Effective Nikuradse Roughness on the Mobile Plan Bed

Nikuradse roughness (ks) is very important in the sediment transport prediction because it is related to the evaluations of the velocity distribution, shear stress and erosion depth. Dimensionless Nikuradse roughness (ks/D, where D is the sediment diameter) is usually given 1–2.5 on the immobile plan bed or at low shear stress. But it behaves differently on the mobile plan bed at high shear stress with much sediment picked up to movement when the Shields parameter (Θ) is larger than 0.8–1.0. The effective Nikuradse roughness on the mobile plan bed was derived indirectly from the erosion depth correlated to the mobile plan bed thickness considering the mass conservation in the present study. The proposed erosion depth confirmed the relation to the Shields parameters with an extra factor consisting of suspended sediment and its damping to turbulence. The decrement of the erosion depth caused by the increment of the sediment diameter at large shear stress was obtained, which was usually absent in classical empirical formulas based on the bedload theory. Good agreement with experiments was achieved by the present prediction of the Nikuradse roughness, erosion depth and sediment transport rate. Discussion was mainly focused on the prediction improvement caused by considering the impact of suspended sediment and its damping to turbulence.     

An experimental investigation of the velocity field under cnoidal waves over the asymmetric rippled bed

1 IntroductionIn coastal areas a ubiquitous phenomenon is theformation of ripples in the seabed. It is now widelyaccepted that the flow and sediment transport overseabed are vital in relation to erosion, surface wavedissipation and pollution dispersion et…     

A traversing system to measure bottom boundary layer hydraulic properties

This study describes a new convenient and robust system developed to measure benthic boundary layer properties, with emphasis placed on the determination of bed shear stress and roughness height distribution within estuarine systems by using velocity measurements. This system consisted of a remotely operated motorised traverser that allowed a single ADV to collect data between 0 and 1 m above the bed. As a case study, we applied the proposed traversing system to investigate bottom boundary layer (BBL) hydraulic properties within Coombabah Creek, Queensland, Australia. Four commonly-employed techniques: (1) Log-Profile (LP); (2) Reynolds stress (RS); (3) Turbulent Kinetic Energy (TKE); and (4) Inertial Dissipation (ID) used to estimate bed shear stresses from velocity measurements were compared. Bed shear stresses estimated with these four methods agreed reasonably well; of these, the LP method was found to be most useful and reliable. Additionally, the LP method permits the calculation of roughness height, which the other three methods do not. An average value of bed shear stress of 0.46 N/m², roughness height of 4.3 mm, and drag coefficient of 0.0054 were observed within Coombabah Creek. Results are consistent with that reported for several other silty bed estuaries.     

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.     

Effects of bed perturbation and velocity asymmetry on ripple initiation: wave-flume experiments

Laboratory experiments using a wave flume were designed to examine the threshold condition for ripple formation under asymmetrical oscillatory flows on an artificially roughened bed. Three types of sand beds were prepared in the experiments: they were flat, notched, and notch-mounded beds with bed roughness increasing in this order. The beds were constructed with three kinds of well-sorted sand with similar density, but different diameters. Data analyses were made using the two dimensionless parameters: the mobility number, M, a simplified form of the Shields number, and the Ursell number, U, a surrogate for asymmetry of flow field. The result confirmed that the threshold for ripple initiation is decreased with increasing bed perturbation and that as the bed perturbation increases, the dependency of this threshold on the flow asymmetry becomes less and finally null for the notch-mounded bed. This relationship is quantified by the following equations: M=17−14.5e^−0.03U on the flat bed, M=5.0−2.5e^−0.1U for the notched bed, and M=2.5 for the notch-mounded bed. A comparison between the previous field data and the present laboratory findings indicates that the threshold in the notch-mounded bed experiment, M=2.5, seems to provide a critical condition for rippling in the natural environment.     

波浪-海流-微地形耦合的沉积动力模式建立及应用

沙纹微地形普遍存在于海底,沙纹的消长能改变底部应力进而影响泥沙的运移。以往研究较多侧重于波致沙纹,并已应用于波浪模式的底摩擦计算,而较少考虑波流联合效应产生的沙纹,也未将其应用于综合的水动力模式和沉积物输运模式。本文在POM水动力模式中嵌入新南威尔士大学泥沙模式,通过耦合波流共同作用的微地形模型与波流相互作用底边界层模型,发展了波浪-海流-微地形（沙纹）耦合的沉积动力模式。本文将该模式应用于澳大利亚Jervis湾,针对波主导和波流联合主导沙纹两种类型,分别进行了沙纹发展状态、几何形态的分布及悬浮泥沙的模拟。结果表明:波致沙纹比波流联合作用的沙波具有更大的波高和波长,因此当波主导时沙纹对悬浮泥沙起着关键作用。通过考虑随沙纹变化的粗糙度,相比于以往模式设置均一的粗糙度,该模型能对悬浮物浓度的骤升过程进行更精细的预测。     

The formation of offshore ripples in the zone under irregular waves

In this article, results obtained from an experimental investigation conducted to determine the wave-induced geometric characteristics of offshore ripples and bars are presented. The experiments were performed using irregular waves. Natural beach sand was used in the study, where the mean diameter was 0.35 mm and the specific gravity was 2.63. The initial slope of the beach was 1:5. Different wave groups were generated over the initially flat beach, and a number of characteristics were determined. These include the ripple number, individual and average ripple heights, individual and average ripple lengths and the length of the offshore bar. The results of the experimental study were evaluated and empirical expressions based on the results were formulated.     

Stability of rubble-mound breakwater using H50 wave height parameter

The prediction of rubble mound breakwaters' stability is one of the most important issues in coastal and maritime engineering. The stability of breakwaters strongly depends on the wave height. Therefore, selection of an appropriate wave height parameter is very vital in the prediction of stability number. In this study, H₅₀, the average of the 50 highest waves that reach the breakwater in its useful life, was used to predict the stability of the armor layer. First, H₅₀ was used instead of the significant wave height in the most recent stability formulas. It was found that this modification yields more accurate results. Then, for further improvement of the results, two formulas were developed using model tree.To develop the new formulas, two experimental data sets of irregular waves were used. Results indicated that the proposed formulas are more accurate than the previous ones for the prediction of the stability parameter. Finally, the proposed formulas were applied to regular waves and a wide range of damage levels and it was seen that the developed formulas are applicable in these cases as well.     

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.     

Prediction of wave-induced scour depth under submarine pipelines using machine learning approach

The scour around submarine pipelines may influence their stability; therefore scour prediction is a very important issue in submarine pipeline design. Several investigations have been conducted to develop a relationship between wave-induced scour depth under pipelines and the governing parameters. However, existing formulas do not always yield accurate results due to the complexity of the scour phenomenon. Recently, machine learning approaches such as Artificial Neural Networks (ANNs) have been used to increase the accuracy of the scour depth prediction. Nevertheless, they are not as transparent and easy to use as conventional formulas. In this study, the wave-induced scour was studied in both clear water and live bed conditions using the M5’ model tree as a novel soft computing method. The M5’ model is more transparent and can provide understandable formulas. To develop the models, several dimensionless parameter, such as gap to diameter ratio, Keulegan-Carpenter number and Shields number were used. The results show that the M5’ models increase the accuracy of the scour prediction and that the Shields number is very important in the clear water condition. Overall, the results illustrate that the developed formulas could serve as a valuable tool for the prediction of wave-induced scour depth under both live bed and clear water conditions.     

波、流共同作用下的泥沙起动

对波、流共存时的床面剪切力及摩阻系数等作了探讨,根据泥沙起动试验,建立了泥沙起动Shields曲线,导出了波、流共同作用下层流和紊流时的泥沙起动公式和起动波高、起动水深.     

Study on the Log-Linear Velocity Profile of Near-Bed Tidal Current in Estuarine and Coastal Waters

Many observed data show that the near-bed tidal velocity profile deviates from the usual logarithmic law. The amount of deviation may not be large, but it results in large errors when the logarithmic velocity profile is used to calculate the bed roughness height and friction velocity （or shear stress）. Based on their investigation, Kuo et al. （1996） indicate that the deviation amplitude may exceed 100%. On the basis of fluid dynamic principle, the profile of the near-bed tidal velocity in estuarine and coastal waters is established by introducing Prandtl＇ s mixing length theory and Von Kannan selfsimilarity theory. By the fitting and calculation of the near-bed velocity profde data observed in the west Solent, England, the results are compared with those of the usual logarithmic model, and it is shown that the present near-bed tidal velocity profile model has such advantages as higher fitting precision, and better inner consistency between the roughness height and friction velocity. The calculated roughness height and friction velocity are closer to reality. The conclusions are validated that the logarithmic model underestimates the roughness height and friction velocity during tidal acceleration and overestimates them during tidal deceleration.     

Modelling and measurement of sand transport processes over full-scale ripples in oscillatory flow

A new series of laboratory experiments was performed in the Aberdeen Oscillatory Flow Tunnel (AOFT) and the Large Oscillating Water Tunnel (LOWT) to investigate time-averaged suspended sand concentrations and transport rates over rippled beds in regular and irregular oscillatory flow. The wave-induced oscillatory near-bed flows were simulated at full-scale. Five series of experiments were carried out. During the two AOFT experimental series, ripple dimensions, ripple migration rates and net sand transport rates were measured under regular and irregular asymmetric flow for two different sand types. The three LOWT experimental series focussed on measurements of the ripple dimensions, ripple migration rates, time-averaged suspended sand concentrations and net sand transport rates under regular asymmetric and irregular weakly asymmetric flow for two different sand types. From analysis of new and other full-scale data, it is concluded that the lower part of the time- and bed-averaged concentration profile (up to two times the ripple height above the ripple crest level) has an exponential profile. A new reference concentration formula is proposed based on the formula of Bosman and Steetzel [Bosman, J.J., Steetzel, H.J., 1986. Time- and bed-averaged concentration under waves. Proc. 20th ICCE Taipei, ASCE, pp. 986–1000], which includes the grain-size influence. Furthermore, it is shown that the concentration decay length is strongly related to the ripple height and that the simple formula R_c = 1.27η gives good agreement with the data. A new transport model is proposed for the wave-related net transport over full-scale ripples based on a modified half wave cycle concept of Dibajnia and Watanabe [Dibajnia, M., Watanabe, A., 1992. Sheet flow under nonlinear waves and currents. Proc. 23rd ICCE Venice, ASCE, pp. 2015–2028; Dibajnia, M., Watanabe, A., 1996. A transport rate formula for mixed sands. Proc. 25th ICCE Orlando, ASCE, pp. 3791–3804]. The magnitudes of the half wave cycle transport contributions are related to the grain-related Shields parameter, the degree of wave asymmetry and a newly defined vortex suspension parameter P, which is the ratio between the ripple height and the median grain-size. The new model has been calibrated using transport data from the new regular flow experiments and has subsequently been validated using other data, including measurements from irregular flow experiments. The new model is seen to perform better overall than existing practical models for ripple regime net sand transport.     

Effect of bed roughness on turbulent boundary layer and net sediment transport under asymmetric waves

This paper presents an investigation of the roughness effects in the turbulent boundary layer for asymmetric waves by using the baseline (BSL) k–ω model. This model is validated by a set of the experimental data with different wave non-linearity index, N_i (namely, N_i = 0.67, N_i = 0.60 and N_i = 0.58). It is further used to simulate asymmetric wave velocity flows with several values of the roughness parameter (a_m/k_s) which increase gradually, namely from a_m/k_s = 35 to a_m/k_s = 963. The effect of the roughness tends to increase the turbulent kinetic energy and to decrease the mean velocity distribution in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the turbulent kinetic energy and the mean velocity distribution is relatively unaffected. A new simple calculation method of bottom shear stress based on incorporating velocity and acceleration terms is proposed and applied into the calculation of the rate of bed-load transport induced by asymmetric waves. And further, the effect of bed roughness on the bottom shear stress and bed-load sediment transport under asymmetric waves is examined with the turbulent model, the newly proposed method, and the existing calculation method. It is found that the higher roughness elements increase the magnitude of bottom shear stress along a wave cycle and consequently, the potential net sediment transport rate. Moreover, the wave non-linearity also shows a big impact on the bottom shear stress and the net sediment transport.     

Variability of wave-induced ripple migration in wave-flume experiments and its implications for sediment transport

A thorough discussion of results from laboratory experiments with regular waves sheds light on the gap that lies between the sediment transport associated with ripple migration and the performance of a standard bedload transport formula in terms of bed shear concept. It is found that the extent of deviations of the bedload transport formula by Ribberink (1998) from the measured rate of sediment transport associated with ripple migration becomes systematically apparent under conditions of increasing settling time factor Ω_s (= η/(w₀T); η is the ripple height, w₀ the settling velocity and T the wave period). Re-examination of previous two field studies demonstrates a further reinforcement for phase-lag argument addressed in this paper.     

Experimental Study on the Bed Shear Stress Under Breaking Waves

The object of present study is to investigate the bed shear stress on a slope under regular breaking waves by a novel instrument named Micro-Electro-Mechanical System (MEMS) flexible hot-film shear stress sensor. The sensors were calibrated before application, and then a wave flume experiment was conducted to study the bed shear stress for the case of regular waves spilling and plunging on a 1:15 smooth PVC slope. The experiment shows that the sensor is feasible for the measurement of the bed shear stress under breaking waves. For regular incident waves, the bed shear stress is mainly periodic in both outside and inside the breaking point. The fluctuations of the bed shear stress increase significantly after waves breaking due to the turbulence and vortexes generated by breaking waves. For plunging breaker, the extreme value of the mean maximum bed shear stress appears after the plunging point, and the more violent the wave breaks, the more dramatic increase of the maximum bed shear stress will occur. For spilling breaker, the increase of the maximum bed shear stress along the slope is gradual compared with the plunging breaker. At last, an empirical equation about the relationship between the maximum bed shear stress and the surf similarity parameter is given, which can be used to estimate the maximum bed shear stress under breaking waves in practice.     

Scour and burial mechanics of conical frustums on a sandy bed under combined flow conditions

The scour and burial of conical frustums placed on a sandy bed under waves alone (WA) and combined flows (CF) conditions was investigated. The observations indicate that equilibrium burial depth is smaller than burial of other objects such as short cylinders laying on a sand bed under equivalent hydrodynamic conditions. Truncated cone offers less resistance to the flow field due to its more round shape when compared to a horizontally placed short cylinder characterized by sharp edges. A smaller disruption to the flow field translates to less turbulent intensity and to smaller sediment transport capacity of the flow around the object and less burial. The equilibrium burial depth shows a significantly weaker dependency on the Shields parameter than on the Keulegan-Carpenter number, contrary to the case of finite short cylinders. A new empirical predictor based on the relative strength of the wave to the wave plus current velocity, the Keulegan-Carpenter number, and the Shields parameter is proposed for estimating the equilibrium burial of truncated cones under combined flows. Both the Keulegan-Carpenter number and the Shields parameter determine the width of the scour hole around the cone. The former however, is the most dominant parameter influencing the length of the scour hole.     

控制流水波痕的外部地质作用

流水波痕可以广泛发育在不同的海、陆相环境中。对流水波痕的研究不能仅仅注意沉积作用方面，更要注意作用于流水波痕的外部条件。     

An energy approach to non-breaking wave-induced motion of bottom sediment particles

A general equation, which applies to incipient motion, general surface motion and disappearance of ripples under non-breaking water waves, is derived using an energy approach. Lower and upper limits of ripple development are derived, showing that existing criteria are not entirely sufficient. An explicit formula for the dissipation factor as a function of D/A (grain diameter near-bed wave amplitude) is also obtained. The formula has been used to evaluate the variation of f_e with increasing flow characteristics for constant grain diameter. Finally, values of the sand grain roughness height, k_s, in relation to grain diameter are given for different types of bottom motion.