Validation of a new generation system for bottom boundary layer beneath solitary wave

Understanding of sea bottom boundary layer characteristics, especially bottom shear stress acting on the sea bed, is an important step needed in sediment transport modeling for practical application purposes. In the present study, a new generation system for bottom boundary layer under solitary wave is proposed. Applicability of this system is examined by comparing measured and numerical solution velocities. Moreover, transitional behavior from laminar to turbulence was investigated. It is concluded that the critical Reynolds number in the experiments shows good agreement with DNS result of Vittori and Blondeaux (2008) and laboratory data of Sumer et al. (2010), indicating validity of the generation system. Since the present generation system enables continuous measurement to obtain ensemble averaged quantities, it can be effectively utilized for future experimental studies on solitary wave boundary layers, including sediment transport experiments with movable bed.     

Non linear shallow water modelling of bore-driven swash: Description of the bottom boundary layer

The paper presents a simple approach to estimate the bottom shear stress in the swash zone by coupling the Non Linear Shallow Water Equations with the momentum integral equation for the bottom boundary layer. The approach allows not only the computation of the frictional dissipation term in the equations but also to have an insight into the flow structure in the water column during a swash event. The numerical results have been compared with a new set of experiments involving a single dam-break generated swash event. Three different grain sizes, ranging from coarse sand to gravel, have been tested in the laboratory.     

An analytic solution to the wave bottom boundary layer governing equation under arbitrary wave forcing

Existing models of the wave bottom boundary layer have focused on the vertical and temporal dynamics associated with monochromatic forcing. While these models have made significant advances, they do not address the more complicated dynamics of random wave forcing, commonly found in natural environments such as the surf zone. In the closed form solution presented here, the eddy viscosity is assumed to vary temporally with the bed shear velocity and linearly with depth, however, the solution technique is valid for any eddy viscosity which is separable in time and space. A transformation of the cross-shore velocity to a distorted spatial domain leads to time-independent boundary conditions, allowing for the derivation of an analytic expression for the temporal and vertical structure of the cross-shore velocity under an arbitrary wave field. The model is compared with two independent laboratory observations. Model calculations of the bed shear velocity are in good agreement with laboratory measurements made by Jonsson and Carlsen (1976, J. Hydraul. Res., 14, 45–60). A variety of monochromatic, skewed, and asymmetric wave forcing conditions, characteristic of those found in the surf zone, are used to evaluate the relative effects on the bed shear. Because the temporal variation of the eddy viscosity is assumed proportional to the bottom shear, a weakly nonlinear interaction is created, and a fraction of the input monochromatic wave energy is transferred to the odd harmonics. For a monochromatic input wave, the ratio of the third harmonic of velocity at the bed to the first is <10%. However, for a skewed and asymmetric input wave, this ratio can be as large as 30% and is shown to increase with increasing root-mean-square input wave acceleration. The work done by the fluid on the bed is shown to be a maximum under purely skewed waves and is directed onshore. Under purely asymmetric waves, the work done is significantly smaller and directed offshore.     

波流作用下海底边界层沉积物再悬浮与影响因素研究

海底沉积物再悬浮及其分布取决于海洋水动力、沉积物类型与床面形态之间复杂的相互作用,准确地理解和确定沉积物再悬浮过程对于沉积物输运的研究具有重要的意义。本文在祥云湾海洋牧场典型海域开展现场原位观测,获取研究区波浪、海流及悬浮沉积物浓度数据;分析了波、流作用下海底边界层悬浮沉积物垂向分布特征,并探究了海洋水动力和床面形态对悬浮沉积物垂向分布的影响。结果表明,研究区波流之间的相互作用不显著,沉积物再悬浮受控于风暴浪作用,风暴浪作用下底床切应力可以达到沉积物临界切应力的10～15倍,沉积物的再悬浮滞后于风暴浪作用2～3 h。在波浪荷载微小的情况下,悬浮沉积物垂向分布呈现"I"型,波浪荷载下,悬浮沉积物垂向分布呈现幂指函数分布,表现为"L"型;床面形态随波、流作用而演化,影响沉积物的再悬浮过程,u_?w/u_?c=1.00可作为波浪和海流起主导控制作用的床面形态的判别依据,纯波浪荷载作用下的u_?w/u_?c显著高于波浪主控作用下,但二者之间的界线随着波浪荷载的增加而升高。     

Mass transport in a two-layer wave boundary layer

The transport of a chemical species under the pure action of surface progressive waves in the benthic boundary layer which is loaded with dense suspended sediments is studied theoretically. The flow structure of the boundary layer is approximated by that of a two-layer Stokes boundary layer with a sharp interface between clear water and a heavy fluid. The simplest model of constant eddy diffusivities is adopted and the exchange of matter with the bed is ignored. For a thin layer of heavy fluid, whose thickness is comparable to the surface wave amplitude and the Stokes boundary layer thickness, effective transport equations are deduced using an averaging technique based on the method of homogenization. The effective advection velocity is found to be equal to the depth-averaged mass transport velocity, while the dispersion coefficient can be shown to be positive definite. Explicit expressions for the transport coefficients are obtained as functions of fluid properties and flow kinematics. Physical discussions on their relations are also presented.     

浅化波浪层流边界层流速分布特性的数值分析

建立了同时考虑波致雷诺应力和时均水平压强梯度影响的二阶波浪边界层数学模型,模型计算得到的浅化波浪层流边界层内瞬时流速剖面、振荡速度幅值和时均流速剖面均与水槽实验数据吻合较好,在此基础上探讨了浅化波浪边界层流速分布特性及其影响机制。随着波浪的浅化变形,边界层内时均流速剖面"底部向岸、上部离岸"的变化特征越来越明显。这是二阶对流项引起的波致雷诺应力和离岸回流引起的时均水平压强梯度共同作用的结果,在床面附近由波致雷诺应力占主导作用并趋于引起向岸流动,在上部区域由时均水平压强梯度占主导作用并趋于引起离岸流动。     

Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity U at each phase is non-uniform, which is directly affected by the mean velocity, . The magnitude of increases from zero at the bottom to a local positive maximum at about z/δ2.02.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ6.07.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component is greater than that of the offshore counterpart except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components, and are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although is greater than and the asymmetry of the maximum free stream velocities (i.e. ) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus ( ) or ( ). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone.     

Bottom Boundary Layer Characteristics in the Hooghly Estuary Under Combined Wave-Current Action

The development of a theoretical model for estimating bottom boundary layer characteristics in the Hooghly estuary, located in the east coast of India, under combined effects of waves and currents is reported. Three numerical models, viz a depth averaged hydrodynamic model, SWAN wave model, and bottom boundary layer model, were integrated. In the bottom boundary layer parameters, maximum bottom stress, effective friction factor, and near-bed velocity both during ebb and flood phases of the tidal forcing are investigated and validated for the Haldia channel. The close match seen from results signifies applicability of this model for entire Hooghly basin.     

一种三次多项式湍黏性底边界层的流场分布

本文通过假定底边界层湍黏性的三次多项式参数化形式,基于简化的Navier–Stokes方程,并利用超几何方程的性质,推导出了湍流粗糙底边界层的速度解析解。同时,得到了底边界层内其他的动力参数,如底剪应力、Ekman传输、Ekman抽吸及近底部速度分布场,从理论上讨论了均匀混合底边界层特征量分布特征。通过数值结果分析,进一步得出底边界层的总速度、亏损速度及其剪应力受平均流的角频率和地球自转影响比较大;而底边界层的动力结构对于底边界层顶部粗糙度不敏感。该涡黏性模式从理论上丰富了底边界层涡黏性的形式,为底边界层的动力系统研究提供了借鉴和理论参考。     

Note on the propagation of a shallow water wave in water of variable depth

In this technical note, the phenomena of non-linear water-wave propagation above a seabed with variable depth is re-examined. The conventional Korteweg-de Vries (KdV) equation is re-derived for the general case of variable water depth. In the new form of KdV equation, the seabed bottom function is included. Two different bottom profiles are considered in this study; case 1: $b^{\prime }\left(x^{\prime }\right)=c\epsilon \sin \lambda x^{\prime }$ and case 2: $b^{\prime }\left(x^{\prime }\right)=c\epsilon {\mathrm{e}}^{-\lambda {\left(x^{\prime }-x_0^{\prime }\right)}^2}$. The effects of three bottom profile parameters, c, λ and ε on the wave profile are examined. Numerical results indicate that both ε and λ affect the wave profile significantly in case 1, while ε significantly affects the wave profile in case 2.     

底边界层水沙观测系统和应用

利用现代先进的光学和声学测量仪器(ADP、PC-ADP、ADV、OBS等),组制四角架观测系统用于底边界层的水沙观测.此观测系统既可获取垂向流速场,更可获取常规水文观测难以获取的高分辨率的近底流速、近底单点紊动过程、近底温盐沙和波浪过程.利用此观测系统于2007年8月在长江口北槽最大浑浊带内进行了实地观测.分析四角架观测数据与同步船测底部数据表明,四角架观测系统在近底(特别是底部明显分层)观测时表现出明显优势.常规水文观测测得底部含沙量一般只相当于距底70～120 cm高度含沙量;船测底部最大含沙量为5.8 kg/m 3,而架测距底30 cm处最大含沙量有25 kg/m 3;近底含沙量较高时往往出现强分层,强分层时实测距底30 cm处含沙量可达距底120 cm处含沙量的5倍;船测底部流速比架测距底30 cm处流速平均偏大45%;但距底30 cm处最大流速仍可达1.2 m/s.船测数据也验证了四角架观测数据的正确性.     

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.     

On the interaction of a solitary wave and a submerged dike

The unsteady, two-dimensional Navier–Stokes equations and the exact free surface boundary conditions were solved to study the interaction of a solitary wave and a submerged dike. A piston-type wavemaker was set up in the computational domain to produce the incident solitary waves. The incident wave and the associated boundary layer flow in a wave tank with a flat bed were compared with the analytical solutions to verify the accuracy of this numerical scheme. Effects of the incident wave height and the size of the dike on the wave transformation, the flow fields, and the drag forces on the dike were discussed. Our numerical results showed that even though the induced local shear stress on the top surface of the dike is large at some particular locations, the resultant pressure drag is much larger than the friction drag. The primary vortex generated at the lee side of the dike and the secondary vortex at the right toe of the dike may scour the bottom and cause a severe problem for the dike.     

粉质土海底边界层动态演化过程波浪水槽实验

The objectives of this study are carried out a series of controlled large wave flume experiments using fine-grained sediment from the Huanghe River Delta, exploring the complete sequence of sediment behavior in the bottom boundary layer(BBL) during wave-induced liquefaction. The results show that:(1) The BBL in silty seabed is exposed to a progressive wave, goes through a number of different stages including compaction before liquefaction, sediment liquefaction, and compaction after liquefaction, which determines the range and thickness of BBL.(2) With the introduction of waves, first, the sediment surface has settled by an amount S(S=1–2 cm) in the course of wave loadings with an insufficient accumulation of pore water pressure. And a thin high concentration layer formed the near-bed bottom.(3) Once the liquefaction sets in, the liquefied sediment with an ‘orbital motion' and the sub-liquefied sediment form a two-layer-sediment region. The range of BBL extends downwards and stopped at a certain depth, subsequently, develops upwards with the compaction process. Meanwhile, resuspended sediments diffuse to the upper water column.(4) During the dynamics process of the BBL beneath progressive waves, the re-suspended sediment increment ranked as sediment liquefaction erosion before liquefaction compaction after liquefaction.     

珠江河口底边界层憩流动力特征

通过在珠江黄茅海河口进行的25 h定点连续观测,分析了潮流底边界层在憩流时刻的动力特征。结果表明,憩流期非恒定性增强,改变了平均流和湍流结构。主要表现:1)平均流结构出现三种不同类型,分别是对数分布(摩擦力主导)、垂向均匀分布(惯性主导)和过渡状态(摩擦力和惯性力平衡);2)湍流各向异性增强,湍谱惯性子区带宽减小。各湍流特征参数在转流时刻达到最小值,表明惯性作用抑制了湍流的发育。     

Numerical investigation of wave elevation and bottom pressure generated by a planing hull in finite-depth water

A numerical investigation of the bottom pressure and wave elevation generated by a planing hull in finite-depth water is presented. While the existing literature addresses the free-surface deformation and pressure field at the seafloor independently, this work proposes a direct comparison between the two hydrodynamic quantities. The dependence of the pressure disturbances at the ocean floor from the waves generated at the free-surface by a planing hull is studied for several values of both the depth and hull Froude numbers. The methodology employed is Smoothed Particle Hydrodynamics (SPH), a numerical technique based on the discretization of the continuum fields of hydrodynamics through mesh-less particles. The SPH code herein chosen is initially validated against experimental data for transom-stern flow. Subsequently, numerical simulations are presented for a planing hull in high-speed regimes. The results show a direct correlation between surface wave dynamics and hydrodynamic pressure disturbances at the seafloor as the value of the Froude number is varied. This is assessed by studying the inverse dependence of the low-pressure wake angle with the Froude number and by comparison of SPH results with similar works in the cited literature.     

Large-scale laboratory measurements of solitary wave inundation on a 1:20 slope

The run-up flow and related pressure of solitary waves breaking on a 1:20 plane beach were investigated experimentally in a super tank (300 m × 5 m × 5.2 m). Swash flow measurements of flow velocities are compared with an existing analytical solution. By incorporating an analytical solution, the hydrodynamic pressure for a quasi-steady flow state is determined and compared with laboratory data. Concerning the evident extra pressure exerted by the impact of swash flow, an empirical drag coefficient for a circular plate is also suggested in the present study.     

珠江河口底边界层湍流积分尺度研究

介绍湍流积分尺度的几种常用计算方法.基于三组珠江口崖门的湍流观测资料,分别计算了一个潮周期内珠江口底边界层湍流积分尺度的变化,并对比不同计算方法的稳定性.计算结果表明,基于Taylor假定的自相关函数积分法的计算结果稳定可靠.湍流积分尺度在一个潮周期内的变化很大,积分尺度的变化与平均流的流速变化有着很好的对应关系,三个测次纵向、横向和垂向积分尺度的平均值分别约为4.9～10.4 cm、3.3～6.2 cm和4.3～5.2 cm.     

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.     

河口底边界层湍流观测后处理技术方法分析

河口底边界层过程是河口海岸研究与工程应用中的重要内容。三维点式高频流速仪(ADV)已经成为湍流现场观测的最有效的工具之一,然而受测量状态、复杂的波流环境、底床几何结构等因素的影响,湍流观测的后处理目前还不成熟。在前人工作的基础上,提出了河口底边界层湍流观测后处理的综合技术方法,包括测量状态判断、数据质量检测、坐标系旋转、去除毛刺及滤波,探讨了这些处理方法中的某些步骤及处理顺序对湍流参数估算可能产生的影响,提出了综合后处理技术的准确性评估方法。该研究对于近岸海洋湍流混合、泥沙输运等重要问题的解决可以提供较为扎实的技术支持。