This paper presents a simple model of the turbulent wave boundary layer for the case where the orbital motion formed by the waves just outside the boundary layer is circular. The analysis is based on the integral momentum method. It turns out that the wall friction under such a flow is larger than the similar 2D-case. It is demonstrated that even though the motion is quite different, the wall friction predictions are not significantly different from the 2D-case, where the orbital motion follows a straight line: the bed friction increases by 15–40% for the circular orbit case, depending on roughness and orbital radius. The analysis includes the case of a weak current superposed the waves. For this case, the flow resistance for the current increases by around 30–55% for a circular orbit compared to a straight motion back and forth.

In this work, the flow and bed load transport over ripple profiles under the influence of oscillatory will be investigated. The investigation is made through a parametric study, where the bed shape and the ripple steepness are varied. For the sediment transport, the Shields parameter relative to the critical one is varied in the range 1.31-3.45. A detailed flow description in terms of phase resolved quantities and period averaged quantities are given. The former are phase lag between the free stream flow and the separation and a description of the lee side vortices behind vortex ripples. The latter are the recirculation zone and its penetration into the main flow. This will be compared to the period averaged bed shear stress. An analysis of the bed load transport, both as a transport capacity in the phase resolved space and an analysis of possible stable ripples is conducted. This leads to some stable ripples and the general conclusion is that sharp crested ripples is thought unlikely to become stable under oscillatory flow due to the large increase in bed shear stresses because of the rapid contraction of the flow around the crest. Further, a dynamically moving ripple crest is investigated. The key focus is to investigate how a perturbation on top of the ripple influences the flow. It will be seen that both the shape and the velocity of the crest are affecting the period averaged flow globally.

The present paper concerns an experimental study of externally generated turbulence and its impact on the bed load sediment transport in an open channel flow. The external turbulence was generated by vertically oscillating a submerged grid, hereafter referred to as turbulence generator, in the flume with a clearance of 11 cm from the bed. Two kinds of experiments were performed: rigid flat-bed and plane sand-bed. One two-dimensional (2-D) LDA was set up to measure the velocity profiles for different values of flow discharge, amplitude and period of oscillations of the turbulence generator. The mean velocities, turbulence intensities, Reynolds shear stress, and their impacts on the rate of sediment transport have been analyzed. The fractional contributions of burst-sweep cycles to the Reynolds shear stress have also been studied. The turbulence generated due to a vertically oscillating-submerged grid is an analogous to the production of turbulence beneath the roller located on the front of broken wave, and the impact thus lies on the sediment transport. The Shields parameter was found to be correlated with the sediment transport rate, and the transport rate as a function of turbulence level is found to increase with turbulence level.

This paper treats the numerical modelling of the behaviour of a sand core covered by rocks and exposed to waves. The associated displacement of the rock is also studied. A design that allows for erosion and deposition of the sand core beneath a rock layer in a coastal structure requires an accurate prediction method to assure that the amount of erosion remains within acceptable limits. This work presents a numerical model that is capable of describing the erosion and deposition patterns inside of an open filter of rock on top of sand. The hydraulic loading is that of incident irregular waves and the open filters are surface piercing. Due to the few experimental data sets on sediment transport inside of rock layers, a sediment transport formulation has been proposed based on a matching between the numerical model and experimental data on the profile deformation inside an open filter. The rock layer on top of a sand core introduces a correction term in the Exner equation (the continuity equation for sediment and change in bed level). The correction term originates from the fact that the sand can only be deposited in the pores of the filter material. The numerical model is validated against additional data sets on the erosion and deposition patterns inside of an open filter. A few cases are defined to study the effect of the sinking of the filter into the erosion hole. The numerical model is also applied to several application cases. The response of the core material (sand) to changes in the wave period and wave height is considered. The effect of different layouts of the filter is studied in order to investigate the effect of different filter profiles on the resulting erosion. Finally, it is studied how much the design of a hydraulically closed filter can be relaxed to obtain a reduction in the design requirements of the filter thickness, while the deformation to the sand core remains acceptably small.

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.

This paper concerns numerical modelling of the impact on the littoral drift and the shoreline from groynes forming a field of equidistant and identical groynes. The most important effect of a groyne on the shoreline morphology is that the littoral drift is blocked completely or partially. A local reduction in the littoral drift around the groyne introduces alongshore gradients in the alongshore sediment transport and sedimentation and erosion around the groyne which will cause re-orientation of the bed contours towards the prevailing wave direction until an equilibrium is reached. A discussion of this mechanism is presented including effects of scales, e.g. the effect of the relative length of the groynes (compared to the width of the surf zone).The model results indicate a strong dependency of the reduction in littoral drift on the initial geometric bypass ratio (Q(geo)*), which is defined from the groyne length and the littoral transport on the undisturbed coastline; Q(geo)* is the transport occurring outside the tip of the groynes divided by the total transport. It is found that the sensitivity of the littoral drift to variations in groyne spacing and the angle, of the approaching waves, is inversely proportional to Q(geo)*. (C) 2016 Elsevier B.V. All rights reserved.

A review of the existing research on the interaction between a pipeline and an erodible bed exposed to waves and/or currents is presented. The review covers three topics: scour, liquefaction, and lateral stability of pipelines. The basic mechanism that leads to scour in two-dimensional (2D) and three-dimensional (3D) cases is first described, as deduced from small-scale laboratory experiments. The onset of scour from piping and the developing tunnel erosion are among the processes described. The lateral expansion of the scour hole along the pipe is described, also based primarily on small-scale laboratory experiments. The state of the art of the mathematical/numerical modeling of the scour processes is presented. The associated self-burial of the pipe is described and compared to field observations. In addition to scour, liquefaction may also constitute a risk for pipeline stability. The cause of liquefaction and the resulting consequence for pipeline stability in a natural environment are discussed. Finally, the lateral stability of pipelines placed on an erodible bed and exposed to waves is briefly described.

Flow and scour around a vertical cylinder exposed to current are investigated by using a three-dimensional numerical model based on incompressible Reynolds-averaged Navier-Stokes equations. The model incorporates (i) k-ω turbulence closure, (ii) vortex-shedding processes, (iii) sediment transport (both bed and suspended load), as well as (iv) bed morphology. The influence of vortex shedding and suspended load on the scour are specifically investigated. For the selected geometry and flow conditions, it is found that the equilibrium scour depth is decreased by 50% when the suspended sediment transport is not accounted for. Alternatively, the effects of vortex shedding are found to be limited to the very early stage of the scour process. Flow features such as the horseshoe vortex, as well as lee-wake vortices, including their vertical frequency variation, are discussed. Large-scale counter-rotating streamwise phase-averaged vortices in the lee wake are likewise demonstrated via numerical flow visualization. These features are linked to scour around a vertical pile in a steady current.

This paper presents the results of an experimental investigation on edge scour adjacent to a stone cover laid on a sandy bed. The three-dimensional flow over the edge of the stone layer has been investigated by the use of particle image velocimetry. The flow measurements show a significant amount of turbulence in the primary flow near the junction between the stone layer and the sand bed and the formation of complex secondary-flow structures. The results show that the flow and the edge scour process in a steady current are governed by the size of the roughness elements and to some extent the side slope of the berm. The edge scour is caused by the combined action of the primary flow and the secondary flow. The primary flow stirs up the sediment and puts it into suspension, and the secondary flow carries it away from the junction between the stone layer and the sand bed, resulting in a scour hole forming adjacent to the toe of the stone layer. The measured scour depth attained a constant level of approximately one times the stone size in the live-bed regime; further, the scour depth showed a slight decrease when the side slope of the berm was increased. Design diagrams are presented for the scour depth and the time scale of the scour process.

When building offshore wind turbines with monopile foundations, scour protection typically is placed to avoid scouring of the soil close to the monopile. An important aspect is that the scour protection itself causes erosion, inflicted by the local increase in current and/or wave velocities and in turn increased bed shear stresses. Scour of the edge material alongside the scour protection may cause deformations and failure of the scour protection of offshore wind turbine foundations. This can reduce the stability of the stone layer and cause exposure of cables running between the monopiles where they go from buried to the transition piece on the foundation. Although much information is available on the design of scour protection systems around monopiles, little is known on the mechanisms causing edge scour and the equilibrium stages of the edge scour process in steady current, waves and combined waves and current.This paper presents an extensive experimental campaign to explain the edge scour process in current and combined irregular waves and current, as well as tidal current. The three-dimensional flow field around the pile and scour protection is resolved by particle image velocimetry and bed shear stress measurements, showing a local increase in the flow velocities and bed shear stresses leading to increased sediment transport and scour. The governing process in steady current is a pair of symmetrical counter-rotating vortices emerging in the near bed region in the wake of the pile and scour protection, causing a significant downstream scour hole. It is found that the equilibrium scour hole depth and length scales with the pile diameter and the ratio between the thickness- and the width of the scour protection.In the second part of the present paper, the results from the experimental campaign are compared with the edge scour experienced in practice, outlined by a survey program of the offshore wind park Egmond Aan Zee and a published field investigation of Scroby Sands OWE by Whitehouse et al. (2011). (C) 2015 Elsevier B.V. All rights reserved.

AbstractThis paper focuses on the optimal location for dumping nourished sand on a barred coastline. This is done by investigating the short-term behavior of the cross-shore redistribution of nourished sediment on a breaker-bar profile in a two-dimensional vertical plane. This is achieved by the use of a complete numerical description of the surf-zone processes with respect to both hydrodynamics and sediment transport. The numerical model is based on the finite-volume approach with a free surface-tracking method, also known as the volume of fluid (VOF), and the sediment transport is calculated applying the Engelund and Fredsoe deterministic concept. The methodology is as follows: a Dean/Bruun equilibrium profile is exposed to regular waves (chosen as H=1.3 m and T=4.8 s). These waves will form bars on the Dean/Bruun equilibrium profile, and the wave impact is continued until a quasi-steady behavior of the bars has been obtained, i.e., bars that have stopped growing in height and only migrate slowly offsho...

In Part 2 of this work, the hydrodynamic model described in Part 1 is applied for the simulation of sediment transport and the associated morphological development of breaker bars. The sediment description is split into bed load and suspended load, and like the hydrodynamics the sediment transport is phase-resolved in order to get on- and offshore directed contributions to the sediment transport from phase lags between the suspended sediment and the hydrodynamics.First, the sediment transport over a morphologically fixed bed of a constant slope is considered, and the transport rates are discussed in terms of three dimensionless parameters: the surf similarity parameters (zeta(0)) and two variants of Dean's parameter (Omega(D) and Omega(HK)). These cover the ranges as zeta(0) is an element of [0.08, 1.19], Omega(D) is an element of [1.1, 27.7] and Omega(HK) is an element of [0.01, 0.52].Secondly, the morphological development of the cross-shore profile is considered, where the initial condition is a profile of constant slope. One reference simulation is discussed in detail and the morphological development due to changes in the hydrodynamic forcing (wave period, wave height, wave irregularity and a net cross-shore current) and in other properties (sediment size and beach slope) is discussed relative to the reference simulation. The coupling between sediment transport rate and morphology is analysed and discussed. (C) 2014 Elsevier B.V. All rights reserved.

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 12h at full practical scales.

This study presents a three-dimensional (3D) numerical modeling study on the backfilling process around monopiles. The numerical model utilized in the study is based on that given by Jacobsen (2011). It is composed of two main modules. The first module is the hydrodynamic model where the fluid flow conditions around the structure and near the bed are solved. The second module is the morphologic model where the sediment transport rates over the bed and around the structure are obtained and used in updating bed elevations around the structure. In the numerical model, the hydrodynamic computations are followed by morphologic computations, resulting in updated bed elevations and mesh structure which are again used to update the hydrodynamics for the next time step. In the hydrodynamic model, Reynolds-averaged Navier-Stokes (RANS) equations are solved with a k-ω turbulence closure. The morphologic model comprises five sub-modules, namely bed load, suspended load, sand slide, bed evolution and 3D mesh motion. The model is constructed in OpenFOAM CFD Package. The present model is applied to several problems of backfilling around a monopile by waves only, where the initial scour hole is generated by steady current. The numerical results appear to be in accord with the existing experimental information.