Mass Transport in a Thin Layer of Bi-Viscous Mud Under Surface Waves

The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-applied stresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow lluid layers are applied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numeri-cally. It is found that the stronger the non-Newtonian behavior of the mud, the more pronounced intermittency of the flow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i. e. , oppo-site to wave propagation) for a certain range of yield stress.     

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.     

Propagation of a solitary wave over rigid porous beds

The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the propagation of a solitary wave over porous beds. The free surface boundary conditions and the interfacial boundary conditions between the water region and the porous bed are in complete form. The incoming waves were generated using a piston type wavemaker set up in the computational domain. Accuracy of the numerical model was verified by comparing the numerical results with the theoretical solutions. The main characteristics of the flow fields in both the water region and the porous bed were discussed by specifying the velocity fields. Behaviors of boundary layer flows in both fluid and porous bed regions were also revealed. Effects of different parameters on the wave height attenuation were studied and discussed. The results of this numerical model indicate that for the investigated incident wave as the ratio of the porous bed depth to the fluid depth exceeds 10, any further increase of the porous bed depth has no effect on wave height attenuation.     

论狭窄潮汐水道中sigma坐标下的余流

在受波动影响的近岸浅水区域,运用sigma坐标是计算平均水位附近的余流的有效途径。本项研究在理论上分析了在狭窄潮汐水道中sigma坐标下的余流的物理意义,并运用一系列的理想化数值模型对分析结果进行了验证。对于浅水波,sigma层和水体中的波动面相一致,因而斯托克斯速度及其分量可以用sigma坐标上的速度来表达。一个sigma层上的余流（即sigma余流）是位于这一sigma层平均深度上的欧拉余流和斯托克斯速度垂向分量的和,可以被看做是半拉格朗日余流。因为斯托克斯速度的垂向分量比其水平分量小一个量级,sigma余流可看做为欧拉余流的近似。在sigma层上的物质输运余流是sigma余流和斯托克斯速度水平分量的和,在大小和方向上和拉格朗日余流近似。     

The “slip law” of the free surface

A “slip law” connects the excess velocity or “slip” of a wind-blown water surface, relative to the motion in the middle of the mixed layer, to the wind stress, the wind-wave field, and buoyancy flux. An inner layer-outer layer model of the turbulent shear flow in the mixed layer is appropriate, as for a turbulent boundary layer or Ekman layer over a solid surface, allowing, however, for turbulent kinetic energy transfer from the air-side via breaking waves, and for Stokes drift. Asymptotic matching of the velocity distributions in inner and outer portions of the mixed layer yields a slip law of logarithmic form, akin to the drag law of a turbulent boundary layer. The dominant independent variable is the ratio of water-side roughness length to mixed layer depth or turbulent Ekman depth. Convection due to surface cooling is also an important influence, reducing surface slip. Water-side roughness length is a wind-wave property, varying with wind speed similarly to air-side roughness. Slip velocity is typically 20 times water-side friction velocity or 3% of wind speed, varying within a range of about 2 to 4.5%. A linearized model of turbulent kinetic energy distribution shows much higher values near the surface than in a wall layer. Nondimensional dissipation peaks at a value of about eight, a short distance below the surface.     

Flow Separation and Vortex Dynamics in Waves Propagating over A Submerged Quartercircular Breakwater

The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a Reynolds-Averaged Navier–Stokes (RANS) flow solver with a Volume of Fluid (VOF) surface capturing scheme (RANS-VOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation, therefore, scour on the leeside of the breakwater.     

Mud-Wave Interaction： A Viscoelastic Model

1 .IntroductionThe interaction between waves propagating onthe surface of a body of water andthe bed materialis a long standing coastal problem.The problemis practicallyimportant because the waves can be at-tenuated at a muchfaster rate whenthe bed materi…     

长江口南港底部边界层特征的观测与分析

对长江口2002年和2003年共4个潮周期的数据进行了分析,通过流速对数剖面公式计算边界层参数,并对各个潮周期内的边界层参数的变化规律进行了分析,同时也对悬沙输送可能对垂向水流结构以及边界层参数造成的影响进行了探讨。结果表明,悬沙的时间分布特征对温度、盐度、水体密度的分布格局有重要影响,主要表现在水体的Rf值普遍较高,分层稳定。此外,悬沙也可影响边界层参数,从而对水流结构产生影响。由于水体的层化作用,使层间的摩擦阻力增大,相当于在垂向上产生不同内边界层,因而影响了流速在垂向上的变化。     

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.     

A freely moving body in a boundary layer: Nonlinear separated-flow effects

In the boundary layer of fluid on a moving solid surface (such as on a moving vehicle e.g. ships) a thin body is translating parallel to the surface. The streamwise movement of the body relative to the solid surface is substantial, with the upstream or downstream velocity being comparable with the free-stream velocity. The dynamic fluid/body interaction here incorporates the effects of incident vorticity, nonlinear and separating flow. Modelling, analysis and reduced computation explore the all-important influences of body shape, moment of inertia and centre-of-mass location. These influences and the initial conditions affect whether nonlinear oscillations of the fluid and body motions continue or fully nonlinear focussing occurs after a finite time.     

Effects of Stokes production on summer ocean shelf dynamics

A two-dimensional numerical model,which is configured on the basis of Princeton ocean model（POM）,is used to study the effect of Stokes production（SP） of the turbulent kinetic energy on a density profile and Ekman transport in an idealized shelf region in summer.The energy input from SP is parameterized and included into the Mellor-Yamada turbulence closure submodel.Results reveal that the intensity of wind-driven upwelling fronts near the sea surface is weakened by the SP-associated turbulent kinetic energy input.The vertical eddy viscosity coefficient in the surface boundary layer is enhanced greatly owing to the impact of SP,which decreases the alongshore velocity and changes the distribution of upwelling.In addition,the SP-induced mixing easily suppresses the strong stratification and significantly increases the depth of the upper mixed layer（ML） under strong winds.     

A Lagrangian model for boundary layer growth and bed shear stress in the swash zone

A new model for the boundary layer development and associated skin friction coefficients and shear stress within the swash zone is presented. The model is developed within a Lagrangian reference frame, following fluid trajectories, and can be applied to both laminar flow and smooth turbulent flow. The model is based on the momentum integral approach for steady, flat-plate boundary layers, with appropriate modifications to account for the unsteady flow regime and flow history. The model results are consistent with previous measurements of bed shear stress and skin friction coefficients within the swash zone. These indicate strong temporal and spatial variation throughout the swash cycle, and a clear distinction between the uprush and backwash phase. This variation has been previously attributed the unsteady flow regime and flow history effects, both of which are accounted for in the new model. Fluid particle trajectories and velocity are computed using the non-linear shallow water wave equations and the boundary layer growth across the entire swash zone is estimated. Predictions of the bed shear stress and skin friction coefficients agree reasonably well with direct bed shear stress measurements reported by Barnes et al. (Barnes, M.P., O’Donaghue, T., Alsina, J.M., Baldock, T.E., 2009. Direct bed shear stress measurements in bore-driven swash. Coastal Engineering 56 (8), 853–867) and, for a given flow velocity, give stresses which are consistent with the bias toward uprush sediment transport which has consistently been observed in measurements. The data and modelling suggest that the backwash boundary layer is initially laminar, which results in the late development of significant bed shear during the backwash, with a transition to a turbulent boundary layer later in the backwash. A new conceptual model for the boundary layer structure at the leading edge of the swash is proposed, which accounts for both the no-slip condition at the bed and the moving wet–dry interface. However, further development of the Lagrangian Boundary Layer Model is required in order to include bore-generated turbulence and to account for variable roughness and mobile beds.     

Modeling a neutrally stratified turbulent air flow over a horizontal rough surface

The neutrally stratified boundary layer over a smooth rough surface is consider. The turbulent flow is simulated using a finite-difference eddy-resolving model of the atmospheric boundary layer (ABL). The model includes different turbulence closure schemes and numerical approximations for advection components of the momentum balance equation. We investigate the quality of reproduction of spectral characteristics of the turbulent flow and the model’s capabilities to reproduce the observed profile of mean wind velocity near the rough surface. It is shown that the best result is obtained by coupling a numerical scheme of higher order of accuracy with a mixed closure scheme based on an adaptive estimation of the mixing length for subgrid-scale fluctuations. Here, we are able to reproduce the asymptotics of the fluctuation spectrum of the longitudinal component of wind velocity near the surface and within the boundary layer as well as the logarithmic profile of mean velocity near the surface.     

Flow under standing waves: Part 1. Shear stress distribution,energy flux and steady streaming

The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet–Higgins from 1953. The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two-dimensional simulations of standing waves have also been made by application of a general purpose Navier–Stokes solver. The results agree well with those obtained by the boundary layer analysis. Wave reflection from a plane sloping wall is also investigated by using the same numerical model and by physical laboratory experiments. The phase shift of the reflected wave train is compared with theoretical and empirical models.     

Coupled dynamic analysis for wave interaction with a truss spar and its mooring line/riser system in time domain

A full time-domain analysis program is developed for the coupled dynamic analysis of offshore structures. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface and free-surface boundary conditions, and the Stokes perturbation procedure is then used to establish the corresponding boundary value problems with time-independent boundaries. A higher-order boundary element method (HOBEM) is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by fourth order Adams–Bashforth–Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. The mooring-line/tendon/riser dynamics are based on the rod theory and the finite element method (FEM), with the governing equations described in a global coordinate system. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring-lines/tendons/risers are solved simultaneously using the Newmark method. The coupled analysis program is applied for a truss Spar motion response simulation. Numerical results including motions and tensions at the top of mooring-lines/risers are presented, and some significant conclusions are derived.     

拉格朗日描述下三层流体系统中界面内波的三阶渐近解

在流体力学中,描述流体运动有Lagrange方法和Euler方法.Euler方法是通过观测通过空间各固定位置点处流体质点的运动行为来描述流体运动规律,而Lagrange方法是跟踪各个流体质点,通过观测它们在时空运动中所走过的路径来描述流体的运动规律.在数学处理上,Euler方法较Lagrange方法简单,但Lagrange方法可以完全描述流体运动的整个流场的所有特性,而Euler方法却无法描述每个流体质点的运动轨迹.本文,我们研究具有刚性边界的三层流体系统中的界面内波,其中上层流体的密度比下层流体的密度大.通过在界面处引入朗格朗日匹配条件并使用微扰法得到了拉格朗日描述下的界面内波的一阶解、二阶解及三阶解,给出了质量输运速度、波频率、平均水平和质点运动轨迹的解.结果表明对于质量输运速度、波频率、平均水平和质点运动轨迹在界面处会有不连续性,但是我们发现在满足一定的三层流体水深比和密度比条件时这种不连续性将会消失.     

Frictionless Generation of a Tidal Eulerian Residual Flow over a Sill in a Narrow Channel

Using a vertically two-dimensional, two-layer model, we have analytically examined the generation mechanism of a nonzero Eulerian residual flow by strong tide-topography interaction in a narrow channel where the frictional effect is not included. In this case, tidally generated baroclinic disturbances are forced non-uniformly in space and time while being advected by a strong tidal flow over the non-uniform slope of the bottom topography. Consequently, nonzero Eulerian residual flow results when averaged over one tidal period. Although the time average of the velocity field is thus nonzero, the associated Eulerian residual transport in each layer is compensated by a Stokes transport so that no Lagrangian residual transport results in both layers. This warns us that simple time averaging of the velocity data obtained at a fixed mooring station might lead to a spurious material transport. This revised version was published online in August 2006 with corrections to the Cover Date.     

长江口浑浊带核心区北槽水动力特征研究

本文根据2015年长江口洪季浑浊带水域座底三脚架全水深范围观测数据,对北槽中下段纵横向流、余流结构、边界层特征等进行了深入研究,结果显示:（1）大潮潮流矢量特征在垂向上的变化差异最为显著;北槽中下段水流出现明显的横向输移,指向航槽北面;（2）横向流速在大潮期间的变化（垂线平均）为-0.10~0.39 m/s,小潮期间的变化为-0.13~0.25 m/s;横向平流对于北槽纵向物质输运有显著调整作用;（3）余流垂向差异大,底部几乎为0,小潮期间余流更强;周期性再悬浮的细颗粒泥沙可作为北槽最大浑浊带的重要物质来源;（4）传统六点对数流速拟合法获得摩阻流速误差较大,近底1 m区域高分辨流速剖面是准确获取底边界层参数的有效途径。     

Direct bed shear stress measurements in bore-driven swash

Direct measurements of bed shear in the swash zone are presented. The data were obtained using a shear plate in medium and large-scale laboratory bore-driven swash and cover a wide range of bed roughness. Data were obtained across the full width of the swash zone and are contrasted with data from the inner surf zone. Estimates of the flow velocities through the full swash cycle were obtained through numerical modelling and calibrated against measured velocity data. The measured stresses and calculated flow velocities were subsequently used to back-calculate instantaneous local skin friction coefficients using the quadratic drag law. The data show rapid temporal variation of the bed shear stress through the leading edge of the uprush, which is typically two–four times greater than the backwash shear stresses at corresponding flow velocity. The measurements indicate strong temporal variation in the skin friction coefficient, particularly in the backwash. The general behaviour of the skin friction coefficient with Reynolds number is consistent with classical theory for certain stages of the swash cycle. A spatial variation in skin friction coefficient is also identified, which is greatest across the surf-swash boundary and likely related to variations in local turbulent intensities. Skin friction coefficients during the uprush are approximately twice those in the backwash at corresponding Reynolds number and cross-shore location. It is suggested that this is a result of the no-slip condition at the tip leading to a continually developing leading edge and boundary layer, into which high velocity fluid and momentum are constantly injected from the flow behind and above the tip region. Finally, the measured stress data are used to determine the asymmetry and cross-shore variation in potential sediment transport predicted by three forms of sediment transport formulae.     

Direct numerical simulations of flow over two-dimensional and three-dimensional ripples and implication to sediment transport: Steady flow

A well resolved and highly accurate direct numerical simulation (DNS) solver has been developed to understand the implication of hydrodynamics to sediment transport. In the first part of the study we focus on steady flow over two-dimensional and three-dimensional ripples at two Reynolds numbers Re_τ = 180 and 400 (defined by channel half-height and wall-friction velocity) in a channel geometry. The DNS scheme is based on a fourth-order vertical velocity and second-order vertical vorticity formulation, which resolves the difficulties in pressure boundary condition encountered when solving the Navier–Stokes equations. The complex boundary introduced due to the ripples has been imposed in the Cartesian domain using an elegant immersed boundary method. Detailed hydrodynamic analysis has revealed turbulence statistics (in particular, the higher order) and henceforth, the flow structures are sensitive — whether the ripples are two-dimensional or three-dimensional. The importance of fluctuating component of the bottom stress in addition to its mean component; and its significance to sediment transport and ripple migration speed have been investigated.