An analysis of wave dissipation at the Hendijan mud coast, the Persian Gulf

Effects of non-rigid muddy bed on the wave climate at the Hendijan coast along the northwestern part of the Persian Gulf have been examined through field measurements and numerical wave transformation modeling. The field survey included measurements of wave characteristics at an offshore and a nearshore station, and mud sampling to obtain the thickness of the fluid mud layer and its rheological properties. Comparisons of wave spectra at the two stations show energy dissipation along the wave trajectory with higher dissipation in the wave period band around 6?s, because depending on the site a given frequency band tends to be more effective in wave–mud interaction. Dissipation induced by the non-rigid bed is introduced into the REF/DIF wave transformation model through the application of viscoelastic constitutive equations for fluid mud. Numerical outputs of the nearshore wave height, for which the viscoelastic parameters included in the model were obtained independently from oscillatory frequency-sweep tests, are found to be comparable with measured values at the nearshore station. This implies that the model is useful for estimating the design wave conditions in the study area.     

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.     

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.     

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.     

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.     

Numerical study on wave propagation over a fluid-mud layer with different bottom conditions

Wave decay over a muddy seabed has been widely reported. In previous studies, the fluid-mud layer is usually treated as a homogeneous layer with a certain thickness lying on the rigid bottom. However, the muddy seabed beneath a fluid-mud layer is usually movable in practice. This study aims to find out the influence of the movable seabed beneath a fluid-mud layer. For this purpose, a numerical model for wave propagation over a multilayered muddy seabed is developed, in which water is treated as a Newtonian fluid, and the rheology of mud is described by a visco-elastic–plastic model. The laboratory experiments of Sakakiyama and Bijker (J Waterw Port Coast Ocean Eng 115(5):614–633, 1989) are chosen to validate the numerical model. The model is then employed to investigate the movement of a fluid-mud layer with different conditions of the underlying mud layer and its influence on wave decay. It is found that the underlying mud layer plays a very important role in the wave–mud interaction and greatly affects the wave decay rate.     

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…     

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.     

A numerical model for simulation of fluid mud with different rheological behaviors

In this paper, a three-dimensional isopycnal approach is presented to simulate the dynamics of fluid mud covering the formation, development, transport, and disappearance of fluid mud. The basic assumption is the assignment of the fluid’s density as the indicating parameter for the rheological behavior. Considering stable stratification, as is usually the case for fluid mud, layers of constant density discretize the vertical domain. The non-Newtonian dynamics of fluid mud is simulated by solving the Cauchy equations for general continuum dynamics. Instead of using a turbulent viscosity approach, the viscosity is allowed to vary according to the rheological behavior of mud suspensions. This apparent viscosity can be determined for different rheological formulations in dependence of the volume solid fraction and the shear rate. An existing three-dimensional isopycnal hydrodynamic model was extended for vertical mass transport processes and was applied on a schematic system with hindered settling. For including the rheological behavior of fluid mud, the Worrall–Tuliani approach was parameterized and implemented. The resulting flow behavior is shown on a model application of fluid mud layers moving down an inclined plane. With these changes, it is demonstrated that the isopycnal model is capable of simulating fluid mud dynamics.     

Sand–mud morphodynamics in a short tidal basin

The influence of sand and mud transport on the morphological behaviour of a short tidal basin is investigated in this paper. For this purpose, a morphological model is applied in which sand and mud transport are included and the temporal and spatial bed composition variations are taken into account. Initially, the morphological development shows a sand wave near the entrance of the basin and a mud deposition wave more landward. A quasi equilibrium bed level profile is found after a long period (order century) with a sandy bed surface over almost the entire basin and only a small muddy area near the landward end. The dimensionless ratio between the deposition and erosion flux turns out to be a crucial parameter for the understanding of the observed behaviour. Comparison with previous studies on short tidal basins for sand indicates only that the presence of mud in a combined sand mud model does not change the equilibrium bed level profile considerably for the applied parameter settings herein, but drastically decreases the morphological time scale. Comparison between model results and field data of the Wadden Sea suggests that the obtained bed level and bed composition profile are realistic, indicating that the process-based sand mud model is a first step towards a better understanding of sand mud distributions in tidal basins.Responsible Editor: Jens Kappenberg     

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.     

Modeling the effect of sediment concentration on the flow-like behavior of natural debris flow

The rheological behavior of natural slurries consisting of fine-grained, reconstituted debris-flow deposits on pyroclastic terrains having different solid concentrations (ranging from 30 to 42%) has been investigated using a rotational rheometer equipped with a vane rotor system. Experiments were done by increasing the applied shear stress step by step; then a decreasing stress ramp was applied following the same shear stress levels. The slurry mixtures exhibit a typical yield-stress fluid behavior with a static yield stress larger than the dynamic yield stress. In the range of the shear rate corresponding to the flow-like behavior the slurry mixtures behave as a dilatant fluid at lower grain concentrations and as a pseudoplastic fluid in correspondence with the higher grain content, showing a strong discrepancy from the Bingham idealization. The rheological behavior is better interpreted by a Herschel-Bulkley model, whose rheological parameters strongly depend on the granular concentration. Therefore, a generalized Herschel-Bulkley model accounting for the bulk sediment concentration effect is proposed.     

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.     

Boundary conditions effect on linearized mud-flow shallow model

The occurrence of roll-waves in mud-flows is investigated based on the formulation of the marginal stability threshold of a linearized onedimensional viscoplastic (shear-thinning) flow model. Since for this kind of non-Newtonian rheological models this threshold may occur in a hypocritical flow, the downstream boundary condition may have a nonnegligible effect on the spatial growth/decay of the perturbation. The paper presents the solution of the 1D linearized flow of a Herschel and Bulkley fluid in a channel of finite length, in the neighbourhood of a hypocritical base uniform flow. Both linearly stable and unstable conditions are considered. The analytical solution is found applying the Laplace transform method and obtaining the first-order analytical expressions of the upstream and downstream channel response functions in the time domain. The effects of both the yield stress and the rheological law exponent are discussed, recovering as particular cases both power-law and Bingham fluids. The theoretical achievements may be used to extend semi-empirical criteria commonly employed for predicting roll waves occurrence in clear water even to mud-flows.     

Numerical simulation of sedimentation processes in reservoirs as a function of outlet location

This paper builds on a recently published one-dimensional moving-boundary model of the coevolution of topset, foreset and bottomset in a reservoir that captures the dynamics of the internal muddy pond typical to reservoirs. This model was modified to account for different outlet locations at the reservoir＇s downstream end. This model considers a river carrying two sustained phases of sediments： coarse （sand） and fine （mud）. The coarse phase deposits in the topset and delta foreset, while the fine phase forms a dilute suspension of wash load in the river. As the river enters the reservoir, the muddy water plunges on the foreset to form a Froude-supercritical （purely depositional） turbidity current. This turbidity current emplaces the bottomset. The modified numerical model was tested against five laboratory experiments previously reported by the author. The model successfully locates the muddy-water/clear-water interface. In addition, modeled and measured bed deposits are in good agreement. Results clearly indicate that the location of the internal hydraulic jump plays a key role in the final bed deposit.     

A first classification scheme of flow-bed interaction for clay-laden density currents and soft substrates

Many aquatic environments exhibit soft, muddy substrates, but this important property has largely been ignored in process-based models of Earth-surface flow. Novel laboratory experiments were carried out to shed light on the feedback processes that occur when particulate density currents (turbidity currents) move over a soft mud substrate. These experiments revealed multiple types of flow-bed interaction and large variations in bed deformation and bed erosion, which are interpreted to be related to the interplay between the shear forces of the current and the stabilising forces in the bed. Changes in this force balance were simulated by varying the clay concentrations in the flow and in the bed. Five different interaction types are described, and dimensional and non-dimensional phase diagrams for flow-bed interaction are presented.     

Steep wave,turbulence, and sediment concentration statistics beneath a breaking wave field and their implications for sediment transport

A new methodology based on wavelet analysis is used to estimate steep wave statistics under depth-limited conditions and the corresponding high concentration sediment statistics. Steep waves here are defined as wave crests within the wavelet transform exceeding a root mean square derived acceleration threshold. The method is applied to laboratory data obtained in a large-scale wave-flume experiment conducted in 2005 at Oregon State University's O. H. Hinsdale Wave Research Laboratory from an acoustic Doppler velocimeter and a fiber optic backscatter sensor array above a mobile sand bed. The steep wave and high concentration statistical results for the erosive condition suggest that sand suspensions are intermittent when a wave-breaking timescale (the ratio of breaking wave height and rms wave velocity) is used to detect the concurrence among steep wave, high velocity turbulent fluctuations, and sand concentration events near the bed. More importantly, at 1 cm above the bed, though the accretive case has more steep wave events, the erosive case has more steep waves and concurrent high concentration events, suggesting a more intense breaking wave process near the sensors. The use of a longer time window, based on the dominant wave period in the detection process of steep wave and high concentration events at 1 cm above the bed, does not change the resulting statistics for the erosive condition. However, increased percentages of high concentration events correlated with steep wave and high velocity turbulence events for the accretive condition are obtained. These increased percentages are conjectured to be due to advection of non-local turbulent events and sediment concentration peaks from upstream.     

A numerical method for simulating non-Newtonian fluid flow and displacement in porous media

Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow.     

Geotechnical properties of the Cassino Beach mud

Knowledge of the marine soils properties, together with hydrodynamic and climatic data, plays an important role for a better understanding of the dynamic behavior of sandy and muddy coasts. This paper deals with reporting and basic interpretation of two campaigns of exploration and characterization of the mud of Cassino Beach, southern Brazil, carried out during the years of 2004 and 2005. Samples were obtained by means of cores collected at some locations offshore, and were submitted to various laboratory geotechnical tests, including determination of the physical index, grain size distribution, Atterberg limits, and shear resistance by both triaxial and shear vane tests. Results confirm the existence of a very soft soil deposit offshore Cassino Beach, highly plastic, compressible, and viscous, forming an important database for further studies.