Stochastic particle based models for suspended particle movement in surface flows

Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches.In this paper,different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions,i.e.,the stochastic diffusion process,stochastic jump process,and stochastic jump diffusion process.While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows,the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows.An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment.In this paper,the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process（i.e.the time lag between the flow particle and the sediment particle in extreme flows is considered negligible）.In the proposed particle tracking models,a random term mainly caused by fluid eddy motions is modeled as a Wiener process,while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process.The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement.The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations.The ensemble mean and variance of particle velocity are verified with available data.Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed.     

Modeling of the effect of flow depth on sediment discharged by rain‐impacted flows from sheet and interrill erosion areas: a review

Sediment, nutrients and pollutants discharged from sheet and interrill erosion areas by rain‐impacted flows may influence water quality in streams and rivers. The depth of water on the soil surface influences the capacity of raindrop impacts to detach soil material underlying rain‐impacted flows, and a number of so‐called process‐based and mechanistic models erroneously use equations on the basis of the effect of water depth on splash erosion to account for this effect. Also, a number of these models require complex mathematical solutions to make them operate and can only predict sediment composition and discharges well if many of their parameters are calibrated specifically to the situations where they are being applied. Experiments with rain‐impacted flows, where flow depth and velocity over eroding surfaces have been controlled, have been reported in the literature and provide more appropriate equations to account for the drop size – flow depth interactions that affect detachment and transport of particles in rain‐impacted flows. There is a need to develop modeling approaches that rely on relevant data obtained under well‐controlled flow conditions where flow depths and velocities are known. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiple time scales of alluvial rivers carrying suspended sediment and their implications for mathematical modeling

Flow, sediment transport and bed deformation in alluvial rivers normally exhibit multiple time scales. Enhanced knowledge of the time scales can facilitate better approaches to the understanding of the fluvial processes. Yet prior studies of the time scales are based upon the concept of sediment transport capacity at low concentrations, which however is not generally applicable. This paper presents new formulations of the time scales of fluvial flow, suspended sediment transport and bed deformation, under the framework of shallow water hydrodynamics, non-capacity sediment transport and the theory of characteristics for the hyperbolic governing equations. The time scale of bed deformation in relation to that of flow depth is demonstrated to delimit the applicability region of mathematical river models, and the time scale of suspended sediment transport relative to that of the pertinent flow information is analyzed to address if the concept of sediment transport capacity is applicable. For shallow flows with high sediment concentrations, bed deformation may considerably affect the flow and a fully coupled model is normally required. In contrast, for deep flows at low sediment concentrations, a decoupled model is mostly justified. This pilot study of the time scales delivers a new theoretical basis, on which the interaction between flow, suspended sediment transport and bed deformation can be potentially better characterized.     

TWO DIMENSIONAL NUMERICAL SIMULATION OF FLOW AND GEO-MORPHOLOGICAL PROCESSES NEAR HEADLANDS BY USING UNSTRUCTURED GRID

1 INTRODUCTION In recent years, due to the increase in population and industrial developments, mankind has faced manyproblems associated with rivers, coastal waters and reservoirs. Some of these problems are flood control,water supply, power generation, and irrigation. In addition, making new hydraulic structures changesnatural conditions. Prediction of these changes is necessary for designing such constructions. For solutionof these problems usually an assessment of flow pattern, sedim…     

A 2D hydrodynamic model for shallow water flows with significant infiltration losses

Infiltration losses may be significant and warrant proper incorporation into mathematical models for river floods in arid and semi-arid areas, rainfall-induced surface runoffs in watersheds and swashes on beaches. Here, a depth-averaged two-dimensional hydrodynamic model is presented for such processes based on the cell-centred finite volume method on unstructured meshes, with the full Green-Ampt equation evaluating the infiltration rate. A local time stepping strategy is employed along with thread parallelization with Open Multi-processing and high-performance computing to reduce model run time and therefore facilitate applications for large-scale processes. The numerical solutions generally agree with the experimental and field-measured data for typical cases with significant infiltration losses. The case study shows that neglecting infiltration leads to an overestimated discharge hydrograph, which cannot be compensated by means of varied bed resistance as estimated by Manning roughness, and the infiltration parameters play disparate roles in modifying shallow flows compared with Manning roughness. In addition, infiltration affects bed shear stress, which in turn modifies the critical bed sediment size that could be initiated for incipient motion by the flow and therefore needs to be properly accounted for when sediment transport and morphological evolution are to be resolved.     

Point vortex dynamics for coupled surface/interior QG and propagating heton clusters in models for ocean convection

Abstract

The dynamic behavior of baroclinic point vortices in two-layer quasi-geostrophic flow provides a compact model for studying the transport of heat in a variety of geophysical flows including recent heton models for open ocean convection as a response to spatially localized intense surface cooling. In such heton models, the exchange of heat with the region external to the compact cooling region reaches a statistical equilibrium through the propagation of tilted heton clusters. Such tilted heton clusters are aggregates of cyclonic vortices in the upper layer and anti-cyclonic vortices in the lower layer which collectively propagate almost as an elementary tilted heton pair even though the individual vortices undergo shifts in their relative locations. One main result in this paper is a mathematical theorem demonstrating the existence of large families of long-lived propagating heton clusters for the two-layer model in a fashion compatible to a remarkable degree with the earlier numerical simulations. Two-layer quasi-geostrophic flow is an idealization of coupled surface/interior quasi-geostrophic flow. The second family of results in this paper involves the systematic development of Hamiltonian point vortex dynamics for coupled surface/interior QG with an emphasis on propagating solutions that transport heat. These are novel vortex systems of mixed species where surface heat particles interact with quasi-geostrophic point vortices. The variety of elementary two-vortex exact solutions that transport heat include two surface heat particles of opposite strength, tilted pairs of a surface heat particle coupled to an interior vortex of opposite strength and two interior tilted vortices of opposite strength at different depths. The propagation speeds of the tilted elementary hetons in the coupled surface/interior QG model are compared and contrasted with those in the simpler two-layer heton models. Finally, mathematical theorems are presented for the existence of large families of propagating long-lived tilted heton clusters for point vortex solutions in coupled surface/interior QG flow.     

Using Hydrochemical Fades to Delineate Ground Water Flowpaths in Fractured Shale

Large differences in chemistry between sampling points separated In short vertical intervals are often observed in contaminant plumes in both granular and fractured aquifers. However, most regional models assume that such differences will be reduced by dispersive mixing during transport. At a field site located in a discharge area on the Oak Ridge Reservation, Tennessee, ground water flows along discrete flowpaths, as evidenced by the presence of four distinct water types—Ca-HCO₃, Ca-Na-HCO₃, and Na-Ca-HCO₃, and Na-Ca-HCO₃-S0₄—in samples collected from shallow (< 3D in) multilevel wells. The preservation of distinct chemical signatures suggests that ground water must he contained in discrete flow zones during much of its transport time. The chemical composition of the water types can be explained primarily by strata-bound flow over varying flowpath lengths and secondarily by mixing of waters during cross-formational flow in a discharge zone. The hydrochemical facies identified by correlation of water types between the boreholes indicate the general orientation of ground water How paths. These inferred flowpaths are oblique to the orientation of the measured hydraulic gradient and are more closely aligned with bedding and the calculated flow direction. Results of this study indicate that discrete multilevel sampling for analysis of major ions, in addition to information gathered from tracer tests, borehole flow tests. and visual core observations, can provide valuable information on flow directions and preferential flowpaths for contaminant transport.     

Evidence of distinct contaminant transport patterns in rivers using tracer tests and a multiple domain retention model

Solute transport in rivers is controlled by surface hydrodynamics and by mass exchanges with distinct retention zones. Surface and hyporheic retention processes can be accounted for separately in solute transport models with multiple storage compartments. In the simplest two component model, short term storage can be associated to in-channel transient retention, e.g. produced by riparian vegetation or surface dead zones, and the long-term storage can be associated to hyporheic exchange. The STIR (Solute Transport In Rivers) multiple domain transport model is applied here to tracer test data from three very different Mediterranean streams with distinctive characteristics in terms of flow discharge, vegetation and substrate material. The model is used with an exponential residence time distribution (RTD) to represent surface storage processes and two distinct modeling closures are tested to simulate hyporheic retention: a second exponential RTD and a power-law distribution approximating a known solution for bedform-induced hyporheic exchange. Each stream shows distinct retention patterns characterized by different timescales of the storage time distribution. Both modeling closures lead to very good approximations of the observed breakthrough curves in the two rivers with permeable bed exposed to the flow, where hyporheic flows are expected to occur. In the one case where the occurrence of hyporheic flows is inhibited by bottom vegetation, only the two exponential RTD model is acceptable and the time scales of the two components are of the same magnitude. The significant finding of this work is the recognition of a strong signature of the river properties on tracer data and the evidence of the ability of multiple-component models to describe individual stream responses. This evidence may open a new perspective in river contamination studies, where rivers could possibly be classified based on their ability to trap and release pollutants.     

Modelling coastal ground‐ and surface‐water interactions using an integrated approach

Beach water table fluctuations have an impact on the transport of beach sediments and the exchange of solute and mass between coastal aquifer and nearby water bodies. Details are given of the refinement of a dynamically integrated ground‐ and surface‐water model, and its application to study ground‐ and surface‐water interactions in coastal regions. The depth‐integrated shallow‐water equations are used to represent the surface‐water flow, and the extended Darcy's equation is used to represent the groundwater flow, with a hydrostatic pressure distribution being assumed to apply for both these two types of flows. At the intertidal region, the model has two layers, with the surface‐water layer being located on the top of the groundwater layer. The governing equations for these two types of flows are discretized in a similar manner and they are combined to give one set of linear algebraic equations that can be solved efficiently. The model is used to predict water level distributions across sloping beaches, where the water table in the aquifer may or may not decouple from the free water surface. Five cases are used to test the model for simulating beach water table fluctuations induced by tides, with the model predictions being compared with existing analytical solutions and laboratory and field data published in the literature. The numerical model results show that the integrated model is capable of simulating the combined ground‐ and surface‐water flows in coastal areas. Detailed analysis is undertaken to investigate the capability of the model. Copyright © 2009 John Wiley & Sons, Ltd.     

Lattice Boltzmann Models for Flow and Transport in Saturated Karst

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law–based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.     

Physical processes around a cuspate foreland:: implications to the evolution and long-term maintenance of a cape-associated shoal

Understanding across-margin transport has long been recognized as crucial for wise management of our coastline and shelf waters. Issues related to sewage outfalls, nutrient and pollutant dispersal, carbon export, and shoreline sediment budgets all require an understanding of these processes. Across-margin transport of water and sediment at cuspate foreland headlands has been largely unrecognized, and the processes responsible for this export unappreciated. We examined physical process on Cape Lookout Shoal, a cape-associated shoal on the North Carolina continental shelf, through numerical modeling and field observations of near-bottom currents. The cuspate foreland setting of the northern South Atlantic Bight has been previously characterized as wave-dominated with a principal alongshore directed sediment transport and physical circulation forced by wave and wind-driven currents along the inner and mid-shelf. Our findings instead suggest that a seaward-directed, tidal-driven headland flow many play a significant role in the direction of net sediment transport on the shoal and ultimately its location and long-term maintenance. The shoal's location relative to the promontory-induced residual eddies and the region of active deposition differs from traditionally held ideas on sedimentary processes at headland-related sand banks. In addition, the headland flows may also serve as a first-order mechanism for rapidly exporting nearshore and estuarine waters to the outer-shelf.     

Modeling Noble Gas Transport and Detection for The Comprehensive Nuclear-Test-Ban Treaty

Detonation gases released by an underground nuclear test include trace amounts of ¹³³Xe and ³⁷Ar. In the context of the Comprehensive Nuclear Test Ban Treaty, On Site Inspection Protocol, such gases released from or sampled at the soil surface could be used to indicate the occurrence of an explosion in violation of the treaty. To better estimate the levels of detectability from an underground nuclear test (UNE), we developed mathematical models to evaluate the processes of ¹³³Xe and ³⁷Ar transport in fractured rock. Two models are developed respectively for representing thermal and isothermal transport. When the thermal process becomes minor under the condition of low temperature and low liquid saturation, the subsurface system is described using an isothermal and single-gas-phase transport model and barometric pumping becomes the major driving force to deliver ¹³³Xe and ³⁷Ar to the ground surface. A thermal test is simulated using a nonisothermal and two-phase transport model. In the model, steam production and bubble expansion are the major processes driving noble gas components to ground surface. After the temperature in the chimney drops below boiling, barometric pumping takes over the role as the major transport process.     

Chemical and isotopic changes in the hydrology of the tauhara geothermal field due to exploitation at wairakei

Depressurisation of the Tauhara field due to massive withdrawal of deep chloride water from the adjacent Wairakei field for geothermal power has caused considerably hydrological and chemical changes at Tauhara. In the undisturbed state (1962), deep chloride water discharged as hot and boiling dilute chloride springs on the east and west flanks of the field (the Terrace and Spa areas, respectively), while steam from the two-phase zone of the deep system produced by absorption into near-surface groundwater, steam-heated sulphatebicarbonate waters and by mixing with chloride water, chloride-sulphate waters. By 1978–1981 the chloride waters had stopped discharging on the western flank, the steam flow towards the surface had greatly increased (by 5–10 fold) increasing the volume and temperature of the steam-heated waters, but the dilute chloride waters of the Terrace area had changed very little. Silica concentrations in the near-surface waters appear to be controlled by the solubility of amorphous silica, which is present in the surface zone rocks (e.g., Taupo pumice breccias). The increased steam flow led to enrichment in the ¹³O and D contents of the steam-heated waters by loss of secondary steam and enlargement of the area and intensity of steaming ground, the latter accompanied by hydrothermal eruptions in 1974 and 1981. Generation of the steam-heated waters has been modelled using mass, heat and isotope balances. The model is consistent with observed heat and cold groundwater flows and requires that a large proportion of the heat from adsorbed primary steam is released as secondary steam. Tritium contents show that the steam-heated waters have a mean residence time of 50–100 years. In the future, invasion of the deep system by cooler surface waters may reduce steam flow and lower surface aquifer temperatures.     

Application of fluid mechanic principles to the study of geodynamic processes at trench-arc-back arc systems

Geological processes at trench-arc-back arc systems are some of the most complex tectonic processes in need of study. A large amount of data based on geological and geophysical observations has been accumulated. To synthesize these data, mathematical models have proven to be very useful. Because geological processes are directly related to the dynamical behavior of the solid earth, many of them can be investigated in terms of fluid flow models. Some applications of fluid flow principles in studying tectonic processes at convergent plate boundaries are discussed in this paper. When mantle processes are modeled as convective systems, they are found to have direct implications for the determination of slab dip angles. Additionally, they can also account for the high heat flows in the back arc basins, provide a mechanism for back arc opening, and resolve the question whether subducted oceanic crust can reach melting at shallow depth for island arc magma generation. Besides mantle processes, flow models can also be used to study surface processes. A simple one-parameter plane flow theory is used to model the evolution of trench geometries. This model is able to fit simulataneously the trench curvature and the differential paleomagnetic rotation between volcanic islands for the Mariana. Despite the simplicity of many of these models, their ability to synthesize geological and geophysical data at convergent plate boundaries is quite remarkable.     

Effect of channel deepening on tidal flow and sediment transport—part II: muddy channels

Natural tidal channels often need deepening for navigation purposes (larger vessels). The depth increase may lead to tidal amplification, salt intrusion over longer distances, and increasing sand and mud import. Increasing fine sediment import, in turn, may start a process in which the sediment concentration progressively increases until the river becomes hyper-turbid, which may lead to increased dredging volumes and to decreased ecological values. These effects can be modeled and studied using detailed 3D models. Reliable simplified models for a first quick engineering evaluation are however lacking. In this paper, we apply both simplified and detailed 3D models to analyze the effects of channel deepening in prismatic and weakly converging tidal channels with saturated mud flow. The objective is to gain quantitative understanding of the effects of channel deepening on mud transport. We developed a simplified tidal mud model describing most relevant processes and effects in saturated mud flows with only minor horizontal transport gradients (quasi uniform conditions). The simplified model is not valid for non-saturated mud flow conditions. This model can either be used in standalone mode or in post-processing mode with computed near-bed velocities from a 3D hydrodynamic model as an input. The standalone model has been compared to various field data sets. Mud transport processes in the mouth region of muddy tidal channels can be realistically represented by the simplified model, if sufficient salinity and sediment data are available for calibration. The simulation of tidal mud transport and the behavior of an estuarine turbidity maximum (ETM) in saturated and non-saturated mud flow conditions cannot be represented by the simplified model and requires the application of a detailed 3D model.     

Numerical modelling of multiphase flow in porous media

The simultaneous flow of immiscible fluids in porous media occurs in a wide variety of applications. The equations governing these flows are inherently nonlinear, and the geometries and material properties characterizing many problems in petroleum and groundwater engineering can be quite irregular. As a result, numerical simulation often offers the only viable approach to the mathematical modelling of multiphase flows. This paper provides an overview of the types of models that are used in this field and highlights some of the numerical techniques that have appeared recently. The exposition includes discussions of multiphase, multispecies flows in which chemical transport and interphase mass transfers play important roles. The paper also examines some of the outstanding physical and mathematical problems in multiphase flow simulation. The scope of the paper is limited to isothermal flows in natural porous media; however, many of the special techniques and difficulties discussed also arise in artificial porous media and multiphase flows with thermal effects.     

The initial cooling of pahoehoe flow lobes

 In this paper we describe a new thermal model for the initial cooling of pahoehoe lava flows. The accurate modeling of this initial cooling is important for understanding the formation of the distinctive surface textures on pahoehoe lava flows as well as being the first step in modeling such key pahoehoe emplacement processes as lava flow inflation and lava tube formation. This model is constructed from the physical phenomena observed to control the initial cooling of pahoehoe flows and is not an empirical fit to field data. We find that the only significant processes are (a) heat loss by thermal radiation, (b) heat loss by atmospheric convection, (c) heat transport within the flow by conduction with temperature and porosity-dependent thermal properties, and (d) the release of latent heat during crystallization. The numerical model is better able to reproduce field measurements made in Hawai'i between 1989 and 1993 than other published thermal models. By adjusting one parameter at a time, the effect of each of the input parameters on the cooling rate was determined. We show that: (a) the surfaces of porous flows cool more quickly than the surfaces of dense flows, (b) the surface cooling is very sensitive to the efficiency of atmospheric convective cooling, and (c) changes in the glass forming tendency of the lava may have observable petrographic and thermal signatures. These model results provide a quantitative explanation for the recently observed relationship between the surface cooling rate of pahoehoe lobes and the porosity of those lobes (Jones 1992, 1993). The predicted sensitivity of cooling to atmospheric convection suggests a simple field experiment for verification, and the model provides a tool to begin studies of the dynamic crystallization of real lavas. Future versions of the model can also be made applicable to extraterrestrial, submarine, silicic, and pyroclastic flows. Received: 26 November 1994 / Accepted: 1 December 1995     

Raindrop‐impact‐induced erosion processes and prediction: a review

Raindrop‐impact‐induced erosion is initiated when detachment of soil particles from the surface of the soil results from an expenditure of raindrop energy. Once detachment by raindrop impact has taken place, particles are transported away from the site of the impact by one or more of the following transport processes: drop splash, raindrop‐induced flow transport, or transport by flow without stimulation by drop impact. These transport processes exhibit varying efficiencies. Particles that fall back to the surface as a result of gravity produce a layer of pre‐detached particles that provides a degree of protection against the detachment of particles from the underlying soil. This, in turn, influences the erodibility of the eroding surface. Good understanding of rainfall erosion processes is necessary if the results of erosion experiments are to be properly interpreted. Current process‐based erosion prediction models do not deal with the issue of temporal variations in erodibility during a rainfall event or variabilities in erodibility associated with spatial changes in dominance of the transport processes that follow detachment by drop impact. Although more complex erosion models may deal with issues like this, their complexity and high data requirement may make them unsuitable for use as general prediction tools. Copyright © 2005 John Wiley & Sons, Ltd.     

Laboratory and numerical investigation of flow and transport near a seepage-face boundary

Laboratory and numerical modeling investigations were completed to study the unconfined ground water flow and transport processes near a seepage-face boundary. The laboratory observations were made in a radial sand tank and included measurements of the height of the seepage face, flow velocity near the seepage face, travel time distribution of multiple tracer slugs, and streamlines. All the observations were reliably reproduced with a three-dimensional, axi-symmetric, variably saturated ground water flow model. Physical data presented in this work demonstrate and quantify the importance of three-dimensional transport patterns within a seepage-face zone. The results imply that vertically averaged flow models that employ Dupuit approximations might introduce error in the analysis of localized solute transport near a seepage-face boundary. The experimental dataset reported in this work will also be of interest for those who are attempting to validate a numerical algorithm for solving ground water and contaminant discharge patterns near a surface-water boundary.     

Modelling dam-break flows over mobile beds using a 2D coupled approach

Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows.