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…     

A Bingham-plastic model for fluid mud transport under waves and currents

Simplified equations of fluid mud motion, which is described as Bingham-Plastic model under waves and currents, are presented by order analysis. The simplified equations are non-linear ordinary differential equations which are solved by hybrid numerical-analytical technique. As the computational cost is very low, the effects of wave current parameters and fluid mud properties on the transportation velocity of the fluid mud are studied systematically. It is found that the fluid mud can move toward one direction even if the shear stress acting on the fluid mud bed is much smaller than the fluid mud yield stress under the condition of wave and current coexistence. Experiments of the fluid mud motion under current with fluctuation water surface are carried out. The fluid mud transportation velocity predicted by the presented mathematical model can roughly match that measured in experiments.     

Numerical Modeling of Water Wave Interaction with A Soft Mud Bed

A vertical 2-D numerical model is presented for simulating the interaction between water waves and a soft mud bed. Taking into aceotmt nonlinear theology, a semi-empirical theological model is applied to this water-mud model, reflecting the combined visco-elasto-plastic properties of soft mud under such oscillatory external forces as water waves. In order to increase the resolution of the flow in the neighborhood of both sides of the inter-surface, a logarithmic grid in the vertical direction is employed for numerical treatment. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes.     

On the second approximation to mass transport in the bottom boundary layer

The second approximation is obtained for the mass transport velocity within the oscillatory bottom boundary layer beneath sinusoidal progressive and standing waves of finite amplitude. This approximation includes a simple new term, which essentially ensures continuity of the vertical gradient of mass transport at the edge of the layer and is of third-order in the perturbation (or wave-slope) parameter. For long progressive waves in conditions of zero net mass flow, the term represents a moderate reduction in mass transport at the edge of the layer, compared with the first approximation of Longuet-Higgins. For standing waves of arbitrary length, the mass transport is reduced (increased) far from (near) the bottom, except near nodal locations where an increase (a reduction) is predicted. The proposed correction to the first approximation yields clearly improved results when compared with appropriate experimental evidence. Deficiencies in the higher-order theories of Sleath and Isaacson for propagating waves are disclosed.     

A Numerical Study on Water Waves Generated by A Submerged Moving Body in A Two-Layer Fluid System

This is a numerical study on the time development of surface waves generated by a submerged body moving steadily in a two-layer fluid system, in which a layer of water is underlain by a layer of viscous mud. The fully nonlinear Navier-Stokes equations are solved on FLUENT with the Volume-of-Fluid (VOF) multiphase scheme in order to simulate the free surface waves as well as the water-mud interface waves as functions of time. The numerical model is validated by mimicking a reported experiment in a one-layer ...     

黄河三角洲埕北海域底质沉积物粒度特征及泥沙输运分析

通过黄河三角洲埕北海域表层沉积物的粒度资料、实测潮流数据以及50 a一遇的波浪要素,分析了埕北海域表层沉积物的分布类型以及粒度参数特征,并计算了表层沉积物的临界起动应力、日平均单宽输沙通量以及波流共同作用下的单宽推移质输沙率。结果表明:研究区表层沉积物主要是粉砂质砂、砂质粉砂、粉砂和泥四种,分选中等偏差,近对称到正偏,中等尖锐到尖锐峰态;对大潮期间埕北海域潮流底应力和表层沉积物的临界起动应力的计算说明潮流在大部分区域具有起动和输运泥沙的作用;秋季潮流作用下的日平均单宽输沙通量均值为372.32 kg/（m·d）,方向为涨潮流向。利用贝克尔（Bijker）和经典的Van Rijn公式计算出的50 a一遇的波流共同作用下单宽推移质日平均净输沙率结果近似相等。     

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.     

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.     

Nonuniform sediment transport under non-breaking waves and currents

Empirical formulas have been developed to calculate the fractional bed-load and suspended-load transport rates and near-bed suspended-load concentration under non-breaking waves and currents for coastal applications. The formulas relate the bed-load transport rate to the grain shear stress, the suspended-load transport rate to the energy of the flow system, and the near-bed suspended-load concentration to the bed-load transport rate, velocity and layer thickness. Adequate methods are adopted to determine the bed shear stress due to coexisted waves and currents. The hiding and exposure mechanism in nonuniform bed material is considered through a correction factor that is related to the hiding and exposure probabilities and in turn the size composition of bed material. The developed formulas have been tested using a large database of single-sized sediment transport and several sets of multiple-sized sediment transport data collected from literature, and compared with several existing formulas. The developed formulas can provide reasonably good predictions for the test cases.     

Propagation of Rossby Waves over Ridges Excited by Interannual Wind Forcing in a Western North Pacific Model

Numerical experiments with a multi-level general circulation model have been performed to investigate basic processes of westward propagation of Rossby waves excited by interannual wind stress forcing in an idealized western North Pacific model with ocean ridges. When the wind forcing with an oscillation period of 3 years is imposed around 180°E and 30°N, far from Japan, barotropic waves excited by the wind can hardly cross the ridges, such as the Izu-Ogasawara Ridge. On the other hand, a large part of the first-mode baroclinic waves are transmitted across the ridges, having net mass transport. The propagation speed of the first-mode baroclinic wave is accelerated (decelerated) when an anticyclonic (cyclonic) circulation is formed at the sea surface, due to a deeper (shallower) upper layer, and to southward (slightly northward) drift of the circulation. Thus, when the anticyclonic circulation is formed on the northern side of the cyclonic one, they propagate almost together. The second-mode baroclinic waves converted from the first-mode ones on the ridges arrive south of Japan, although their effects are small. The resulting volume transport variation of the western boundary current (the Kuroshio) reaches about 60% of the Sverdrup transport variability estimated from the wind stress. These characteristics are common for the interannual forcing case with a longer oscillation period. In the intraseasonal and seasonal forcing cases, on the other hand, the transport variation is much smaller than those in the interannual forcing cases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mud mass transport due to waves based on an empirical rheology model featured by hysteresis loop

A vertical 2-D water–mud numerical model is developed for estimating the rate of mud mass transport under wave action. A nonlinear semi-empirical rheology model featured by remarkable hysteresis loops in the relationships of the shear stress versus both the shear strain and the rate of shear strain of mud is applied to this water–mud model. A logarithmic grid in the vertical direction is employed for numerical treatment, which increases the resolution of the flow in the neighborhood of both sides of the interface. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes.     

Modelling of wave damping at Guyana mud coast

The Guyana coastal system is characterized by very thick deposits of Amazon mud and high mud concentrations in its coastal waters. The mud deposits can be quite soft and may liquefy under incoming waves. Subsequently, the liquefied mud damps the incoming waves effectively. This paper presents a simple model to predict wave attenuation over soft (fluid) mud beds. This model is based on the two-layer approach by Gade [Gade, H.G., 1958, Effects of a non-rigid, impermeable bottom on plane surface waves in shallow water, Journal of Marine Research, 16 (2) 61–82.] which is implemented in the standard version of the state-of-the-art wave-prediction model SWAN. Input to the mud wave damping module consists of the extension, thickness, density and viscosity of the liquefied (fluid) mud layer.     

3-D fluid-mud dynamics in the Jiaojiang Estuary, China

A 3-D model has been developed for the muddy Jiaojiang Estuary and adjoining coastal waters, and verified against field observations. To simulate fluid-mud formation, the model uses a fine resolution grid near the bottom and involves coupling processes between hydrodynamics and fluid mud such as the sediment-induced buoyancy, increasing turbulent kinetic energy sink and kinematic viscosity, mixing by internal waves riding on the lutocline, and non-Newtonian properties of fluid mud. The effective hydrodynamic drag was reduced in the presence of fluid mud. It is shown that the estuary is infilled by tidal pumping and that longitudinal and transversal gradients of suspended sediment concentration, salinity, and currents control the formation of mud banks. Thus a 3-D model is necessary to estimate the fate of mud, although the model results are very sensitive to details of the parameterization of the hydrodynamics-mud feedback processes.     

风浪和海洋飞沫对海表面拖曳系数和风廓线的影响

基于埃克曼理论,本文将波致应力和飞沫应力引入到海-气边界层的界面应力中,来研究海表面风浪和海洋飞沫对海-气边界层动量交换的影响,并得到修改后的埃克曼模型的理论解。波致应力是由风浪谱和波增长函数估计,并得到在中低风速下,波致应力、飞沫应力与湍流应力相比,对海表面拖曳系数和风廓线的影响非常小。当风速高于25米/秒时,海洋飞沫通过飞沫应力对海-气界面应力的作用远高于波致应力,以至于波致应力可以忽略。海表面拖曳系数在高风速下,随着风速的增大而减小。通过采用风浪谱的不同波龄,得到海洋飞沫的产生会导致海-气边界层风速的增加。最后,理论解与现场的观察数据进行了对比。对比后的数据表明,在中高风速下,飞沫对海-气边界层的影响远大于表面风浪。     

A 2D Mathematical Model for Sediment Transport by Waves and Tidal Currents

In this study, the combined actions of waves and tidal currents in estuarine and coastal areas are considered and a 2D mathematical model for sediment transport by waves and tidal currents has been established in orthogonal curvilinear coordinates. Non-equilibrium transport equations of suspended load and bed load are used in the model. The concept of background concentration is introduced, and the formula of sediment transport capacity of tidal currents for the Oujiang River estuary is obtained. The Dou Guoren formula is employed for the sediment transport capacity of waves. Sediment transport capacity in the form of mud and the intensity of back silting are calculated by use of Luo Zaosen＇ s formula. The calculated tidal stages are in good agreement with the field data, and the calculated velocities and flow directions of 46 vertical lines for 8 cross sections are also in good agreement with the measured data. On such a basis, simulations of back silting after excavation of the waterway with a sand bar under complicated boundary conditions in the navigation channel induced by suspended load, bed load and mud by waves and tidal currents are discussed.     

Experimental study of turbulent oscillatory boundary layers in an oscillating water tunnel

A high-quality experimental study including a large number of tests which correspond to full-scale coastal boundary layer flows is conducted using an oscillating water tunnel for flow generations and a Particle Image Velocimetry system for velocity measurements. Tests are performed for sinusoidal, Stokes and forward-leaning waves over three fixed bottom roughness configurations, i.e. smooth, “sandpaper” and ceramic-marble bottoms. The experimental results suggest that the logarithmic profile can accurately represent the boundary layer flows in the very near-bottom region, so the log-profile fitting analysis can give highly accurate determinations of the theoretical bottom location and the bottom roughness. The first-harmonic velocities of both sinusoidal and nonlinear waves, as well as the second-harmonic velocities of nonlinear waves, exhibit similar patterns of vertical variation. Two dimensionless characteristic boundary layer thicknesses, the elevation of 1% velocity deficit and the elevation of maximum amplitude, are found to have power-law dependencies on the relative roughness for rough bottom tests. A weak boundary layer streaming embedded in nonlinear waves and a small but meaningful third-harmonic velocity embedded in sinusoidal waves are observed. They can be only explained by the effect of a time-varying turbulent eddy viscosity. The measured period-averaged vertical velocities suggest the presence of Prandtl's secondary flows of the second kind in the test channel. Among the three methods to infer bottom shear stress from velocity measurements, the Reynolds stress method underestimates shear stress due to missed turbulent eddies, and the momentum integral method also significantly underestimates bottom shear stress for rough bottom tests due to secondary flows, so only the log-profile fitting method is considered to yield the correct estimate. The obtained bottom shear stresses are analyzed to give the maximum and the first three harmonics, and the results are used to validate some existing theoretical models.     

Time and density-dependent properties of fluid mud suspensions,NE brazilian continental shelf

Fluid mud suspensions, defined as containing between 10 to 480 g/liter, occur in numerous estuarine and nearshore continental shelf environments. The quantities of sediment incorporated in fluid mud are enormous, and they must be considered to be of major importance in the transport and deposition of fine-grained sediment in these environments.This study was performed on the NE Brazilian Continental Shelf, a muddy coastline that reaches from the Amazon to the Orinoco, a distance of 1600 km. The fluid mud forms a thick (3 to 5 m) boundary layer that extends 100-km offshore and generally coincides with the 10-m depth contour.The fluid muds appear well-adjusted to the current regime on the NE Brazilian continental shelf. Near-bottom current velocities were seldom greater than 50 cm/sec during the sampling interval. Consequently, yield stress in fluid muds of 1.20 × 10³ kg/m³ and greater was seldom exceeded, and consolidation proceeded without interruption.     

Bottom friction and its effects on periodic long wave propagation

A new set of Boussinesq-type equations describing the free surface evolution and the corresponding depth-integrated horizontal velocity is derived with the bottom boundary layer effects included. Inside the boundary layer the eddy viscosity gradient model is employed to characterize Reynolds stresses and the eddy viscosity is further approximated as a linear function of the distance measured from the seafloor. Boundary-layer velocities are coupled with the irrotational velocity in the core region through boundary conditions. The leading order boundary layer effects on wave propagation appear in the depth-integrated continuity equation to account for the velocity deficit inside the boundary layer. This formulation is different from the conventional approach in which a bottom stress term is inserted in the momentum equation. An iterative scheme is developed to solve the new model equations for the free surface elevation, depth-integrated velocity, the bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity. A numerical example for the evolution of periodic waves propagating in one-dimensional channel is discussed to illustrate the numerical procedure and physics involved. The differences between the conventional approach and the present formulation are discussed in terms of the bottom frictional stress and the free surface profiles.     

Internal flow structure of short wind waves

The internal flow structure of wind waves in a wind-wave tunnel was investigated on the bases of the measured vorticity distributions, streamline patterns, internal pressure fields, and stress distributions at the water surface for some waves in the field. In part I the experimental method and the internal vorticity structure relative to the individual wave crests are described. The measured vorticity distributions of distinct waves (waves with waveheight comparable with or larger than that of significant wavesH _1/3) in the field indicate that the surface vorticity layer is extraordinarily thickened near the crest, and the vorticity near the water surface shows a particularly large value below the crest. The flow near the crest of distinct waves is found to be in excess of the phase speed in a very thin surface layer, and the tangential stress distribution has a dominant peak near the crest. It is argued that the occurrence of the region of high vorticity in distinct waves is associated with the local generation of vorticity near the crest by tangential stress which attains a peak, under the presence of excess flow.     

Recent Advancement in Modeling Seafloor Dissipative Mechanism in Shallow Water

In this paper, the recent development in modeling seabed dissipative mechanisms in shallow water is reviewed. Specifically, laminar and turbulent boundary layer solutions as well as viscous mud flow solutions under transient waves are presented. These analytical solutions are compared with experimental data for both solitary waves and cnoidal waves. Very goed agreement is ohtained. The Boussinesq equations with boundary layer effects and the muddy seabed effects are also shown.