pressure at the front, lateral, and lee side of mono-pile, the distinct nonlinear wave effect on pore water pressure was shown. Simulated results confirmed that the presence of mono-pile foundation in a porous seabed had evident blocking effect on the vertical and horizontal development of pore water pressure. Increasing embedded depth enhances the blockage of vertical pore pressure development and hence results in somewhat reduced momentary liquefaction depth of the soil around the mono-pile foundation.

Seabed consolidation state is one of important factors for evaluating the foundation stability of the marine structures. Most previous studies focused on the seabed consolidation around breakwaters standing on the seabed surface. In this study, a numerical model, based on Biot's poro-elasticity theory, is developed to investigate the unsaturated seabed consolidation around a nearshore pile foundation, in which the pile inserted depth leads to a different stress distribution. Seabed instabilities of shear failure by the pile self-weight and the potential liquefaction under the dynamic wave loading are also examined. Results indicate that (1) the presence of the inserted pile foundation increases the effective stresses below the foundation, while increases and decreases the effective stresses around the pile foundation for small (de/R 3.3) inserted depths, respectively, after seabed consolidation, (2) the aforementioned effects are relatively more significant for small inserted depth, large external loading, and small Young's modulus, (3) the shear failure mainly occurs around the inserted pile foundation, rather than below the foundation as previously found for the located marine structures, and (4) wave-induced momentary liquefaction near the inserted pile foundation significantly increases with the increase of inserted depth, due to the change of seabed consolidation state.

Wave-induced seabed instability caused by the residual liquefaction of seabed may threaten the safety of an offshore foundation. Most previous studies have focused on the structure that sits on the seabed surface (e.g., breakwater and pipeline), a few studies investigate the structure embedded into the seabed (e.g. a mono-pile). In this study, by considering the inertial terms of pore fluid and soil skeleton, a three-dimensional (3D) integrated model for the wave-induced seabed residual response around a mono-pile is developed. The model is validated with five experimental tests available in the literature. The proposed model is then applied to investigate the spatial and temporal pattern of pore pressure accumulation as well as the 3D liquefaction zone around a mono-pile. The numerical simulation shows that the residual pore pressure in front of a pile is larger than that at the rear, and the seabed residual response would be underestimated if the inertial terms of pore fluid and soil skeleton are neglected. The result also shows that the maximum residual liquefaction depth will increase with the increase of the embedded depth of the pile.

This paper presents field measurements in which dye solute was injected into coastal sand to investigate contaminant advection in intertidal beach sand. The measurements show the pathways of a contaminated plume in the unsaturated zone during both the flood and ebb tides. A prescribed amount of dye tracer solution was directly injected through the topsoil, with average porosity 0.3521 ± 0.01, at predetermined locations of the River Mersey's outer estuarial beach during ebb-tide. The injected dye was monitored, sampled and photographed over several tidal cycles. The distinctive features of the plume (full two dimensional cross-sections), sediments and water-table depth were sampled in-situ, close to the injection point (differing from previous contaminant monitoring tests in aquifers). The advective movement is attributed to tidal impact which is different from contaminant transport in aquifers. The experimental results show that plumes have significantly large spatial variability, diverging upwards and converging downwards, with a conical geometric shape which is different from the usual spherical/elliptical shape reported in literature. The mean vertical motion of the plume reaches three times the top-width within ten tidal cycles, exceeding the narrow bottom-width by a factor of order 2. The observed transport features of the plume within the beach sand have significant relevance to saltwater intrusion, surface water and groundwater quality. The field observations are unique and can serve as a valuable benchmark database for relevant numerical studies.

This paper presents the results from laboratory experiments and theoretical analysis to investigate the development of scour around submarine pipeline under steady current conditions. Experiments show that the scour process takes place in two stages: the initial rapid scour and the subsequent gradual scour development stage. An empirical formula for calculating the equilibrium scour depth (the maximum scour depth) is developed by using the regression method. This formula together with the maximum entropy theory can be applied to establish a formula to predict the scour process for given water depth, diameter of pipeline and flow velocity. Good agreement between the predicted and measured scour depth is obtained.

An integrated Finite Element Method (FEM) model is proposed to investigate the dynamic seabed response for several specific pipeline layouts and to simulate the pipeline stability under waves loading. In the present model, the Reynolds-Averaged Navier–Stokes (RANS) equations are used to describe the wave motion in a fluid domain, while the seabed domain is described using Biot's poro-elastic theory. The interface between water and air is tracked by conservative Level Set Method (LSM). The FEM and backward differentiation formula (BDF) are applied for spatial and temporal discretization respectively in the present model. One-way coupling is used to integrate flow and seabed models. The present model is firstly validated using several available laboratory experiments. It is then further extended to practical engineering applications, including the dynamic seabed response for the pipeline mounted on a flat seabed or inside a trench. The results show that the pipeline buried to a certain depth is better protected than that under partially buried in terms of transient liquefaction.

Laboratory experiments have been carried out to investigate wave damping over the seabed, in which the excess pore pressure and free surface elevations are synchronously measured for examining the wave-induced soil dynamics and wave kinematics. Two types of soil, namely fine sand and silt, are tested to examine the role of soil in the wave damping. Observation of experiments shows that (i) soil liquefaction takes place for some tests with silty bed and soil particles suspend into the water layer when the bed is made of silt; (ii) sand ripples can be generated for experiments with sand bed. Measurements reveal that the wave damping greatly depends on the soil dynamic responses to wave loading and the wave damping mechanism over the silty seabed differs from that over the sand bed. On the one hand, the wave damping rate is greatly increased, when soil liquefaction occurs in the silty bed. On the other hand, the presence of sand ripples generated by oscillatory flow in the sand bed experiments also increases the wave damping to some extent. Furthermore, experimental results show that soil particle suspension in the silt bed test contributes to the wave damping. Theoretical analysis is presented to enhance discussions on the wave damping. The theoretical calculations demonstrate that the wave damping is mainly induced by the shear stress in the boundary layer for the cases when no liquefaction occurs. While for the cases when soil liquefaction takes place, the viscous flow in the liquefied layer contributes most towards to the wave damping.

Results are presented from a numerical simulation to investigate the vertical buoyant wall jet discharged into a linearly stratified environment. A tracer transport model considering densit...

In this study, a new three-dimensional model was developed to provide a better understanding of the mechanism for wave-induced seabed response around the mono-pile. Based on the poro-elastic theory, the fully dynamic formulations were adopted in the present model to simulate the pore pressure, soil stresses and the displacements of both soil and mono-pile. Good agreement between the numerical simulation and experimental results was obtained. Based on the parametric study, the numerical results concluded that (1) the wave diffraction and reflection have significant effects on the pore pressure and soil displacements around the mono-pile; (2) the largest discrepancy of pore pressure due to the variation in seabed parameters appears in front of mono-pile, while the smallest discrepancy is at the position of angle 3π/4 with respect to the incident wave direction and (3) the increase in the mono-pile horizontal displacement corresponds to the increase in the wave height and the decrease in the seabed Young's m...

Zhang, J.; Song, S.; Zhai, Y.; Tong, L., and Guo, Y., 2019. Numerical study on the wave-induced seabed response around a trenched pipeline. Journal of Coastal Research, 35(4), 896–906. Coc...

A two dimensional (2D) RNG k–e sediment model including the effects of secondary currents is developed to simulate the sediment transport and bed deformation in rivers with continuous bends. Non-uniform suspended and bedload sediment transports and the variation of effective bed material size distribution are included in the model. A semi-coupled scheme for sediment model is proposed, which can be used for simulating both the long- and short term sediment transport whenever riverbed changes. The model is applied to simulate the flow and sediment transport in the upper reach of the Yellow River which is a typical natural river reach with continuous bends. The river bed deformations caused by suspended and bedload sediments are investigated. Good agreement between the numerically simulated results and the field measurements is obtained, indicating that the model is capable of simulating the sediment transport and predicting the bed deformation of rivers having continuous bends with reasonable accuracy.

This study proposes a new approach in which an impermeable plate is placed under the pipeline to prevent the local scour around the pipeline. In order to understand the performance of this approach, the finite volume method (FVM) and volume of fluid (VOF) method are adopted to simulate the flow field around the pipeline. The pressure distribution along the sandy bed surface is obtained by considering the variation of water surface. Furthermore, the effects of water depth, unidirectional and bidirectional impermeable plates on pressure difference are discussed. The seepage flow field of sandy bed near underwater pipeline is numerically simulated using the laminar and porous media model. On this basis, the effect of the impermeable plate length on hydraulic gradient is investigated and the critical length of impermeable plate is obtained. The simulated results show that when the water depth is smaller than 5.00D (D is the diameter of pipeline), the effect of the water depth on the pressure difference is remarkable. The pressure differences between two endpoints of both the unidirectional and bidirectional plates decrease with the increase of the plate length. The variations of the pressure differences for both the unidirectional and bidirectional plates are similar. With the increase of plate length, the hydraulic gradient decreases and the piping at the seepage exit is avoided effectively as long as it reaches a certain length. Such a critical length of the plate decreases with the increase of the water depth. When water depth is larger than 4.00D, the effect of the water depth on the critical length is small. For the same water depth, the critical length of impermeable plate increases with the increase of the dimensionless flow parameter. Numerical simulation results are in good agreement with the available experimental measurements.

Zhang, J., Zheng, J., Zhang, C., Jeng, D. and Guo, Y., 2013. Numerical study on the interaction between waves and twin pipelines in sandy seabed In offshore engineering practice, the construction of an identical cylinder close to the existing pipeline may largely affect the near flow field and hydrodynamic forces on the pipelines. The interaction between incident ocean wave and twin pipelines in sandy seabed plays an important role in the design of submarine pipelines. A mathematical model based on the Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) equations, a two-equation k-e turbulence closure and an internal source term wave maker is adopted to describe this complex phenomenon. The sandy bed where the pipelines are partly buried is treated as a rigid porous material, and its impact on wave-pipeline interaction is considered in the VARANS model in terms of porosity and equivalent mean diameter of porous material. The impacts of burial depth and distance between the centers of twin pi...

A two-dimensional (2-D) numerical model and a three-dimensional (3-D) numerical model of the Yangtze Estuary, including tidal flow, suspended sediment transport and bed evolution, were established based on the Delft3D-FLOW model respectively. The models were calibrated with the field data. The calibrated models were employed to predict the morphological evolution process of the Yangtze Estuary for the next 20 years, with the predicted area covering the Chongming Eastern Beach and the Nanhui Tidal Flat. According to the simulated results in the medium term, due to the progress of the Three Gorges, erosion will happen in the southeast and south region and deposition will happen in the northeast and north region of the Chongming Eastern Beach, while a deep channel will be formed gradually in the middle part. The Nanhui Tidal Flat will develop southeastwards. Five scenarios of different river discharges and sediment loads are obtained from an exponential regression equation between flow rate and suspended sediment concentration deduced from the monthly averaged flow rate and suspended sediment concentration during 2003–2009. These five scenarios were used for investigating the topographic responses of the Chongming Eastern Beach and the Nanhui Tidal Flat to different river discharge and sediment supply conditions. The predictions show that the erosion rate will decrease and the deposition rate will increase with the increase of sediment supply, i.e., less the sediment supply leads to more recession.

Results from a numerical modeling study are presented to investigate the tidal elevations, tidal current velocity, bed deformation, and suspended sediment concentration in the Qiantang Estuary, China. The Qiantang Estuary is well-known for its macrotide, which generates a hydrodynamically complex environment. This presents challenges for numerical modelers to accurately simulate the flow field and sediment transport in the region. This paper presents a mathematical model using finite volume method with unstructured mesh to simulate the tide-induced water elevation, current velocity, bed deformation, and suspended sediment transport in the Qiantang Estuary. The parameters in the model were determined using the long-term observed field data of the Qiantang Estuary. The simulated tidal elevations and current velocities agree well with the field observations. The numerical prediction of the bed deformation in 5 months is reasonably compared with the field measurements carried out in the same period. H...

Flow resistance in fluvial open channels, especially in steep gravel-bed channels, still presents challenges to researchers and engineers. This article presents some new data from both the flume experiments and field measurements. Data analysis using the divided hydraulic radius approach shows that the relative roughness plays a significant role in the bed form resistance. A new set of formulas that incorporate the relative roughness are proposed. As compared with several existing formulas, the proposed formulas can be used to better estimate the bed form resistance.

Three-dimensional (3D) numerical study is presented to investigate the turbulent flow in meandering compound open channels with trapezoidal cross-sections. The flow simulation is carried out by solving the 3D Reynolds-averaged continuity and Navier–Stokes equations with Reynolds stress equation model (RSM) for steady-state flow. Finite volume method (FVM) is applied to numerically solve the governing equations of fluid flow. The velocity magnitude, tangential velocity, transverse velocity and Reynolds stresses are calculated for various flow conditions. Good agreement between the simulated and available laboratory measurements was obtained, indicating that the RSM can accurately predict the complicated flow phenomenon. Comparison of the calculated secondary currents of four cases (one being inbank flow and other three being overbank flow) with different water depths reveals that (i) the inbank flow exhibits different flow behaviors from that of the overbank flow does and (ii) the water depth has significant effects on the magnitude and direction of secondary currents. Copyright © 2010 John Wiley & Sons, Ltd.

The interaction between wave and offshore deposits is of great importance for the foundation design of marine installations. However, most previous investigations have been limited to connecting separated wave and seabed sub-models with an individual interface program that transfers loads from the wave model to the seabed model. This research presents a two-dimensional coupled approach to study both wave and seabed processes simultaneously in the same FEM (finite element method) program (COMSOL Multiphysics). In the present model, the progressive wave is generated using a momentum source maker combined with a steady current, while the seabed response is applied with the poro-elastoplastic theory. The information between the flow domain and soil deposits is strongly shared, leading to a comprehensive investigation of wave-seabed interaction. Several cases have been simulated to test the wave generation capability and to validate the soil model. The numerical results present fairly good predictions of wave generation and pore pressure within the seabed, indicating that the present coupled model is a sufficient numerical tool for estimation of wave-induced pore pressure.

Results are presented to investigate the characteristics of turbulent flow in a pressure conduit, such as water supply pipes and flood discharging tunnels. The turbulent flow governing equations, the Reynolds-averaged Navier–Stokes equations, in conjunction with a k–e turbulent model are numerically solved using SIMPLEC. The study focuses on the modeling and calculation of the flow velocity field, pressure distribution, and the incipient cavitation number of the surface irregularities in the conduit. Different types and sizes of irregularities are simulated for various incoming flow velocities. The computed results are in good agreement with laboratory experimental data.

Turbulent flow in a 3-D blade passage of a Francis hydro turbine was simulated with the Large Eddy Simulation (LES) to investigate the spatial and temporal distributions of the turbulence when strongly distorted wakes in the inflow sweep over the passage. In a suitable consideration of the energy exchanging mechanism between the large and small scales in the complicated passage with a strong 3-D curvature, one-coefficient dynamic Sub-Grid-Scale (SGS) stress model was used in this article. The simulations show that the strong wakes in the inflow lead to a flow separation at the leading zone of the passage, and to form a primary vortex in the span-wise direction. The primary span-wise vortex evolves and splits into smaller vortex pairs due to the constraint of no-slip wall condition, which triggers losing stability of the flow in the passage. The computed pressures on the pressure and suction sides agree with the measured data for a working test turbine model.

Results are described from a combined laboratory and analytical study of the dense, deep-water flow through the Faroe Bank Channel. Archival field data have been used to specify the velocity and density field conditions in an idealized, distorted laboratory model in which the spatial and temporal development of a turbulent, dense source flow has been studied parametrically in terms of the source Rossby and Froude numbers, respectively. Measurements are presented to show that the flow (i) maintains geostrophic balance within the topographically varying channel and (ii) adjusts on the Ekman time scale to changing flow conditions. The outflow structure is shown to consist of a dominant axial (i.e., along channel) core component, with a significant transverse (i.e., side slope) secondary circulation driven by Ekman drainage and topographic divergence processes. Density field measurements are presented to show the mixing occurring between the turbulent outflow and the overlying water mass. Buoyancy anomaly data are derived to quantify the spatial variations of mixing processes along and across the channel. An analytical model based on Ekman dynamics is developed for flow in the channel, and the predictions of the dimensions of the outflow in terms of the external flow and topographic parameters are shown to agree well with the laboratory data.

Laboratory model experiments have been conducted to investigate the interaction of a tidally forced stratified flow with a continental shelf. Results collected from a wide range of parametric experiments covering sub-, critical and super-critical tidal forcing are presented to show that the resulting flow regimes can be classified conveniently by the dimensionless parameters Fr=Usb/cw and μ=ω2/N02α, where Usb is the maximum velocity at the shelf break of slope angle α, cw is the long-wave speed of the lowest internal mode, ω is the frequency of the forcing and N0 is the buoyancy frequency of the initial undisturbed flow. Three distinct and characteristic flow regimes are observed, namely (i) shelf break eddies, (ii) intense downslope jets associated with offshore filamentary transport and (iii) pure up- and down-slope oscillatory jet flow, the occurrence of each of which is well-determined within Fr:μ parameter space. Measurements show a monotonic increase in eddy size (normalised by the amplitude A of the tidal forcing) with increasing Fr, while the thickness of the up- and downslope jet is shown to scale with A and to have no significant dependence on Fr. Measurements of the perturbation density field show significant intra-cycle variability in the local mixing and overturning parameters such as the buoyancy anomaly g′(zi), the available potential energy function ξ and the r.m.s. density ρr.m.s., with evidence of weak mixing and overturning (but significant internal wave activity) at slack tide conditions. Maximum values of both ξ and ρr.m.s. within a cycle show monotonic increases with increasing Fr and a strong dependence upon α and offshore location. Overall qualitative agreement with aspects of related numerical model results of Xing and Davies (J. Phys. Oceanogr. 27 (1997) 2100) and Holloway and Barnes (Cont. Shelf Res. 18 (1998) 31) is shown to be encouraging.

An experimental laboratory study has been carried out to investigate the propagation of an internal solitary wave of depression and its distortion by a bottom ridge in a two-layer stratified fluid system. Wave profiles, density fields and velocity fields have been measured at three reference locations, namely upstream, downstream and over the ridge. Experiments have been performed with wave amplitudes in the range 0.2– 1.9 times the depth of the upper layer, and a ratio between the lower and the upper layer in the range 3.0–8.5. The ridge slope was varied from 0.1 to 0.33 and the maximum ridge height was two-thirds of the thicker fluid layer. Over the ridge, the flow has been classified into: (i) cases when the bottom ridge has little influence on the propagation and spatial structure of the internal solitary wave, (ii) cases where the internal solitary wave is significantly distorted by the blocking effect of the ridge (though no wave breaking occurs), and (iii) cases for which the internal solitary wave is broken as it encounters and passes over the bottom ridge. A detailed description of the processes leading to wave breaking is given. Breaking has been found to take place when the fluid velocity in the lower layer exceeds 0.7 of a local nonlinear wave speed, defined at the top of the ridge. The breaking condition is also expressed in terms of the amplitude of the incident wave, the layer thickness ratio and the relative height of the ridge. The wave breaking can be determined from the input parameters of the experiment. The transmitted waves have been found to always consist of a leading pulse (solitary wave) followed by a dispersive wavetrain. The (solitary) wave amplitude is significantly reduced only when breaking takes place at the ridge. Internal waves of mode two are generated in cases with strong breaking.

Results are presented from a series of laboratory modelling studies carried out as part of the international multidisciplinary project CANIGO. The focus of interest has been the phenomenon of flow adjustment within the Gulf of Cadiz of the Mediterranean outflow plume, modelled by a turbulent, negatively-buoyant jet discharging into a rotating stratified reservoir scaled to the idealised topography of the Gulf. The results show that the fully developed flow pattern that forms close to the entrance to the Gulf consists of a relatively intense jet that divides when it encounters the southern Iberian coastal boundary; part of the jet is deflected westwards to form a boundary current at intermediate depth along the coastline and part is deflected eastwards and back towards the Strait to form a closed weak circulation near the diverging right wall of the Gulf. Within this closed circulation (the typical horizontal dimensions of which scale with the source Froude number when normalised with the inertial radius), small-scale eddy features are embedded. The degree of entrainment into the descending turbulent jet is seen to be determined primarily by the receiving water Froude number (and is relatively insensitive to the Burger and Rossby numbers of the flow), resulting in the formation of a boundary current of intermediate density that follows the Iberian coastal boundary with a typical velocity determined primarily by the effective driving head at the source and weakly by the Burger number of the flow.

Results are presented from two sets of laboratory model experiments on the effects of an isolated seamount upon the flow of an intermediate-water slope current along a continental shelf. The experimental results for initial ambient conditions of respectively two-layer and linearly stratified fluids show that the structure of such a boundary current depends primarily on the values of the appropriate set of dimensionless dynamical parameters (namely the Burger (Bu), Ekman (Ek) and Rossby (Ro) numbers), as well as the dimensionless lateral separation of the seamount and shelf and the proportional height of the seamount relative to the distance from the bottom at which the intermediate-water flows. Comparisons of the present results with those from a previous two-layer fluid study with no obstacle present reveals that the presence of the obstacle does not alter significantly the stability of the current even when situated close to the shelf. However, for such configurations, the density, velocity and vorticity fields in the local zone of interaction between the current and the obstacle are distorted significantly by the presence of the obstacle, provided that the summit of the obstacle penetrates the level of current flow. Measurements of density, velocity and vorticity fields show no significant dependence of the flow interaction upon the detailed bathymetry of the shelf-slope. For stable intermediate-water slope currents, the nature of the interaction with the obstacle is determined primarily by (i) the lateral separation of the obstacle and the shelf edge and (ii) the Ro of the flow. For sufficiently low values of the former and high values of the latter, the interaction results in a splitting of the incident flow around the obstacle, with cyclonic and anticyclonic eddy pairs being generated in the lee. Geostrophic equilibrium is seen to be maintained in the current, even in the near wake of the obstacle. For cases in which the summit of the seamount is below the initially-undisturbed intermediate water level, no Taylor column-like division of the slope current occurs and no significant distortion of the current structure (velocity and density) occurs for the parameter ranges investigated. For linearly stratified cases, measurements show that no significant local elevation or depression of the density interfaces is observed in the interaction zone. The distributions of the local buoyancy frequencies calculated from the density profiles reveal that the minimum value of the frequency upstream of the obstacle is smaller than that downstream, indicating that the flow interactions generate local mixing downstream, with consequent erosion of the density interfaces.

Laboratory experiments are presented from a modelling investigation into the influence of shelf and slope topography on f-plane surface and intermediate flows along ocean boundaries. The surface flows are formed from an upstream source by the release of fresh water into a rotating tank containing salt water, while for the intermediate-water counterpart flows, neutrally-buoyant fluid was released from a submerged source into stably-stratified (two-layer) and quiescent receiving waters in solid body rotation. It is shown that the stability of these buoyancy-driven currents can be described satisfactorily by a combination of the dimensionless parameters Bu=N2/f2, Ek=2ν/fD02 and Ro=U0/fL0, where N and f are the buoyancy and Coriolis frequencies respectively, D0, L0 and U0 are the initial depth, width and velocity of the currents, respectively, and ν is the kinematic viscosity of the fluid. Furthermore, comparison with physical models of surface and intermediate flows along a vertical wall and over a flat bottom reveals that the stability regimes are not significantly altered by the presence of shelf topography. Variation of the depth of the surface flows with respect to the total fluid depth above the underlying shelf is shown to have a significant effect on the velocity and density structure of these flows. When the depth and width ratios are small, the surface flow is not affected by the varying topography. However, when the current occupies a considerable height above the shelf and is at least as wide as the shelf, upper layer fluid is transported offshore through the bottom Ekman layer, where it is arrested above the sloping bottom. At this location, a deepening of the upper layer develops due to potential vorticity conservation of the lower layer, accompanied by a local alongshore velocity maximum. This shelf break front prevents significant offshore transport of upper layer fluid far beyond the shelf break, even in cases where the flow is unstable. Comparison of the intermediate currents with dynamically-similar currents above a flat bottom does not reveal a stabilising effect of the slope. For unstable intermediate currents, offshore transport is not prohibited (as it is shown to be for surface currents over narrow shelves, due to the presence of the slope), and large scale instability patterns can extend over great distances from the slope. It is shown that the geostrophic nature of these currents is destroyed close to the sloping bottom. Here, the upper and lower density interfaces, denoting the vertical extents of the intermediate current, tilt sharply downwards.

The response of a stratified fluid to the imposition of a surface stress has long been a topic of interest in geophysical fluid dynamics because of the relevance of the problem to mixing and overturning in large lakes, reservoirs and ocean basins. In the first definitive laboratory investigations (e.g Kato and Phillips, 1969; Kantha et al., 1977; Scranton and Lindberg, 1983) in this area, a linearly-stratified fluid contained in an annular tank was subjected to a constant surface stress imposed by the motion of a rotating screen and the process of entrainment was thereby initiated. As a result, a so-called mixed layer was generated, the thickness of which grew with time at a rate dependent upon the appropriate Richardson number of the established flow. In the annular geometry, the presence of secondary flows ensured that the development of the mixed layer was three-dimensional. Further experiments have been carried out by many authors since the above investigations and the reader is referred specifically to the recent article by Fernando (1991) for a comprehensive record and review of the resulting data