Bedform evolution around a submarine pipeline and its effects on wave-induced forces under regular waves

The paper presents an experimental investigation of seabed evolution behavior around a submarine pipeline and the hydrodynamic forces on the pipeline under regular waves. Unlike the previous flume tests that have largely used beds with median sands, this study focuses on fine sediments such as sandy silt and silt. The primary objective of the study was to investigate: (i) the scour process under different wave conditions and with different sediments and (ii) the influence of the bedform evolution on the hydrodynamic forces experienced by the pipeline. In terms of scour and ripple formation, four distinct regimes of the near-field bed evolution behavior are identified which are: (I) no scour, (II) scour without ripples, (III) scour with small ripples and (IV) scour with large ripples. The influence of bedform evolution on wave forces was found to vary significantly in different regimes. In regime I, the wave forces were quite stable; in regime II and III, the wave forces underwent a gradual reduction before reaching their equilibrium values at fairly early stages of the scour process; in regime IV, the wave forces were significantly affected by the migrating ripples and can be rather unsteady throughout the testing period.     

Morphodynamics and cobbles behavior in and near the surf zone

The evolution of an initially flat sandy slope and the dynamics of large objects (cobbles/mines) emplaced on it are studied in a laboratory wave tank under simulated surf conditions. Upon initiation of wave forcing, the initially flat beach undergoes bedform changes before reaching a quasi-steady morphology characterized by a system of sand ripples along the slope and a large bar near the break point. Although the incoming wave characteristics are held fixed, the bottom morphology never reaches a strict steady state, but rather slowly changes due to the migration of ripples and bar transformation. When the wave characteristics are changed, the bedform adjusts to a new quasi-steady state after a suitable adjustment time. Studies conducted by placing model cobbles/mines on the evolving sandy bottom subjected to wave forcing show four distinct scenarios: (i) periodic cobble oscillations with zero mean displacement and small scour around the cobbles, (ii) mean onshore motion of relatively light cobbles, (iii) periodic burial of relatively heavy cobbles when their sizes are comparable to those of sand ripples, and (iv) the burial of relatively large cobbles under the bar, when the bar migrates due to changes of incoming waves. Quantitative data on the characteristics and dynamics of the bedform, including ripple-formation front propagating down the slope, ripple growth and drift, and flow around ripples, are presented. Physical explanations are provided for the observations.     

Burial and scour around short cylinder under progressive shoaling waves

The results of a laboratory experimental program aimed at better understanding the scour around and burial of heavy cylindrical objects under oscillating flow on a sandy bed are described. This study was motivated by its application to the dynamics of isolated cobbles/mines on a sandy floor under nonlinear progressive waves, such as that occur in shallow coastal waters beyond the wave-breaking region. In the experiments, nonlinear progressive waves were generated in a long wave tank of rectangular cross-section with a bottom slope. Model mines (short cylinders) were placed on the sandy bottom and the temporal evolution of the bed profile and the velocity field in the near field of the object were observed. Experiments were conducted at relatively high Reynolds numbers for a range of flow conditions, which can be characterized by the Keulegan–Carpenter number and Shields parameter. Depending on the values of these parameters, four different scour regimes around the cylinder including periodical burial of cylinder under migrating sand ripples were observed; they were classified as: (i) no scour/burial, (ii) initial scour, (iii) expanded scour, and (iv) periodic burial cases. A scour regime diagram was developed and the demarcation criteria between different regimes were deduced. Semi-empirical formulae that permit estimation of the scour depth with time, the equilibrium maximum scour depth and length, and conditions necessary for the burial of the cylinder as a function of main external parameters are also proposed.     

北部湾南部海域近底悬沙输运及地貌演变

利用1个海洋沉积动力过程原位监测系统在北部湾南部浅海陆架海域采集了18个潮周期的波浪、潮流、悬浮沉积物浓度、底床变化数据,分析了悬沙浓度变化特征,计算了近底悬沙通量并分析了潮流和波浪对底床演变的影响,结果表明:观测期间近底悬沙浓度的变化主要受水位波动、潮流的共同影响,波浪作用较弱;悬沙浓度的异常高值可能是上游沙波表面的泥沙滑落沉降所致;观测期间悬沙通量的波动规律与近底潮流速度变化一致,潮周期和涨落潮之间的悬沙通量有显著差别;在潮流作用下观测期间悬沙向西的净输运量约为15 158 kg/m,向北净悬沙通量为2 934 kg/m,东西向净通量远大于南北向净通量;近东西向波谷地形对南北向悬沙输运的限制作用可能导致了输运通量的显著差异;底床高程的变化在潮周期之间有差异,变化值在0.8~16.7 cm之间波动,厘米级底床高程的快速变化主要是由潮流流速的大小及往复潮流的不对称性造成的。这种变化可能与沙纹的运移有关,沉积物向下游方向的运移以及沙纹剖面形态的改变可以较合理地解释底床高程的变化特点。     

Self-Burial of Short Cylinders Under Oscillatory Flows and Combined Waves Plus Currents

Self-burial processes of finite-length cylinders under oscillatory flows and waves plus currents were examined with the following two different experimental facilities: a large oscillating water-sediment tunnel (LOWST) and a large wave-current tank. More than 130 experiments, with different model cylinders, were conducted within both facilities. The burial mechanisms studied include burial due to local scour and bedform migration. Burial due to fluidization in the tunnel was also explored, but only in a qualitative way. In the case of experiments with LOWST, the equilibrium burial depth was found to be a power function of the shields parameter (thetas). In the wave-current tank, the equilibrium burial depth was also found to be a function of the Shields parameter, albeit with larger scatter. The experimental observations made in both facilities have similar trends but different magnitudes. For equivalent values of the Shields parameter, smaller equilibrium burial depths were observed in the wave flume when compared to the ones in LOWST. After burial induced by local scour takes place, bedform (ripples and sandwaves) formation and evolution play a strong and, in some cases, dominant role on the equilibrium burial depth of the cylinders. Depending on how the vertical dimensions of bedforms compare to the specimen's diameter, cyclical covering and uncovering of the object may take place due to the passage of the migrating sandwaves. In such case, burial depth B_d no longer coincides with the vertical displacement (V_d) of the object as in the case when the burial process is dominated by local scour.     

Boundary roughness and bedforms in the surf zone

Hydrodynamical models of the nearshore system frequently assume that a single friction coefficient is sufficient to represent flow conditions at a point in the surf zone. Furthermore, models attempting to relate bed configuration to surf zone flows have relied primarily upon the wave orbital velocity as an indicator of potential bedforms, and thus as the control on boundary roughness. The data presented here point out potential errors arising from either of these approaches. The results of a field experiment conducted at Wendake Beach, Ontario, show that at a single location in an active surf zone, the Darcy-Weisbach friction coefficient, f, varied by approximately 250% (in this case between 0.016 and 0.041).

It is also shown that existing bedform models, based upon primary wave motions alone, do not accurately predict conditions at this study site. For a relatively constant wave orbital velocity and velocity asymmetry, it is found that changes in bed roughness, as a result of bedform development, are reflected mainly in the vertical profile of the long-shore current velocity. A sequence of bedforms, from oscillatory ripples through flat bed, is inferred from the data, and found to be supported by diver observations and preserved primary sedimentary structures.     

Geometry and migration characteristics of bedforms under waves and currents: Part 2: Ripples superimposed on sandwaves

This paper presents results of a series of detailed measurements of geometric and migrating characteristics of ripples superimposed upon sandwaves under the action of combined waves and currents. Velocity measurements within the fluid, surface wave characteristics and 3D mapping of the bottom were recorded with an Acoustic Doppler Velocimeter (ADV), an acoustic water level sensor and a 32 composite element array of sub-aquatic acoustic sensors, respectively. Bottom records were statistically analyzed to obtain height, length and migration rates of ripples. Experiments examined ripple heights and wavelengths for the mobility factors (as defined in Eq. (4)) and the Reynolds wave number within the ranges 10 < ψ < 88 and 16 × 10³ < Re_w < 5 × 10⁵, respectively. Measured values were compared with laboratory and field data together with semi-empirical and analytical formulae from the literature. Good correlation was obtained when plotting measured ripple length and length in dimensionless form as a function of the Reynolds wave number Re_w. Under a given hydraulic condition, it was observed that ripples with different geometric characteristics may coexist at different locations over the sandwave. Ripple steepness is presented as a function of the Shields parameter although characterized with rather large scatter. Finally, average ripple migration speed is presented as a function of the Shields parameter and the mobility number.     

Predicting bed form roughness: the influence of lee side angle

Flow transverse bedforms (ripples and dunes) are ubiquitous in rivers and coastal seas. Local hydrodynamics and transport conditions depend on the size and geometry of these bedforms, as they constitute roughness elements at the bed. Bedform influence on flow energy must be considered for the understanding of flow dynamics, and in the development and application of numerical models. Common estimations or predictors of form roughness (friction factors) are based mostly on data of steep bedforms (with angle-of-repose lee slopes), and described by highly simplified bedform dimensions (heights and lengths). However, natural bedforms often are not steep, and differ in form and hydraulic effect relative to idealised bedforms. Based on systematic numerical model experiments, this study shows how the hydraulic effect of bedforms depends on the flow structure behind bedforms, which is determined by the bedform lee side angle, aspect ratio and relative height. Simulations reveal that flow separation behind bedform crests and, thus, a hydraulic effect is induced at lee side angles steeper than 11 to 18° depending on relative height, and that a fully developed flow separation zone exists only over bedforms with a lee side angle steeper than 24°. Furthermore, the hydraulic effect of bedforms with varying lee side angle is evaluated and a reduction function to common friction factors is proposed. A function is also developed for the Nikuradse roughness (k _s), and a new equation is proposed which directly relates k _s to bedform relative height, aspect ratio and lee side angle.     

The dimensions of sand ripples in full-scale oscillatory flows

New large-scale experiments have been carried out in two oscillatory flow tunnels to study ripple regime sand suspension and net sand transport processes in full-scale oscillatory flows. The paper focuses on ripple dimensions and the new data are combined with existing data to make a large dataset of ripple heights and lengths for flows with field-scale amplitudes and periods. A feature of the new experiments is a focus on the effect of flow irregularity. The combined dataset is analysed to examine the range of hydraulic conditions under which oscillatory flow ripples occur, to examine the effects of flow irregularity and ripple three-dimensionality on ripple dimensions and to test and improve existing methods for predicting ripple dimensions.The following are the main conclusions. (1) The highest velocities in a flow time-series play an important role in determining the type of bedform occurring in oscillatory flow. Bedform regime is well characterised by mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth peak velocities in the case of irregular flow. (2) For field-scale flows, sand size is the primary factor determining whether equilibrium ripples will be 2D or 3D. 2D ripples occur when the sand D₅₀ ≥ 0.30 mm and 3D ripples occur when D₅₀ ≤ 0.22 mm (except when the flow orbital diameter is low). (3) Ripple type (2D or 3D) is the same for regular and irregular flows and ripple dimensions produced by equivalent regular and irregular flows follow a similar functional dependence on mobility number, with mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth velocities in the case of irregular flow. For much of the ripple regime, ripple dimensions have weak dependency on mobility number and ripple dimensions are similar for regular and irregular flows with the same flow orbital amplitude. However, differences in ripples produced by equivalent regular and irregular flows become significant at the high mobility end of the ripple regime. (4) Ripple dimensions predicted using the Wiberg and Harris formulae are in poor agreement with measured ripple dimensions from the large-scale experiments. Predictions based on the Mogridge et al. and the Nielsen formulae show better overall agreement with the data but also show systematic differences in cases of 3D ripples and ripples generated by irregular flows. (5) Based on the combined large-scale data, modifications to the Nielsen ripple dimension equations are proposed for the heights and lengths of 2D ripples. The same equations apply to regular and irregular flows, but with mobility number appropriately defined. 3D ripples are generally smaller than 2D ripples and estimates of 3D ripple height and length may be obtained by applying multipliers of 0.55 and 0.73 respectively to the 2D formulae. The proposed modified Nielsen formulae provide an improved fit to the large-scale data, accounting for flow irregularity and ripple three-dimensionality.     

Modelling ripple development under non-uniform flow and sediment supply-limited conditions in a laboratory flume

Results are reported herein of an open channel flow laboratory based study of the development of ripples on a fine silica sand bed, and under non-uniform turbulent subcritical flow conditions. The hydraulic model used included a diverging channel, which resulted in a variation of hydraulic and sediment transport parameters along the channel. Sediment supply limitation occurred during experimentation, impacting bed form development. The overall aim of this study was to improve the understanding and modelling capability of the development of bed forms under limited sediment supply and non-uniform flow conditions. In particular, the applicability of an existing empirical model capable of predicting ripple development was tested for the conditions of this study, using measured ripple dimensions. The ripple height and length results were extracted from detailed bed profile records, obtained using an acoustic Doppler probe traversed longitudinally over the sediment bed, at various experimentation time intervals. It was found that the non-uniform flow conditions affected the development rate of the bed forms, while sediment supply limitation impacted their steady state dimensions. The measured steady state ripple dimensions were lower, on average, than the corresponding equilibrium dimensions predicted using existing empirical equations. Non-uniform flow also caused the simultaneous occurrence of bed forms at different stages of development along the hydraulic model, where 3D and 2D ripples and incipient bed forms were recorded. Such a scenario can occur in estuarine and coastal flows, due to changing hydraulic conditions and/or a limitation of sediment supply. The ripple development model tested was verified for the conditions of this study, with its accuracy being shown to depend on an accurate determination of steady state parameters.     

Estimation of the wave-related ripple characteristics and induced bed shear stress

A large data set on ripples was collected and examined. A set of new formulas for the prediction of the ripple characteristics is proposed with an emphasis on the disappearance of the ripples. The ripple wavelength was observed to be proportional to the bottom wave excursion but also to be a function of the grain-related Shields parameter and wave period parameter introduced by Mogridge et al. (1994). The ripple steepness was found to be nearly constant for orbital ripples, and with a sharp decrease for suborbital ripples. Two empirical functions are added including the effects of the critical Shields parameters (inception of transport and inception of sheet flow), i.e. giving the boundaries for the ripple existence's domain. The proposed formulas yield better prediction capabilities compared to the previously published formulas, especially when ripples are washed out. The effect of the ripple characteristics on the roughness height and the calculation of the bed shear stress is also discussed. It appeared that the bed shear stress calculation is more sensitive to the empirical coefficient a_r introduced in the estimation of the ripple-induced roughness height or to the limits of existence of the ripples than the ripple characteristics themselves.     

The wave plus current flow over vortex ripples at an arbitrary angle

This work concerns the wave plus current flow over a sand bed covered by vortex ripples, with the current and the waves coming from different angles. Experiments were performed in a basin, where current and waves were perpendicular, in order to determine the conditions (current strength) leading to a regular ripple pattern formation. Numerical simulations were conducted changing the direction between the waves and the current from 0° to 90° and the ratio between the current strength and the wave orbital velocity from 0.2 to 1.5. Close to the bed, the current aligns parallel to the ripple crests, leading to a veering current profile with the vertical coordinate. The current-related friction coefficient was calculated. It was found that it decreases as the angle approaches 90°, while it increases for decreasing values of the current with a trend that can be described by a power law.     

Reconstruction of ancient sea conditions with an example from the Swiss Molasse

Ancient sea conditions can be estimated from the grain size, spacing and steepness of preserved ripple-marks. The element of greatest uncertainty in such reconstructions is the relationship between near-bed orbital diameter of water particles and the ripple spacing. This relationship is simple for vortex ripples of high steepness but is problematical for the low-steepness forms known as post-vortex, rolling-grain or anorbital ripples.

The existence field for wave ripples is between the threshold velocity for sediment movement and the onset of sheet flow, most low-steepness forms occurring close to the bed planation threshold. A range of maximum period of formative waves can be obtained using combinations of orbital diameter and orbital velocity, assuming linear wave theory to be a reasonable approximation.

Probable wave heights, wave lengths and water depths can be investigated using the transformation of wave parameters in shallowing waters and the constraints on wave dimensions provided by the wave-breaking condition. Given reasonable estimates of wave height, crude estimates of wave power allow a comparison of ancient wave-influenced sequences with modern counterparts.

Wave ripple-marks preserved in the Upper Marine Molasse of western Switzerland have been investigated. Results, which are in agreement with regional geology, suggest deposition in a seaway of approximately 100 km width, where moderate period waves (T = 3–6 s) were generated. The depositional facies belts were adjusted to the prevailing waves, tides and fluvial outflows.     

Hydrodynamic instability of the Equatorial Countercurrent in the Tropical Atlantic

Unstable wave disturbance parameters and their seasonal variability are considered using a multi-level quasi-geostropic model of a large-scale current. It has been postulated that hydrodynamically unstable processes become more intensive during the winter-spring period, with the dominating wavelength being 600 km and the period 350 days. The decay of the Equatorial Countercurrent in spring is related to a mixed type of hydrodynamic instability and to the generation of planetary waves. During the summerautumn period, when the Equatorial Countercurrent's hydrodynamic instability is developing, meandering occurs, with the lengths of the waves, slowly migrating across the ocean in an easterly direction, being 950–1500 km.Translated by V. Puchkin.     

人工岬角和海滩养护下泥沙输运与海床演变

实施人工岬角和海滩养护的软硬措施相结合的方法是探索解决海滩侵蚀问题的新举措之一。基于验证良好的水动力模型建立了泥沙输运和海床演变模型,对秦皇岛市新开河口至南山岸线海滩经整治修复工程实施后的泥沙输运和海床演变规律进行模拟分析。结果表明:大潮与常浪耦合作用下,研究区域周围海域流速整体上落急时刻大于涨急时刻,沙坝掩护水域的流速较弱,波浪在沙坝处增强并在沙坝后破碎并减弱;在沙坝处出现高悬沙浓度区域,悬沙浓度分布主要由底床切应力控制,部分受水动力影响。大潮与强浪耦合作用下,在沙坝处出现远大于常浪时的增强水流(波生流),方向与强浪向一致,波浪在沙坝处已破碎且沙坝对强浪的削减效率大于常浪;与常浪作用下不同,悬沙浓度场在强浪作用下沙坝处没有出现明显的高浓度区域。波流耦合作用下,人工岬角单独存在时护岸效果有限,工程实施后在人工岬角和人工沙坝的配合下,沙坝处侵蚀而沙坝后侧掩护区域淤积,沙坝起到了有效养护海滩的作用。     

Prediction of swash motion and run-up including the effects of swash interaction

Modifications to a model describing swash motion based on solutions to the non-linear shallow water equations were made to account for interaction between up-rush and back-wash at the still water shoreline and within the swash zone. Inputs to the model are wave heights and arrival times at the still water shoreline. The model was tested against wave groups representing idealized vessel-generated wave trains run in a small wave tank experiment. Accounting for swash interaction markedly improved results with respect to the maximum run-up length for cases with rather gentle foreshore slopes (tanβ=0.07). For the case with a steep foreshore slope (tanβ=0.20) there was very little improvement compared to model results if swash interaction was not accounted for. In addition, an equation was developed to predict the onset and degree of swash interaction including the effects of bed friction.     

Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method

In this paper, a well-developed numerical model based on the immersed boundary (IB) method is used to study oscillatory flows over a bed with large-amplitude ripples in a systematic manner. The work shows that the complex flow over the rippled bed can be numerically dealt with in Cartesian coordinate by the IB method and that the IB method is able to provide main features of the flows near the ripples. An accurate simulation of vortices generation as a result of flow separation at the rippled bed is obtained. It is found that the oscillatory flows start to separate during the flow deceleration when the Keulegan–Carpenter (KC) number is small. The steady streaming for various ripple steepness is simulated and the criterion for separating the single and double structure streaming is also discussed. Moreover, a new type of steady streaming which consists of a pair of embedded recirculations in the vicinity of the ripple trough is obtained for relatively steep ripples in this work. The numerical results, including the steady streaming in particular, may be helpful to improve the understanding of the sediment transport and the seabed evolution with natural ripples under sea waves.     

Suspended-sediment reference concentration under waves: field observations and critical analysis of two predictive models

Two commonly adopted but fundamentally different approaches for predicting time-averaged suspended-sediment reference concentration (C̄_REF) under waves are tested against field measurements and compared with each other. The first model relates C̄_REF to the cube of the non-dimensional skin friction, whereas the second model adopts a more complex function of excess skin friction incorporating the empirical constant γ₀. The dataset is from the zone of wave shoaling seaward of an open-coast surfzone and includes measurements of waves, currents, suspended sediment and bedforms. Estimates of C̄_REF are derived from acoustic backscatter data, and the seabed and suspension process are described from video footage. When waves were energetic, the bed was deformed into large hummocks; during less energetic conditions, the bed was rippled. The time-averaged concentration profiles over the ripples were consistent with settling flux balanced by pure gradient diffusion and a sediment diffusivity that is constant with elevation above the bed. C̄_REF in that case is shown to apply at z=0, where z is the elevation above the bed. Over the hummocks, there was a sheet flow at the base of the suspension and C̄_REF is shown to apply at z=1 cm. The concentration profiles over the hummocks implied sediment diffusivity that varied linearly with elevation within ∼10 cm of the bed and constant sediment diffusivity above that level. For both rippled and hummocky beds, γ₀ derived from the field data was found to be sensitive to the value assumed for critical stress for initiation of sediment motion, which could explain the range of values reported in the literature for γ₀. γ₀ was also found to vary in a complex way with skin friction, which suggests that the reference-concentration model based on excess skin friction is not correctly formulated. Nevertheless, two functions for γ₀ (one applying to rippled beds and the other to hummocky beds) were contrived to make the model fit the data. The model based on non-dimensional skin friction was found to be a good predictor of C̄_REF when a correction was made for flow contraction over ripples. The correction was not required for the hummocky bed, where sediment was being entrained in a thin sheet flow layer. The model based on non-dimensional skin friction correctly portrayed the relationship between flow and sediment response without contrivance and therefore should be the favoured approach in predicting reference concentration.