A two-dimensional horizontal wave propagation and mud mass transport model

The present study offers a two-dimensional horizontal wave propagation and morphodynamic model for muddy coasts. The model can be applied on a general three-dimensional bathymetry of a soft muddy coast to calculate wave damping, fluid mud mass transport and resulting bathymetry change under wave actions. The wave propagation model is based on time-dependent mild slope equations including the wave energy dissipation due to the wave-mud interaction of bottom mud layers as well as the combined effects of the wave refraction, diffraction and breaking. The constitutive equations of the visco-elastic–plastic model are adopted for the rheological behavior of fluid mud. The mass transport velocity within the fluid mud layer is calculated combining the Stokes’ drift, the mean Eulerian velocity and the gravity-driven mud flow. The results of the numerical model are compared against a series of conducted wave basin experiments, wave flume experiments and field observations. Comparisons between the computed results with both the field and laboratory data reveal the capability of the proposed model to predict the wave transformation and mud mass transport.     

A comparative study on the rheology and wave dissipation of kaolinite and natural Hendijan Coast mud, the Persian Gulf

The objective of this paper is to investigate the rheological behavior of kaolinite and Hendijan mud, located at the northwest part of the Persian Gulf, and the dissipative role of this muddy bed on surface water waves. A series of laboratory rheological tests was conducted to investigate the rheological response of mud to rotary and cyclic shear rates. While a viscoplastic Bingham model can successfully be applied for continuous controlled shear-stress tests, the rheology of fluid mud displays complex viscoelastic behavior in time-periodic motion. The comparisons of the behavior of natural Hendijan mud with commercial kaolinite show rheological similarities. A large number of laboratory wave-flume experiments were carried out with a focus on the dissipative role of the fluid mud. Assuming four rheological models of viscous, Kelvin-Voigt viscoelastic, Bingham viscoplastic, and viscoelastic-plastic for fluid mud layer, a numerical multi-layered model was applied to analyze the effects of different parameters of surface wave and muddy bed on wave attenuation. The predicted results based on different rheological models generally agree with the obtained wave-flume data implying that the adopted rheological model does not play an important role in the accuracy of prediction.     

Numerical investigation of fluid mud motion using a three-dimensional hydrodynamic and two-dimensional fluid mud coupling model

A water-fluid mud coupling model is developed based on the unstructured grid finite volume coastal ocean model (FVCOM) to investigate the fluid mud motion. The hydrodynamics and sediment transport of the overlying water column are solved using the original three-dimensional ocean model. A horizontal two-dimensional fluid mud model is integrated into the FVCOM model to simulate the underlying fluid mud flow. The fluid mud interacts with the water column through the sediment flux, current, and shear stress. The friction factor between the fluid mud and the bed, which is traditionally determined empirically, is derived with the assumption that the vertical distribution of shear stress below the yield surface of fluid mud is identical to that of uniform laminar flow of Newtonian fluid in the open channel. The model is validated by experimental data and reasonable agreement is found. Compared with numerical cases with fixed friction factors, the results simulated with the derived friction factor exhibit the best agreement with the experiment, which demonstrates the necessity of the derivation of the friction factor.     

Effect of self-weight consolidation on a hydro-sedimentological model for the Río de la Plata estuary

The effect of the consolidation process on the morphodynamics and fine sediment dynamics of the Río de la Plata estuary is explored through a circulation-wave-sediment transport model. The consolidation model is calibrated based on settling column experimental data. Different simulations are done in order to initialize the mud layer distribution and to investigate the impact of different erosion parameter assumptions on the modeled sediment dynamics. Finally a two-year simulation is done with and without the consolidation process and realistic hydrodynamic forcings. Considering the consolidation process, the model correctly reproduces measured vertical density profiles in the Montevideo Bay access channel. The simulated suspended sediment dynamics behavior in Montevideo Bay with the consolidation process provides a more realistic deposition pattern in regard to the dredging activities.     

Two-dimensional numerical model of two-layer shallow water equations for confluence simulation

This study presents a finite-volume explicit method to solve 2D two-layer shallow water equations. This numerical model is intended to describe two-layer shallow flows in which the superposed layers differ in velocity, density and rheology in a two-dimensional domain. The rheological behavior of mudflow or debris flow is called the Bingham fluid. Thus, the shear stress on rigid bed can be derived from the constitutive equation. The computational approach adopts the HLL scheme, a novel approach for the purpose of computing a Godunov flux and solving the Riemann problem approximately proposed by Harten, Lax and van Leer, as a basic building block, treats the bottom slope by lateralizing the momentum flux, and refines the scheme using the Strang splitting to manage the frictional source term. This study successfully performed 2D two-layer shallow water computations on a rigid bed. The proposed numerical model can describe the variety of depths and velocities of substances including water and mud, when the hyperconcentrated tributary flows into the main river. The analytical results in this study will be valuable for further advanced research and for designing or planning hydraulic engineering structures.     

Field measurement and modeling of near-bed sediment transport processes with fluid mud layer in Tokyo Bay

Tokyo Bay is one of the estuaries in Japan with a high population of almost 26 million people in the basin area. One of the major concerns for the environment in this water area is the decreasing ecosystem functions including the deterioration of water and sediment qualities caused by various anthropogenic activities. Since the bottom sediments around almost the entire area of the inner bay consist of fine materials with a high organic content, which cause the deterioration of water quality through processes such as hypoxia, an understanding of the fine sediment dynamics in the Bay is crucial for an environmental assessment of the water area. This paper proposes a model for the key processes of fine sediment dynamics, which reflects field data about muddy bed structures and their dynamics obtained during the monitoring campaign in 2007. One of the specific features of the sediment in the Bay at present is the persistent existence of fluid mud layers (water content over 300?%) with a thickness of around a few decimeters, which might be caused by deposition of abundant organic particles due to eutrophication. The present study shows that diffusion flux model delivers quite reliable results for estimating erosion flux from the top of fluid mud layers after calibrating the model parameter against the time series data of vertical flux measured by an acoustic Doppler velocimeter system. This study also derives analytical solutions, based on the Bingham fluid concept, of advection flux in the fluid mud layer on which external shear stress force is applied.     

Characterization of a mud deposit offshore of the Patos Lagoon,southern Brazil

Rapid deposition of mud on the beach along the shoreface of Rio Grande do Sul, Brazil dramatically influences the normal operations in the littoral zone. In the surf zone, fluid and suspended mud opposes water-wave movement and dissipates water-wave energy; on the beach, mud limits trafficability. As part of a multinational, multidisciplinary program to evaluate the influence of mud strength, density and viscosity on water-wave attenuation, sediments were evaluated in situ or collected for evaluation from an area offshore of Cassino Beach, slightly south of the Patos Lagoon mouth. Shear strength of deposited sediments ranged from 0.6 kPa at the seafloor to 3.4 kPa at ∼1 m below the seafloor. Mud sediments were also collected to simulate the in situ response of fluid mud to shear stresses. For this determination, rheological evaluations were made using a strain-controlled Couette viscometer on numerous remixed samples that ranged in density from 1.05 to 1.30 g/cm³. It was determined that this mud is a non-ideal Bingham material in that it has a true initial yield stress as well as a upper Bingham yield stress. Initial yield stress ranged from 0.59 to 2.62 Pa, upper Bingham yield stress ranged from 1.05 to 7.6 Pa. Apparent viscosity ranged from 0.02 to 4.7 Pa s with the highest viscosities occurring between the two yield stresses. Sediment strength in the remixed samples is 2 to 3 orders of magnitude lower than the horizontal shear strength of the sediment bed as determined by shear vane or predicted from penetrometer measurements. This difference is partially due to the fact that rheological evaluations are made on fully remixed sediments, whereas horizontal shear strength is determined within relatively undisturbed sediments. Similar values of viscosity and shear strength are comparable to those determined for mud in other coastal areas where fluid mud deposits occur.     

Role of basic rheological models in determination of wave attenuation over muddy seabeds

Among rheological models for estimating the rate of dissipation of non-breaking waves in muddy seabeds, those representing viscoelastic and poroelastic behaviors are used widely. In that regard, the dependence of the wave attenuation coefficient derived from basic rheological representations of mud behavior is examined on a cursory basis. For wave attenuation due to viscoelastic muds, results based on a semi-analytical model incorporating the effects of typically thin mud layers are summarized. This and an existing model for poroelastic beds are tested against selective laboratory data. Relying on these tests, it is emphasized that fluid-like mud should be modeled as a viscoelastic fluid medium, and that only non-fluid beds can be modeled as poroelastic media. Mechanisms for energy dissipation depend on bed compactness specified by the solids volume fraction, porosity or density, and on a characteristic Péclet number defined in terms of particle size, permeability and wave frequency. Due to the role of the latter parameter, for simulation of wave attenuation the chosen rheological model for a bed of given compactness must be applicable over the expected range of wave frequency.     

Mud erosion by waves: a laboratory study

The role of mud erosion under waves in governing cohesive sediment transport in estuarial and coastal waters is well known. A laboratory study was conducted in order to elucidate the mechanism by which soft muds erode under progressive waves in a flume. Two types of cohesive sediment were used, a commercial kaolinite and an estuarial mud. Beds were formed by pouring in a pre-prepared sediment-water slurry and allowing the deposit to consolidate for a period ranging from 2 to 14 days. A multi-layered hydrodynamic model, which considers the mud to be viscoelastic, has been developed and used to evaluate the bed shear stress at the oscillating mud-water interface. The viscoelastic property of the mud has been confirmed by rheological measurements, and model results on velocity, pressure and wave attenuation verified against flume data. Concentration profiles indicate a distinct evolutionary pattern resulting in a highly stratified suspension. Just above the bed, a thin layer of fluid mud is generated. Above this layer, the suspension concentration is significantly lower. This two-layered feature of the concentration profile is related to the oscillatory response of the mud and water layers, and the associated momentum exchange and mass diffusion characteristics. An expression relating the rate of erosion to the bed shear stress in excess of bed shear resistance has been developed. Generation of fluid mud during erosion is a significant feature of the role of waves over mud.     

Mass transport in a thin layer of power-law mud under surface waves

The mass transport velocity in a two-layer system is studied theoretically. The wave motion is driven by a periodic pressure load on the free water surface, and mud in the lower layer is described by a power-law rheological model. Perturbation analysis is performed to the second order to find the mean Eulerian velocity. A numerical iteration method is employed to solve the non-linear governing equation at the leading order. The influence of rheological properties on fluid motion characteristics including the flow field, the surface displacement, the mass transport velocity, and the net discharge rates are investigated based on theoretical results. Theoretical analysis shows that under the action of interfacial shearing, a recirculation structure may appear near the interface in the upper water layer. A higher mass transport velocity at the interface does not necessarily mean a higher discharge rate for a pseudo-plastic fluid mud.     

Field measurement and modeling of near-bed sediment transport processes with fluid mud layer in Tokyo Bay

Tokyo Bay is one of the estuaries in Japan with a high population of almost 26 million people in the basin area. One of the major concerns for the environment in this water area is the decreasing ecosystem functions including the deterioration of water and sediment qualities caused by various anthropogenic activities. Since the bottom sediments around almost the entire area of the inner bay consist of fine materials with a high organic content, which cause the deterioration of water quality through processes such as hypoxia, an understanding of the fine sediment dynamics in the Bay is crucial for an environmental assessment of the water area. This paper proposes a model for the key processes of fine sediment dynamics, which reflects field data about muddy bed structures and their dynamics obtained during the monitoring campaign in 2007. One of the specific features of the sediment in the Bay at present is the persistent existence of fluid mud layers (water content over 300 %) with a thickness of around a few decimeters, which might be caused by deposition of abundant organic particles due to eutrophication. The present study shows that diffusion flux model delivers quite reliable results for estimating erosion flux from the top of fluid mud layers after calibrating the model parameter against the time series data of vertical flux measured by an acoustic Doppler velocimeter system. This study also derives analytical solutions, based on the Bingham fluid concept, of advection flux in the fluid mud layer on which external shear stress force is applied.

     

EXPERIMENTAL STUDY ON WAVE ENERGY DISSIPATION AND COHESIVE SEDIMENT TRANSPORT IN SILT COAST

EmmmL STonY ON w^rs EareGY DlsSunnox AunCOIIES1VE SEDonT TRANSPORT 1N SirT COASTShaong HUl and Onyx WAI2Abstract:The interahon betwee the wave and fluld mud laye Plays an twrtan fOle in the develOPmen ofsilt coast. Sediment is essenhally transported in the form of rheological flow of mud laye unds thewave achon, and on the other hand, the fluid Inud layer dams the wave consfory. ms papestUdies the laws of wave energy dissiPation and mud bed deformhon, and the moveInen of…     

Fluidization and representative wave transformation on muddy beds

Irregular wave-induced mud fluidization and wave spectrum transformation on muddy profiles are studied through representative wave technique. The constitutive equations of visco-elastic model are adopted for the rheological behavior of fluid mud, while the behavior of stationary mud is assumed to be elastic. A set of representative waves are employed to investigate wave–mud interaction. The results are verified using real field data. Comparing the performance of common representative waves, it is concluded that the phenomena can be better predicted by root mean square wave.     

Spatial heterogeneity in estuarine mud dynamics

The fate of mud in an estuary over an entire year was unravelled using complementary, independent, spatially explicit techniques. Sequential ERS-2 SAR and Envisat MERIS-FR data were used to derive synoptic changes in intertidal bottom mud and suspended particulate matter (SPM) in the top of the water column, respectively. These satellite data were combined with in situ measurements and with a high resolution three-dimensional cohesive sediment model, simulating mud transport, resuspension, settling and deposition under the influence of tides, wind, waves and freshwater discharge. The spatial distribution of both bottom mud and SPM as observed by in situ and satellite techniques was largely explained by modelled estuarine circulation, tidal and wind-induced variations in vertical mixing and horizontal advection. The three data sources also showed similar spring-neap and seasonal variations in SPM (all factor 1.5 to 2), but semi-diurnal tidal variations were underestimated by the model. Satellite data revealed that changes in intertidal bottom mud were spatially heterogeneous, but on average mud content doubled during summer, which was confirmed by in situ data. The model did not show such seasonal variation in bed sediment, suggesting that seasonal dynamics are not well explained by the physical factors presently implemented in the model, but may be largely attributed to other (internal) factors, including increased floc size in summer, temporal stabilisation of the sediment by microphytobenthos and a substantially lower roughness of the intertidal bed in summer as observed by the satellite. The effects of such factors on estuarine mud dynamics were evaluated.     

Numerical investigation of the factors influencing the vertical profiles of current,salinity, and SSC within a turbidity maximum zone

The flow-sediment interaction plays a considerable role on the vertical (internal) profiles of current,salinity and suspended sediment concentration (SSC) within a turbidity maximum zone (TMZ).Numerical modeling provides valuable insights into the complex estuarine physical processes.By combining numerical modeling with field observations,the influencing factors of fine sediment dynamics within the TMZ of Yangtze Estuary have been explored in this study.Firstly,during the neap tide,the measured data present that the current is too weak to break the density stratification,and the vertical flow structure is effectively altered.Secondly,a three-dimensional numerical model based on the Delft3D has been developed and a range of numerical sensitivity analyses were carried out to distinguish the dominant mechanisms and physical processes responsible for the phenomena observed from the measurement data.The numerical investigation highlights the following findings.(1) The vertical profile of currents within the TMZ is largely affected by saltwater intrusion,especially during lower currents when the baroclinic pressure gradient can significantly reshape the local vertical profiles of velocity.(2) The baroclinic effects are primarily determined by the stratification of salinity.(3) In addition to salinity,SSC also influences the local density stratification when its contribution to fluid density is comparable to that of salinity.(4) The settling velocity determines the overall sediment distribution and vertical profiles of the SSC in the water column.The SSC-dependent settling velocity (including the flocculation-induced acceleration and hindered settling deceleration phases) affects the longitudinal movement of the sediments.(5) The vertical profiles of current,salinity and SSC within the TMZ are highly associated with the turbulence determined by the model.The approach to modulate the vertical eddy viscosity in the model,based on the empirical dependency between Rig and Prt,may lead to a numerical instability in the stratified flow.In order to improve the stratification of SSC,additional turbulence damping effect is suggested to be implemented in the model.     

Siltation by sediment-induced density currents

This paper describes the results of numerical experiments with a three-dimensional hydrodynamic and mud transport model in which sediment–fluid interaction is taken into account through the effects of hindered settling, buoyancy destruction in the turbulence k– model and sediment-induced barocline pressure gradients in the momentum equations. The model was applied to a schematic case representing a coastal area with a tidal river, navigation channel and harbour basin, and a real-world case, viz. Rotterdam harbour area in The Netherlands. The results show that the sediment transport into the harbour area, and subsequent siltation rates, increase by a factor 3 to 5 due to the sediment–fluid interaction. It is shown that the larger contribution stems from an increase in vertical gradients in suspended sediment.Responsible Editor: Jens Kappenberg     

Effects of Density and Viscosity in Modeling Heat as a Groundwater Tracer

Decoupled simulation of groundwater flow and heat transport assuming constant fluid density and viscosity is computationally efficient and simple. However, by neglecting the effects of variable density and viscosity, numerical solution of heat transport may be inaccurate. This study investigates the conditions under which the density and viscosity effects on heat transport modeling can be neglected without any significant loss of computational accuracy. A cross-section model of aquifer-river interactions at the Hanford 300 Area in Washington State was employed as the reference frame to quantify the role of fluid density and viscosity in heat transport modeling. This was achieved by comparing the differences in simulated temperature distributions with and without considering variable density and viscosity, respectively. The differences between the two sets of simulations were found to be minor under the complex field conditions at the Hanford 300A site. Based on the same model setup but under different prescribed temperature gradients across the simulation domain, a series of heat transport scenarios were further examined. When the maximum temperature difference across the simulation domain is within 15°C, the mean discrepancy between the simulated temperature distributions with and without considering the effects of variable density and viscosity is approximately 2.5% with a correlation coefficient of above 0.8. Meanwhile, the speedup in runtime is roughly 225% when the maximum temperature difference is at 15°C. This work provides some quantitative guidelines for when heat transport may be simulated by assuming constant density and viscosity as a reasonable compromise between accuracy and efficiency.     

Some hydrodynamic problems for a nepheloid zone

Summary A layer of a few hundred meters thickness with suspended matter (a nepheloid zone) was discovered byEwing andThorndike [4]³⁾ near the bottom on the continental slope of the North Atlantic. A downward pressure gradient is produced in this layer due to increment of water density with suspensoid. When only the Coriolis force balances with this pressure gradient, a bottom nepheloid current flows southwestward parallel to the depth contours with a velocity of about 10 (cm/sec) for a slope of one degree. The pressure gradient for fluid with locally variable density above a sloping bottom is treated and an extra term due to density gradient along the slope is derived. The vertical profiles of the nepheloid current with an effect on the vertical eddy viscosity are computed. Two kinds of vertical distributions of eddy viscosity are determined from the observed nepheloid distributions and used in the calculations: constant but different values at two layers and those increasing with height. The effect of the change of density along the bottom is treated by introducing dimensionless variables. Rossby number of the nepheloid current becomes about 10^–2 indicating inertia terms to be negligible. Rossby number of turbidity currents ranges from 2 (in a decaying area) to 5 (developing area), suggesting that inertia terms are more important than Coriolis terms. The trajectories of turbidity currents are computed from motion of a mass of mud under the Coriolis force and friction, and the results are applied to those inferred byHand andEmery [6] in the San Diego Through off California.LGO Contribution Number 925.     

A three-dimensional model for tides and salinity in the Bristol Channel

A three-dimensional hydrodynamic numerical model is applied to the simulation of tides, salinity and density currents in the Bristol Channel. The model incorporates a sigma coordinate transformation through the vertical and a grid ☐ system throughout.A suitable formulation is chosen for vertical eddy viscosity by comparing elevations and currents from the model with observations. Two simulations of salinity are made, for February and July 1978. The resulting density current patterns for July 1978 are presented at various levels through the vertical.