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Scour around a circular monopile in coastal regions has been investigated extensively over the past decades, but the time development of scour depth around an offshore-wind monopile under large current–wave ratio still lacks a predictive model. By considering the conservation of sand volume and adopting the conventional exponential law for temporal variation, a semi-empirical model, which has three parameters, i.e., an equilibrium scour depth, a shape coefficient and a scour characteristic time scale, is developed for predicting the time development of scour depth around a monopile under live-bed conditions of combined wave–current flows. A series of laboratory experiments was conducted in current-only and wave–current flows to obtain data for model calibration and validation. Experimental results indicate that adding weak waves on current accelerates scour development, which is successfully captured by the proposed model through using the far-field bottom shear stress as a key model input. The overall model inaccuracy is within 25%, and the model's applicability is further confirmed by field measurements from an offshore wind farm in east China. This model can help to determine the timing of installing scour protection around offshore monopiles, especially for the circumstances with very strong local sediment transport (live-bed). • A new model for scour time development around a circular pile is proposed. • A set of scour tests was conducted in live-bed conditions for calibration and validation. • A field study was carried out for an offshore monopile wind farm in eastern China. [ABSTRACT FROM AUTHOR]

Abstract Monopile foundations are the most common foundation type of offshore wind turbines. In the ocean environment, in addition to threats related to scour of the foundation, offshore monopiles of wind turbines also are subjected to lateral vibrations induced by waves and winds. Over the past decades, the scour process induced by flow and pile-soil interactions has been independently investigated by researchers from the fields of hydraulic/coastal engineering and soil mechanics, respectively. Very few studies can be found in the published literature on lateral vibration effects on scour at monopile foundations. The objective of this experimental study is to improve understanding of the mechanics of current-induced scour at monopiles subjected to lateral vibrations with a non-cohesive bed. When compared to a non-vibrating monopile, the results show that scouring around its vibrating counterpart is comparatively faster during the first few hours of the test. This is primarily due to soil densification and the subsidence process induced by monopile-seabed interactions. Increasing both the frequency and amplitude of the monopile vibration would decrease the equilibrium scour depths and scour hole slopes. The reduction of equilibrium scour depth likely is due to the effect of sediment ratcheting motions on the surface of the scour hole. An empirical dimensionless equation is proposed to estimate equilibrium scour depth at monopiles subjected to lateral vibrations. Highlights • New experimental results of temporal evolution of scour depth and final scour geometry at vibrating monopiles. • New conceptual model of scour mechanism around monopile foundations subjected to lateral vibrations. • New relationship between scour reduction and vibration properties of a monopile. [ABSTRACT FROM AUTHOR]

Abstract Submarine pipelines are widely used for the conveyance of hydrocarbons, oil or other fluids in the offshore industry. Although much progress has been made on pipeline-seabed interactions in the past decades, an experimental study solely devoted to investigating interactions between the flow fields, scour and forced vibrating pipelines in a quiescent water environment still has not been conducted. In practice, this condition, to a certain extent, resembles a Steel Catenary Riser (SCR) in deep offshore environments in the absence of currents and waves. The present study aims to obtain an improved understanding of the mechanics of scour around a forced vibrating pipeline in quiescent water. Tests with the same initial gap ratio G 0 / D = 1 and two different induced frequencies were conducted. A circular cylinder with a diameter of 3.5 cm was used as the pipeline model. With the help of a high-speed camera, the details of flows, pipeline motion and scour process are vividly presented in this paper. The magnitudes of flow velocity, vorticities, and turbulence fluctuations are found to be strongly dependent on the frequency of the vibrating pipeline. The scour mechanism of the two tests is different because of the complex interactions between the flow fields and pipeline motion. For the low-frequency case, the flow field associated with the falling stage of the vibrating pipeline controls the formation of the scour trench. On the other hand, for the high-frequency test, the scour process is controlled by the flow field during the rising stage of the vibrating pipeline. Highlights • An extensive experimental study of scour around a forced vibrating pipeline in quiescent water using PIV techniques. • Synchronous quantification of pipeline dynamic responses, turbulent flow fields and near bed shear stresses. • The scour process and geometry are strongly linked to the dynamic responses (amplitude and frequency) of the pipeline. • The fluid-pipeline-sediment interaction relating to a forced vibrating pipeline with a non-cohesive seabed. [ABSTRACT FROM AUTHOR]

Abstract This paper presents 25 new laboratory experiments involving the wave-induced backfilling of wave-induced scour holes beneath submarine pipelines (so-called wave-to-wave backfilling scenarios). The experiments complement the previous 8 wave-to-wave backfilling experiments of Fredsøe et al., as well as recent current-to-wave backfilling experiments of Bayraktar et al. It is found that the wave-induced backfilling time scale is generally an order of magnitude larger than for scour, and is relatively insensitive to the initial (current- or wave-induced) pre-backfilling scour profile. Based on this, the data sets involving wave-induced backfilling are collectively analyzed, resulting in a new generalized expression for estimating the wave-induced backfilling time scale beneath pipelines in the live-bed regime. This expression accounts for primary dependence on the Shields parameter, as well as secondary dependence based on the difference between the (estimated or known) initial and expected final equilibrium scour depth due to the backfilling wave condition. Highlights • We study wave-induced backfilling of wave-induced scour beneath submarine pipelines. • 25 new experiments have been conducted at laboratory scale. • New and existing data are analyzed regarding the time scale of backfilling, T b. • T b is relatively insensitive to the initial (current- or wave-induced) scour hole. • A new generalized formula is proposed for the wave-induced backfilling time scale. [ABSTRACT FROM AUTHOR]

Empirical formulations for the engineering prediction of equilibrium scour depths, as well as time scales (for both scour and backfilling), are re-visited for monopiles. Following prior work, it is argued on physical grounds that dimensionless time scales ought to scale proportionally to the Shields parameter raised to the − 3 / 2 power, based on scaling common to numerous sediment transport rate formulae. This is in contrast to stronger power dependence found in many existing formulations based on laboratory experiments, which may become unreliable when extrapolated to (storm/strong) field scales. In light of this, existing data sets for scour and backfilling time scales are re-analyzed. Novel parameterizations are developed for their prediction which are in line with the argument above, while maintaining similar coherency with existing data as in previous parameterizations. Re-analysis of existing data sets for equilibrium scour depths is likewise performed. An existing framework valid for slender monopiles is extended to incorporate the so-called large monopile regime (non-negligible diffraction), especially important e.g. for modern wind turbine installations. • Existing parameterizations of scour and backfilling time scales are reparametrized. • Suggested time scales scale according to the Shields parameter to the −3/2 power. • Existing framework for predicting equilibrium scour depth is extended to include large monopiles. [ABSTRACT FROM AUTHOR]

Despite offshore wind farms being mostly situated in tidally dominated waters, only limited research on the effects of tidal flow on the scour process around offshore foundation structures has been carried out so far. To further improve the prediction of scour around those structures, systematic laboratory tests were conducted in a closed-circuit flume on the processes and time development of scour around a monopile in tidal flow. The tidal currents were adapted by bidirectionally reversing currents with continuously changing flow velocity. Therewith, multidirectional flow aspects were simplified into flow components in tidal main direction. Tidal cycles and flow intensities were scaled with regard to field measurements at the FINO 1 platform in the North Sea. The model tests were conducted at a length scale of 1:40 and scour depths were measured at multiple positions around the monopile by a camera system. Novel insights on the intrinsic progression of sediment displacement and time scale of the scour process were gained and in the following presented as a function of flow intensity for clear-water and live-bed conditions. In addition, baseline tests with unidirectional currents were conducted, in which the constant flow velocity was either based on the maximum peak or the root mean square velocity of the tidal currents. Significantly slower scour progression and smaller scour depths in tidal currents were found, compared to unidirectional currents based on the maximum peak velocity. In contrast, scour depths in tidal currents exceed those for unidirectional currents by up to 51%, if the unidirectional currents are based on the root mean square value. The comparison further implies that a flow velocity of around 15–20% larger than the root mean square flow velocity of the tide is needed to accurately estimate tidal current induced scour depth by unidirectional current. Thereby, the results underline the importance of selecting suitable conditions for the design process of offshore structures. For design purposes, the evolution of tidally induced scour could be well predicted with a time discretised stepping approach. [ABSTRACT FROM AUTHOR]

This study continues the investigation of flow and scour around a vertical pile, reported by Roulund et al. (2005). Flow and scour/backfilling around a vertical pile exposed to waves are investigated by using a three-dimensional numerical model based on incompressible Reynolds averaged Navier-Stokes equations. The model incorporates (1) k-ω turbulence closure, (2) vortex shedding processes, (3) sediment transport (both bed and suspended load), as well as (4) bed morphology. The numerical simulations are carried out for a selected set of test conditions of the laboratory experiments of Sumer et al. (1997, 2013a), and the numerical results are compared with those of the latter experiments. The simulations are carried out for two kinds of beds: rigid bed, and sediment bed. The rigid-bed simulations indicate that the vortex shedding for waves around the pile occurs in a "one-cell" fashion with a uniform shedding frequency over the height of the cylinder, unlike the case for steady current where a two-cell structure prevails. The rigid-bed simulations further show that the horseshoe vortex flow also undergoes substantial changes in waves. The amplification of the bed shear stress around the pile (including the areas under the horseshoe vortex and the lee wake region) is obtained for various values of the Keulegan-Carpenter number, the principal parameter governing the flow around the pile in waves. The present model incorporated with the morphology component is applied to several scenarios of scour and backfilling around a pile exposed to waves. In the backfilling simulations, the initial scour hole is generated either by a steady current or by waves. The present simulations indicate that the scour and backfilling in waves are solely governed by the lee-wake flow, in agreement with observations. The numerical model has proven successful in predicting the backfilling of scour holes exposed to waves. The results of the numerical tests indicate that the equilibrium depth of scour holes is the same for both the scour and the backfilling for a given Keulegan-Carpenter number, in full agreement with observations. [ABSTRACT FROM AUTHOR]

A multi-dimensional Eulerian two-phase model for sediment transport, called SedFoam, is presented. The model was developed under the open-source framework via the CFD toolbox OpenFOAM. With closures of particle stresses and fluid-particle interactions, the model is able to resolve processes in the concentrated region of sediment transport and hence does not require conventional bedload/suspended load assumptions. A modified k − ϵ closure was adopted for the carrier flow turbulence. The model was validated for Reynolds-averaged steady and oscillatory sheet flows and verified with empirical formulae for scour downstream of an apron. The model was used to study momentary bed failure (or plug flow) under sheet flow conditions. Model results revealed the existence of instabilities of the near-bed transport layer when momentary bed failure criteria was exceeded. These instabilities evolved into 5–10 cm billows and were responsible for the large transport rate. The instabilities were associated with a large erosion depth, which was triggered by the combination of large bed shear stresses and large horizontal pressure gradients. Further numerical experiments confirmed the conjecture by previous studies that a criterion for onset of momentary bed failure in oscillatory sheet flow was a function of both the Shields parameter and Sleath parameter. [ABSTRACT FROM AUTHOR]

This paper presents results of complementary experimental and numerical studies involving wave-induced backfilling of current-generated scour holes beneath submarine pipelines. The laboratory experiments are conducted in a wave-plus-current flume, utilizing Laser Doppler Anemometry to measure velocities, synchronized flow visualizations using digital image technology, along with live-bed scour and backfilling measurements. Each experiment is based on a two-stage process: (1) initial scour induced by a pure current, followed by: (2) backfilling induced by pure waves (either regular or irregular). The time series of scour depths are closely monitored through video recordings. Systematic analysis of these has resulted in a closed form expression for the backfilling time scale, which is demonstrated to be a full order of magnitude greater than the well-known time scale of scour (with both governed primarily by the Shields parameter). The developed expression is strictly valid for the current-to-wave backfilling scenarios considered, while likely serving as an upper limit for more general wave-induced backfilling circumstances. The experiments are complemented by similar backfilling simulations utilizing a fully-coupled hydrodynamic and morphodynamic CFD model. The numerical simulations demonstrate the ability of the model to predict backfilling towards expected equilibrium scour depths based on the new wave climate, with time scales reasonably in line with experimental expectations. [ABSTRACT FROM AUTHOR]

Sediment transport-induced changes to the embedment of three 26 km long sections of subsea pipeline are analysed and subsequently explained using model scale experiments. Rather than the scour and scour-induced sinking and sagging traditionally thought to dominate post-lay pipeline spanning and embedment change, the change for these pipelines is shown to be caused by sedimentation. The pipelines traverse a range of metocean and soil conditions; the variation in embedment correlates well with the variation in metocean conditions, with most change occurring in an area where multidirectional high-velocity short-duration flows associated with internal waves propagate at near-perpendicular angles to the pipeline. To understand the mechanism driving these changes, a series of model scale tests in O-tube flumes have been completed under flow conditions mimicking those recorded in the field. Good agreement is found between the field and laboratory results, both in terms of the process timescale and the post-sedimentation profile. The consistency of the embedment changes between the pipelines, their correlation with metocean conditions, and the ability to replicate these changes in model scale tests suggests that such changes can be accounted for in more effective pipeline design. Spans are relatively rare along the pipelines but where they do occur fish rather than scour are shown to be the principal agent of span formation. [ABSTRACT FROM AUTHOR]

Seven years of field survey measurements of a subsea pipeline obtained using sonar profilers and underwater video indicate significant lowering of the pipeline into the seabed due to sediment mobility and scour. The majority of the lowering occurs within 2 years of pipeline laying and appears to result from sustained ambient tidal and soliton currents as opposed to large storms. The lowering results in an increase in pipeline embedment relative to the far field seabed of up to 0.8 times the pipe diameter (referenced at a distance ± 8 D from the pipeline). At most locations along the pipeline, this increase in far-field embedment is uniform and occurs after the formation of many closely spaced scour holes. This suggests that the pipeline lowered mainly through sinking into the seabed at span shoulders, rather than sagging into widely spaced scour holes, for much of the pipeline length. A beam bending analysis confirmed the dominance of sinking, but did show some evidence of pipeline sagging, calculating deflections of up to 0.3 pipeline diameters at the time of surveying. In contrast to the traditional conception of span growth and self-burial, which conceives of complete pipeline burial as an endpoint, this pipeline primarily appears to exhibit ‘self-lowering’ towards a mature state that consists of a pseudo-static profile of alternating spanning and embedded sections that are distributed at regular intervals. The observed changes appear to be predictable given sufficient pipeline setting data, which suggests that they can be quantified in the stability design of new pipelines. This opens up the possibility of more efficient on-bottom stability design, as the beneficial shielding and support provided by the self-lowering process is not usually accounted for. [ABSTRACT FROM AUTHOR]

Nearshore submerged structures made of sand-filled geosystems are an interesting use for this type of coastal protection technology. These systems have an advantage over more traditional materials such as concrete units or rock, which is the limited and non-permanent impact on natural coastal processes. On top of that are also some important research achievements and improvements at the level of the materials. However, at more exposed hydraulic conditions under high wave energy its application is still hampered by the lack of knowledge about their performance. This paper describes research results based on a series of laboratory measurements of the hydrodynamic and morphodynamic change produced in the vicinity of submerged nearshore structures. An analysis of the different model outputs produced, with respect to sediment transport, wave reflection and wave-induced pressures, has been made and is discussed throughout the paper. Such a comparative analysis provides insights into the efficiency of each defence scheme in maintaining a beach and in protecting the shoreline. The sand-filled geosystems as nearshore submerged structures proved to be efficient in retarding the offshore movement of sediments and in maintaining the shoreline, even if instabilities due to elements' displacement and local scour have been observed. [ABSTRACT FROM AUTHOR]

A fully-coupled hydrodynamic/morphodynamic numerical model is presented and utilized for the simulation of wave-induced scour and backfilling processes beneath submarine pipelines. The model is based on solutions to Reynolds-averaged Navier–Stokes equations, coupled with k − ω turbulence closure, with additional bed and suspended load descriptions forming the basis for sea bed morphology. The morphological evolution is updated continuously, rather than being based e . g . on period- or other time-averaging techniques. Simulations involving wave-induced scour over the range of Keulegan–Carpenter number 5.6 ≤ KC ≤ 30 demonstrate reasonable match with previous experiments, both in terms of the equilibrium scour depth as well as the scour time scale. Wave-induced backfilling processes are additionally studied by subjecting initial conditions taken from scour simulations with larger KC to new wave climates characterized by lower KC values. The simulations considered demonstrate the ability of the model to predict backfilling toward expected equilibrium scour depths based on the new wave climate, in line with experimental expectations. The simulated backfilling process is characterized by two stages: (1) An initial re-distribution phase involving re-organization of sediments in the immediate vicinity of the pipeline, potentially followed by (2) a more lengthy backfilling evolution toward equilibrium scour depth. The simulated backfilling time scales are of the same order of magnitude as in experiments, though the multi-stage process complicates a more systematic characterization. The simulated sequences of scour and backfilling achieved within the present work are estimated to represent temporal durations of up to approximately 12 h at full practical scales. [ABSTRACT FROM AUTHOR]

Scour beneath piggyback pipelines laid on a sandy seabed is numerically investigated by solving two-dimensional (2D) Unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The fluid flow and the sediment transport are resolved using a two-phase flow Eulerian-Eulerian numerical solver SedFoam based on the open-source code OpenFOAM. A parametric study is performed for different Shields parameters defined as θ = U f 2 / (s − 1) g d 50 of 0.068, 0.18 and 0.33 where U f denotes the shear friction velocity on the seabed, the specific density of the sediment grains is s = ρ s / ρ f where ρ s and ρ f are the density of the solid and fluid phases, respectively, g is the gravitational acceleration and d 50 is the median grain diameter. Scour processes beneath piggyback pipelines under steady current flow condition are studied for different gap ratios of G / D = 0,0.15 , 0.25 and 0.35 between the main cylinder and the additional ones with a diameter ratio of d / D = 0.3 between them. Mesh convergence studies based on the scour depth and the sediment profile are performed to obtain an appropriate grid resolution. A validation study is performed by comparing the scour depth of the single cylinder cases with the published experimental results obtained by Mao (1986). The effects of different θ and geometry configurations on the scour depth and the sediment profile are obtained and discussed. • Scour beneath piggyback pipelines is investigated. • The fluid flow and the sediment transport are resolved using a two-phase flow solver. • Influences of different Shields parameters on the scour depth and the sediment profile are investigated. • Influences of different piggyback geometry configurations on the scour depth and the sediment profile are investigated. [ABSTRACT FROM AUTHOR]

Abstract: The paper describes the results of a numerical and experimental investigation of flow and scour around a half-buried sphere exposed to a steady current. Hot-film bed shear stress and Laser Doppler Anemometer measurements were made with a half sphere mounted on the smooth bed in an open channel. The hydrodynamic model is a 3-D general purpose N–S flow solver. The k-omega SST turbulence model was used for closure. The flow model was used to study the horseshoe vortex and lee-wake vortex flow processes around the sphere. The flow model was coupled with a morphologic model to calculate scour around the half-buried sphere in currents. The morphologic model includes a sediment-transport description, and a description of surface-layer sand slides for bed slopes exceeding the angle of repose. The sediment transport description includes, for the first time, the effect of externally-generated turbulence (induced by the horseshoe-vortex flow and the lee-wake flow processes) on sediment transport. The results show that the scour depth increases and time scale decreases when the effect of externally-generated turbulence is incorporated in the calculations. Empirical expressions representing the numerically obtained data on the equilibrium scour depth and the time scale are presented. The results show that the equilibrium maximum scour depth in the live-bed regime can be approximated by 0.5 D in which D is the sphere diameter. [Copyright &y& Elsevier]

Abstract: A universal formula for the estimation of equilibrium scour depth around a single cylindrical pile under the action of steady currents, tidal and short waves is presented. Following a dimensional analysis, the controlling parameters of scour was found to be the Keulegan–Carpenter number and the ratio between the flow velocity and the critical velocity for the initiation of motion of the sediment particles, u/uc. Based on this finding a new formula for the prediction of equilibrium scouring depths was derived in this paper. Measurements of the scouring process and the action of waves and/or currents from literature are used with KC and u/uc ranging between 6 and 105, and 0.6 and 4.5, respectively for the parameterization and verification of the newly proposed formula. The predicted scour depths and the investigated measurements show clearly the influence of the bed properties which have not been reported before in the literature. Predictions using the new approach have been compared with previous measurements and other formulations presented in the specialized literature. The proposed empirical formula accounts for the effect of waves, currents and sediment characteristics on the scouring process and shows better results than previous ones. [Copyright &y& Elsevier]

Abstract: Local scour below a vibrating pipeline under steady current is investigated by a finite element numerical model. The flow, sediment transport and pipeline response are coupled in the numerical model. The numerical results of scour depths and pipeline vibration amplitudes are compared with measured data available in literature. Good agreement is obtained. It is found that pipeline vibrations cause increases of scour depth below the pipeline. The scour pit underneath a two-degree-of-freedom vibrating pipeline is deeper than that under a pipeline vibrating only in the transverse flow direction. The effects of water depth are also investigated. The present numerical result shows that water depth has weak effect on the scour depth. However it does affect the time scale of the scour. The shallower the water depth is, the less time it requires to reaches the equilibrium state of scour. It is found that the vibration forces vortices to be shed from the bottom side of the pipeline. Then vortex shedding around a vibrating pipeline is closer to the seabed than vortex shedding around a fixed pipeline. This contributes to the increase of the scour depth. [Copyright &y& Elsevier]

Abstract: A laboratory study is presented herein investigating the two-dimensional onshore scour along the base of submerged vertical and semicircular breakwaters. Experiments were conducted with normally incident monochromatic waves breaking at the breakwater on both sloping and horizontal sandy bottoms. A principle conclusion of this investigation is that the characteristics of onshore breakwater scour are independent of submerged breakwater shape/type. It is also concluded that the onshore scour patterns can be divided into two distinct regimes that solely rely on the Keulegan–Carpenter number (; W bw — breakwater crest width, H i — incident wave height). For KC values larger than π, the scour forms “detached” from the breakwater while for KC values smaller than or equal to π, the scour occurs “attached” to the onshore breakwater face. Three important scour characteristics are investigated: maximum scour depth (S max), scour length (L s), and the distance of S max location from the onshore breakwater face (D s). S max value is observed to be regime independent and rely on both KC and the mobility number (; g⁎ — reduced gravitational acceleration, d — median diameter of the sediment, k — wave number, h — still water depth, T — wave period) while L s and D s are observed to be regime dependent and rely only on KC. Semi-empirical parameterizations to predict S max, L s, and D s values for onshore breakwater scour are proposed. [Copyright &y& Elsevier]

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

Abstract: A 3-D general purpose Navier–Stokes solver was used to calculate the 2-D flow in front of the breakwater. The k–ω, SST (shear–stress transport) model was selected as the turbulence model. The morphologic model of the present code couples the flow solution with a sediment transport description, and routines for updating the computational mesh based on the mass balance of sediment. Laboratory experiments of scour also were conducted in a wave flume to obtain data for model verification. Both in the numerical simulations and in the laboratory experiment, two kinds of breakwaters were used: A vertical-wall breakwater; and a sloping-wall breakwater (Slope: 1:1.5). Numerically obtained scour-deposition profiles were compared with the experiments. The numerical results show that the equilibrium scour depth normalized by the wave height decreases with increasing water-depth-to-wave-length ratio. Although the numerical results obtained for vertical-wall breakwaters are consistent with the existing experimental data (including the present experiment), the numerical results for the sloping-wall case appear to be not very satisfactory. [Copyright &y& Elsevier]

Local scour around structures is an important hydraulic phenomenon that involves multiple coupled physical processes, including turbulent flow, sediment transport, and the evolution of erodible bed. This paper presents a new three-dimensional (3D) scour model, ibScourFoam , which is based on an immersed boundary method. This model is capable of dealing with scour around complex structures and thus it paves the way for practical use of 3D scour models. A special wall function has been developed to overcome the non-smoothness problem of wall shear stress in previous immersed boundary methods. Smooth and accurate wall shear is of critical importance for successful simulation of scour. The model was validated against cases reported in the literature and one flume experiment conducted in this work. The validation case of flow and scour around a vertical pile was reproduced well by our model. The flume experiment is for scour around a partially-buried, horizontal cylinder placed on a foundation. The horizontal cylinder is of finite length and the scour is initiated by flow contraction. The model revealed the distinct stages of scour in the experiment. The complex process of undermining and exposure of initially buried cylinder and foundation was captured well by the model. • An open-source three-dimensional (3D) scour model based on an immersed boundary method has been developed. • The model utilizes a new algorithm to produce smooth and accurate wall shear, which is key for sediment transport. • The model can simulate scour around structures with complex geometries under currents, paving the way for practical use of 3D scour modeling. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

New experiments involving the three-dimensional current-induced live-bed scour beneath submerged horizontal pipelines are presented, spanning larger Shields parameter and cylinder-to-sediment diameter ratio than previous studies. Specific emphasis is on gaining a better understanding of, and ability to predict, the span migration velocity during the initial and subsequent development of such a scour hole. Consistent with previous experimental observations, both a primary (faster) and secondary (slower) span migration are observed. Process visualization of suspended sediment patterns are in line with prior speculation that this transition coincides with reduced local bed shear stress amplifications as the scour hole both deepens and widens. Dimensional analysis and physical insight are combined, leading to a new rational model for predicting the span migration velocity in both live-bed and clear-water regimes, with predictions naturally coinciding at the limit of far field incipient motion conditions. In both regimes the data cluster as predicted, and fitted closed-form expressions are provided for predicting the span migration velocity. The rational approach likewise includes a new and simple criterion for the transition from primary to secondary migration in the live-bed regime. In the clear-water regime the model incorporates primary dependence on the ratio of the Shields parameter to its critical value, resolving apparent contradictions with a previous study which suggests that the depth-based Froude number is the most important governing parameter. The developed rational model can be used to quantitatively predict all known major features of the span migration velocity in the early stages of the three-dimensional (live-bed and clear-water) scour beneath submerged horizontal cylinders induced by perpendicular flow, and can hence be regarded as the first complete model for this evolution. • New experiments are conducted involving 3D scour beneath submerged circular cylinders exposed to steady currents. • Both a primary (faster) and secondary (slower) span migration velocity are observed, consistent with prior studies. • A new rational model is proposed for predicting the primary span migration velocity in both live-bed and clear-water scour regimes. • Predictions for live-bed and clear-water regimes coincide naturally at the limit of far field incipient motion conditions. • A new and simple criterion is proposed for the transition from primary to secondary span migration in the live-bed regime. [ABSTRACT FROM AUTHOR]

The progressive expansion of offshore wind energy towards greater water depths demands for an optimization of foundation structure designs to a wider range of load conditions. In offshore waters, wind driven wave irregularity and directionality become important aspects of realistic sea states. To further improve the scour prediction in marine environment a novel experimental study was conducted to investigate the influence of directionally spread (3D) irregular waves on the scouring process. The tests were carried out in the 3D wave basin of the Ludwig-Franzius-Institute, Leibniz University Hannover, Germany. A monopile structure was simulated by a transparent pile made of acrylic glass. The study was set up to progress understanding and explore dissimilarities of scour development and patterns induced by directionally spread (3D) and unidirectional (2D) waves. The model tests were complemented by tests with superimposed oblique currents. Despite identical total wave energy in terms of m 0 between the directionally spread and unidirectional wave spectra, minor but distinct differences in scour depth and rate could be observed, which inevitably can only be attributed to the presence and role of the wave spread. For wave-only conditions final scour depths S / D induced by directionally spread waves were on average 33% smaller than those for unidirectional waves. Furthermore, final scour depths decreased with increasing wave spreading and displayed a growing dependency on KC numbers with increasing wave spreading. In combined wave and current conditions of up to U c w < 0.62 scour depths were found to be slightly larger and scour progression over time faster for directionally spread than for unidirectional waves. Differences regarding the scouring rates and depths have been found to decline with flow conditions further approaching current dominated regime. A prediction approach to estimate the maximum scour depth induced by either directionally spread or unidirectional random waves is proposed. Reasonable results and insights of the present study help advancing the understanding of scour development under more realistic, i.e. natural sea-state, conditions for a more reliable design of marine and offshore infrastructure. • Novel experimental study on the scouring process around a pile due to directionally spread waves is presented. • A comparison of scour depths and rate induced by directionally spread and unidirectional waves is carried out. • Distinct differences in scour depth and rate could be observed, that are linked to the presence of wave directionality. • A prediction approach to estimate the maximum scour depth induced by directionally spread random waves is proposed. • Results help understand the scour development under natural sea-states for a more reliable design of offshore structures. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study on scour at complex bridge piers exposed to combined waves and current. Regular waves were produced with various strength and superimposed on co-directional current with constant velocity. The key parameters tested and discussed include Keulegan–Carpenter (K C) number, relative current strength U c w , pile-cap elevation, and pier skewness. The scour hole patterns and scour mechanism were found to depend on the flow type combination, and, compared with steady current, the superposition of waves may restrain the development of scour hole due to migrating bed-forms. Three types of scour temporal evolution (i.e. ascend-descend, asymptotic, and transferred type) were identified, and the scouring processes (structure exposure, cyclic sediment motion, etc) at the scour initiation and development stages were also discussed. The dimensional time scale decreased for higher bed mobility with a power functional relationship, while the non-dimensional time scale peaked when the maximum near-bed velocity components contributed by current and waves are similar. The dependence of the equilibrium scour depths, both original and normalized, on the tested parameters was also analysed. It was found that the normalized scour depth at complex piers increases with greater K C and U c w and tends to be much larger than that for single piers. The increase of bed mobility did not lead to scour peaks at the clear-water threshold as what is usually observed for current-only scour. The influence of pile-cap elevation on the equilibrium scour depth was found to be much weaker than that under steady current. Furthermore, new scour prediction method is proposed to incorporate extra terms taking the influence of pile-cap elevation and pier skewness into account. The prediction accuracy is improved significantly. Finally, more suggestions regarding design considerations are also given. • Scour patterns under combined co-directional waves and current at complex piers with different skewness. • Three temporal scour evolution types are observed for different pier configurations. • The relationship between current strength, or Shields parameter, with time scales can be expressed by power functions. • The effects of KC, current strength, Shields parameter, pile-cap elevation, and pier skewness on scour depth are discussed. • A new scour prediction method for complex bridge piers is proposed with significantly improved accuracy. [ABSTRACT FROM AUTHOR]

A numerical model of scour beneath subsea structures considering the effect of upward seepage in the seabed is proposed. A small seepage can cause significant changes to the hydrodynamic force on the bed surface and stability of bed particles, which can further affect the sediment transport processes and scour patterns around subsea structures. The present model is developed based on a fully-coupled hydrodynamic and morphologic sediment transport model. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations are solved together with the k − ω turbulence closure. In the presence of seepage, the bed friction velocity, the bed shear stress, and the bed load transport rate will be changed as compared to conditions without seepage. The sediment particle stability is also affected and the critical Shields parameter is changed. In the presence of upward seepage forces, the repose angle of the sediment is also reduced. The present model is validated against existing experiments in terms of streamwise flow velocity distribution subjected to upward seepage. The fully-coupled hydrodynamic and morphologic model is validated against existing experiments of scour beneath a pipeline in the live-bed regime and clear-water regime, respectively. The validated model is then applied to investigate the scour development beneath a submarine pipeline subjected to different upward hydraulic gradients. It is found that the equilibrium scour width is increased with a large upward hydraulic gradient. The equilibrium scour depth stays in the range of 0.6–0.8 of the pipeline diameter for the live-bed cases. For the clear-water case, with a large upward hydraulic gradient, the equilibrium scour depth slightly decreases. • A RANS-based CFD model of scour beneath subsea structures considering the effect of upward seepage in the seabed is proposed. • A small seepage can cause significant changes to the hydrodynamic force and bed particle stabilities and further affect sediment transport processes. • Scour development beneath a submarine pipeline with different upward hydraulic gradients in the live-bed and clear-water regimes is investigated. • The equilibrium scour width is increased with a large upward hydraulic gradient. [ABSTRACT FROM AUTHOR]

This paper presents the results of an experimental study on the scour development of a hydraulic-transparent offshore foundation exposed to combined waves and current. Irregular waves propagating perpendicular to a current were simulated in a wave-current basin. The physical model tests were conducted in a length scale of 1:30 while measurements of the scour development over time were achieved by echo sounding devices placed at several locations at the upstream and downstream side of the jacket structure. Insights were gained on the scour development and time scale of the scouring process around a complex jacket structure for different wave-current conditions. The results were presented with respect to the Keulegan-Carpenter KC number and the relative wave-current velocity. Wave conditions were adjusted so that KC numbers between 6.7 and 23.4 could be tested in a systematic wave-current test program with tests reaching from wave dominated conditions up to current dominated conditions. Measured scour depths were critically assessed by an extrapolation to expected equilibrium scour depths. With respect to the current flow direction, the experiments showed generally larger scour depths at the upstream side and lower scour depths on the downstream side for each pile of the jacket structure. The development of global scour around the structure intensified with increasing relative wave-current velocity. As a result, a practical formulation is proposed for the reliable prediction of local scour depths around a jacket foundation in combined wave-current conditions. Finally, dimensionless time scales and observed as well as predicted scour depths are compared to values for the scour development around monopiles. • Systematic laboratory tests on the scouring process around a jacket structure in combined waves and currents are presented. • The scour development over time was measured with eight echo sounding devices at the front and back side of the structure. • Scour depths and time scales are given as a function of the Keulegan-Carpenter number and the relative wave-current velocity. • Dimensionless time scales and observed as well as predicted scour depths are compared to those for monopiles. [ABSTRACT FROM AUTHOR]