MODELING UNSTEADY TURBIDITY CURRENTS IN A STEEP NARROW RESERVOIR

1.IN~DUCTIONTurbiditycurrentisoneclassofflowsnameddensitycurrentorgravitycurrent(therHunterRouse(Yih(1980)),whichdePictstheintmsionofheaVyfluidintoalighterone.Usually,thedensitydifferencebetWeentWonuidisrelativelysmallandmixingacrosstheimerfaceoccurs.ThedrivingforceofdensitycurrentsisnotdensitydifferenceitselfbutthedifferenceinspeCmcweights.Turbiditycurrentisnamedwhenthedensitydifferenceisespeciallycausedbysuspendedfinesedimentparticles.Sincesediment-ladenflowcaninteraCtwiththelowerbou…     

Spatio-temporal deposition profile of an experimentally produced turbidity current with a continuous suspension supply

A turbidity current is a turbulent, particle-laden gravity current that is driven by density differences resulting from the presence of suspended sediment particles. The current travels downslope, bearing a large amount of sediment over a great distance, and forms fluvial and submarine bedforms. Knowledge of the spatio-temporal deposition profile of turbidity-deposited sediment is important for a better understanding of sediment transport by turbidity currents. In the current study, the depositi...     

Numerical modeling of the propagation and morphological changes of turbidity currents using a cost-saving strategy of solution updating

Existing layer-averaged numerical models for turbidity currents have mostly adopted the global minimum time step (GMiTS) for solution updating, which confines their computational efficiency and limits their attractiveness for field applications. This paper presents a highly efficient layer-averaged numerical model for turbidity currents by implementing the combined approach of the local graded-time-step (LGTS) and the global maximum-time-step (GMaTS). The governing equations are solved for unstructured triangular meshes by the shock-capturing finite volume method along with a set of well-balanced evaluations of the numerical flux and geometrical slope source terms. The quantitative accuracy of the model, given reasonably estimated empirical and model parameters (e.g., bed friction, water entrainment, sediment deposition and erosion coefficients), is demonstrated by comparing the numerical solutions against laboratory data of the current front positions and deposition profiles, as well as field data of the current front positions. The improved computational efficiency is demonstrated by comparing the computational cost of the present model against that of a traditional model that uses a GMiTS. For the present simulated cases, the maximum reduction of the computational cost is approximately 80% (e.g., a simulation that cost 1 h before will only require 12 min with the new model).     

Fully coupled mathematical modeling of turbidity currents over erodible bed

Turbidity currents may feature active sediment transport and rapid bed deformation, such as those responsible for the erosion of many submarine canyons. Yet previous mathematical models are built upon simplified governing equations and involve steady flow and weak sediment transport assumptions, which are not in complete accordance with rigorous conservation laws. It so far remains unknown if these could have considerable impacts on the evolution of turbidity currents. Here a fully coupled modeling study is presented to gain new insights into the evolution of turbidity currents. The recent analysis of the multiple time scales of subaerial sediment-laden flows over erodible bed [Cao Z, Li Y, Yue Z. Multiple time scales of alluvial rivers carrying suspended sediment and their implications for mathematical modeling. Adv Water Resour 2007;30(4):715–29] is extended to subaqueous turbidity currents to complement the fully coupled modeling. Results from numerical simulations show the ability of the present coupled model to reproduce self-accelerating turbidity currents. Comparison among the fully and partially coupled and decoupled models along with the analysis of the relative time scale of bed deformation explicitly demonstrate that fully coupled modeling is essential for refined resolution of those turbidity currents featuring active sediment transport and rapid bed deformation, and existing models based on simplified conservation laws need to be reformulated.     

Interactions among waves,current, and mud: Numerical and laboratory studies

Interactions between waves, current, mud and turbulence are very complicated in the coastal and estuarine turbid waters. It is still necessary to improve our understanding of the fundamental physical processes governing the cohesive sediment transport in the coastal and estuarine waters. A numerical model is developed to study the interactions among waves, current, and mud. An eddy viscosity model for wave and current is proposed in order to close the equations of wave motion or of current motion in a combined flow, respectively. The equations of mud transport are derived based on the visco-elastic properties of mud. Coupling the equations of wave motion or of current motion for water layer with those of mud layer can give (1) wave height; (2) distributions of current velocities in the water layer; (3) distributions of transport velocities at the water–mud interface; and (4) distributions of mass transport velocities within the mud layer. These modeled results are in a reasonable agreement with experimental results. Results suggest that (1) the rate of wave attenuation increases in the opposing currents (currents against in the direction in which the waves propagate) and decreases in the following currents (currents in the same direction as that in which the waves propagate); (2) the opposing currents would have more significant effects on the rate of wave height attenuation than the following currents; (3) the effect of current on the rate of wave attenuation on the muddy bottom is larger than that on the rigid bottom; (4) mud transport rate increased in the following currents but decreased in the opposing currents; and (5) the rate of wave height attenuation on the mud bottom is one order of magnitude larger than that on the rigid bottom.     

Forward-modeling of co-evolution of turbidity currents,sediment transport,and cyclic steps in the Rio Muni Basin

Previous quantitative studies of field-scale cyclic steps are mostly based on analysis of field data. Such studies have shed light on the erosion/deposition patterns over these morphological features as well as the magnitudes of the turbidity current parameters back estimated using the measured geometry data. However, it remains unclear to what extent such back estimated hydraulic features and erosion/deposition patterns can be numerically reproduced by process-based numerical models. Here, a tw...     

Comparison of different turbulence models in predicting cohesive fluid mud gravity current propagation

A numerical study of propagation of cohesive fluid mud gravity currents in the form of lock-exchange was done using the OpenFOAM open source toolbox. An Eulerian approach solution for three separate phases was developed by incorporating a rheological model to predict the front position of cohesive fluid mud gravity currents. The model also simulates features in the complete movement phases including slumping, self-similar, and viscous in which the dynamics of propagation are affected by the balance of viscous and buoyancy forces, and the inertia force is negligible. The influence of using different turbulence models containing sub-grid scale (SGS), modified SGS, detached eddy simulation (DES), delayed-detached eddy simulation (DDES), Launder-R eece-Rodi (LRR), and k-ɛ models on the accuracy of simulation results was evaluated by comparing with available experimental data. The results show that the selection of the proper turbulence model is one of the most important issues for this type of the numerical modeling. The more efficient turbulence model was suggested and tabulated for each stage of propagation and different selected concentrations of 1,045, 1,140, and 1,214 g/L. Although different turbulence models (except k-ɛ) lead to front propagation dynamic simulation results that are in good agreement with the experimental measurements in the early stage of propagation for low concentrations, only DES, SGS, and modified SGS are able to capture the Kelvin-Helmholtz instability vortex shapes at the dense fluid interface, which is the main characteristic of the gravity current through the slumping phase. The calculated accuracies of SGS and modified SGS in predicting gravity current propagation for the both self-similar and viscous phases also are slightly better than DES, DDES, and LRR model results. The results of this study confirmed the performance and efficiency of the modified SGS model in which the interaction coefficients between phases are calibrated for the numerical modeling of fluid mud gravity current propagation.     

Effects of chemical reactions on density-dependent fluid flow: on the numerical formulation and the development of instabilities

A three-dimensional, reactive numerical flow model is developed that couples chemical reactions with density-dependent mass transport and fluid flow. The model includes equilibrium reactions for the aqueous species, kinetic reactions between the solid and aqueous phases, and full coupling of porosity and permeability changes that result from precipitation and dissolution reactions in porous media. A one-step, global implicit approach is used to solve the coupled flow, transport and reaction equations with a fully implicit upstream-weighted control volume discretization. The Newton–Raphson method is applied to the discretized non-linear equations and a block ILU-preconditioned CGSTAB method is used to solve the resulting Jacobian matrix equations. This approach permits the solution of the complete set of governing equations for both concentration and pressure simultaneously affected by chemical and physical processes. A series of chemical transport simulations are conducted to investigate coupled processes of reactive chemical transport and density-dependent flow and their subsequent impact on the development of preferential flow paths in porous media. The coupled effects of the processes driving flow and the chemical reactions occurring during solute transport is studied using a carbonate system in fully saturated porous media. Results demonstrate that instability development is sensitive to the initial perturbation caused by density differences between the solute plume and the ambient groundwater. If the initial perturbation is large, then it acts as a “trigger” in the flow system that causes instabilities to develop in a planar reaction front. When permeability changes occur due to dissolution reactions occurring in the porous media, a reactive feedback loop is created by calcite dissolution and the mixed convective transport of the system. Although the feedback loop does not have a significant impact on plume shape, complex concentration distributions develop as a result of the instabilities generated in the flow system.     

On the basic structure of oceanic gravity currents

Results from numerical simulations of idealised, 2.5-dimensional Boussinesq, gravity currents on an inclined plane in a rotating frame are used to determine the qualitative and quantitative characteristics of such currents. The current is initially geostrophically adjusted. The Richardson number is varied between different experiments. The results demonstrate that the gravity current has a two-part structure consisting of: (1) the vein, the thick part that is governed by geostrophic dynamics with an Ekman layer at its bottom, and (2) a thin friction layer at the downslope side of the vein, the thin part of the gravity current. Water from the vein detrains into the friction layer via the bottom Ekman layer. A self consistent picture of the dynamics of a gravity current is obtained and some of the large-scale characteristics of a gravity current can be analytically calculated, for small Reynolds number flow, using linear Ekman layer theory. The evolution of the gravity current is shown to be governed by bottom friction. A minimal model for the vein dynamics, based on the heat equation, is derived and compares very well to the solutions of the 2.5-dimensional Boussinesq simulations. The heat equation is linear for a linear (Rayleigh) friction law and non-linear for a quadratic drag law. I demonstrate that the thickness of a gravity current cannot be modelled by a local parameterisation when bottom friction is relevant. The difference between the vein and the gravity current is of paramount importance as simplified (streamtube) models should model the dynamics of the vein rather than the dynamics of the total gravity current. In basin-wide numerical models of the ocean dynamics the friction layer has to be resolved to correctly represent gravity currents and, thus, the ocean dynamics.     

Quasi-stationary flow structure in turbidity currents

A turbidity current is a particle-laden current driven by density differences due to suspended sediment particles. Turbidity currents can transport large amounts of sediment down slopes over great distances, and play a significant role in fluvial, lake and submarine systems. To better understand the sediment transport process, the flow system of an experimentally produced turbidity current in an inclined flume was investigated using video processing. We observed that the current progresses with constant frontal velocity and maintains an unchanged global interface geometry. In addition, the spatio-temporal profiles of the inner mean and turbulence velocity obtained by ultrasound velocity profiler (UVP) showed that similar distributions were maintained, with low dissipation. The results indicate that the turbidity current progressed in a quasi-stationary state, which enabled long-distance sediment transport. To understand the mechanisms behind the quasi-stationary flow, we analyzed the forces acting on the turbidity current. We found that under particular densities of suspended particles, the gravitational force is balanced by the viscous forces along the slope direction. We conclude that this specific force balance induces the quasi-stationary flow structure, enabling the long-distance transport of a substantial amount of sediment downstream with low dissipation.     

Experimental study on the effects of artificial bed roughness on turbidity currents over abrupt bed slope change

A series of experimental observations are presented in the current study to discuss the effects of artificial bed roughness on the turbidity current flowing in a rectangular channel with an abrupt change in bed slope.For this purpose,two different types of elements,sinusoidal and trapezoidal,with various heights and arrangements are considered as artificial bed roughness.A Vectrino velocity meter was used to measure the velocity and sediment concentration profiles.The effects of inlet sediment concentration on front velocity,body velocity,unit discharge,sediment concentration,and suspended load transport rate also were investigated.Accurate equations were developed for estimation of the velocity of a turbidity current over smooth and rough beds.The unexpected experimental results showed that unlike the effect of roughness height,a change in the roughness arrangement has no significant influence on the velocity of a turbidity current.Also,the effect of bed roughness on the front velocity of a denser current is more significant.     

Numerical prediction of turbidity currents on unsteady sediment-supply

A three-dimensional(3D) numerical model of unstable turbidity currents is developed based on the mechanism of sediment transport and turbulence theory.In this model,numerical simulation of turbidity currents without subsequent supply of muddy water was conducted using the same parameters as were used in the flume experiments.The evolution process of turbidity currents of completely losing supplies observed in the experiment was simulated by the model;validation of the numerical model and the algorithm was conducted.If momentarily interrupted process is regarded as a special case of the gradually interrupted,based on the preceding numerical simulation validity,it is feasible to simulate the motion law of turbidity currents under losing gradually supplies.By this method in this article,the characteristic of sediment-laden flow of losing gradually supplies was obtained,as well as its relationship between front velocity and sediment concentration.     

Gravity currents over a rigid and emergent vegetated slope

Lock-exchange experiments are conducted to investigate the effects of emergent vegetation on gravity currents flowing down a slope. Rigid and emergent cylinders are used to represent vegetation such as reeds in aquatic environments. The results show that the head of gravity currents without cylinders forms a semi-elliptic shape, similar to the flat bed case. For the slope-induced gravity, however, the head of gravity currents gradually grows and accelerates. A steeper slope without cylinders causes the evident entrainment and subsequent energy dissipation of gravity currents with ambient fluid. When the cylinder population becomes denser, developments of the head become slower, and the semi-elliptic head can be only seen at the very front end. As the density reaches 6.9%, the interface between the saltwater and freshwater performs an inclined straight line, corresponding to the pervious theoretical derivation. The gravity current event could go through two different routes under the similar toe speeds. The current head without cylinders grows along the downslope path, and the enrollment and mixing with ambient fluid could occur at the edge of the head; while the currents within dense cylinders (∼6.9%) has a nearly constant thickness and a smaller and more streamlined head at the very front end. As the cylinder density increases, the front speed of gravity currents transforms from acceleration to deceleration phases. The experimental results reveal that the head would accelerate over the downslope course if the cylinder density is less than 2%.     

DEPTH-AVERAGED 2-D CALCULATION OF TIDAL FLOW,SALINITY AND COHESIVE SEDIMENT TRANSPORT IN ESTUARIES

A depth-averaged 2-D numerical model for unsteady flow, salinity and cohesive sediment transport in estuaries is established using the finite volume method on the non-staggered, curvilinear grid. The convection terms are discretized by upwind schemes, the diffusion terms are by the central difference scheme, and the time derivative terms are by the three-time-level implicit scheme. The coupling of flow velocity and water level in the 2-D shallow water equations is achieved by the SIMPLEC algorithm with the Rhie and Chow's momentum interpolation method. The sediment model calculates the settling, deposition, erosion and transport of cohesive sediment, taking into account the influence of sediment size, sediment concentration, salinity and turbulence intensity on the flocculation of cohesive sediment. The flow model is first tested against the measurement data in the Tokyo Bay and San Francisco Bay, showing good agreements. And then, the entire model of flow, salinity and sediment transport is verified in the Gironde Estuary. The water elevation, flow velocity, salinity and sediment concentration are well predicted.     

Behaviour of a hydrodynamic finite element model

A finite element model which solves the vertically integrated momentum and continuity equations is described. Linear triangular elements are used to describe the geometry and parameter variations. The Galerkin method of weighted residuals is employed to cast the equations in a form amenable to numerical solution. The model is based on a fully implicit formulation using finite differences for the temporal derivatives.Means of evaluating the non-linear terms of the governing equations are described, and model results are presented for a frictionless tidal channel. The example is chosen such that the non-linearities have a large influence on the solution, and as a result the linearization scheme significantly affects the model's behaviour.Suppression of the non-linear instabilities generated by the convective terms in the momentum equations is examined for the case of flow around a 180° bend. Both the imposition of artificially high roughness coefficients and the use of an effective eddy viscosity are examined in terms of their ability to damp the oscillations which arise for this example.Finally, model results are presented for a case study involving determination of remedial measures to improve flow conditions at a river outfall in Southern Ontario.     

Solution of the nonlinear transport equation using modified Picard iteration

The transport and fate of reactive chemicals in groundwater is governed by equations which are often difficult to solve due to the nonlinear relationship between the solute concentrations for the liquid and solid phases. The nonlinearity may cause mass balance errors during the numerical simulation in addition to numerical errors for linear transport system. We have generalized the modified Picard iteration algorithm of Celia et al.⁵ for unsaturated flow to solve the nonlinear transport equation. Written in a ‘mixed-form’ formulation, the total solute concentration is expanded in a Taylor series with respect to the solution concentration to linearize the transport equation, which is then solved with a conventional finite element method. Numerical results of this mixed-form algorithm are compared with those obtained with the concentration-based scheme using conventional Picard iteration. In general, the new solver resulted in negligible mass balance errors (< ∥10⁻⁸∥%) and required less computational time than the conventional iteration scheme for the test examples, including transport involving highly nonlinear adsorption under steady-state as well as transient flow conditions. In contrast, mass balance errors resulting from the conventional Picard iteration method were higher than 10% for some highly nonlinear problems. Application of the modified Picard iteration scheme to solve the nonlinear transport equation may greatly reduce the mass balance errors and increase computational efficiency.     

Turbulence-particle interactions under surface gravity waves

The dispersion and transport of single inertial particles through an oscillatory turbulent aquatic environment are examined numerically by a Lagrangian particle tracking model using a series of idealised test cases. The turbulent mixing is incorporated into the Lagrangian model by the means of a stochastic scheme in which the inhomogeneous turbulent quantities are governed by a one-dimensional k- ε turbulence closure scheme. This vertical mixing model is further modified to include the effects of surface gravity waves including Coriolis-Stokes forcing, wave breaking, and Langmuir circulations. To simplify the complex interactions between the deterministic and the stochastic phases of flow, we assume a time-invariant turbulent flow field and exclude the hydrodynamic biases due to the effects of ambient mean current. The numerical results show that the inertial particles acquire perturbed oscillations traced out as time-varying sinking/rising orbits in the vicinity of the sea surface under linear and cnoidal waves and acquire a non-looping single arc superimposed with the high-frequency fluctuations beneath the nonlinear solitary waves. Furthermore, we briefly summarise some recipes through the course of this paper on the implementation of the stochastic particle tracking models to realistically describe the drift and suspension of inertial particles throughout the water column.     

Detecting surface geostrophic currents using wavelet filter from satellite geodesy

According to the features of spatial spectrum of the dynamic ocean topography (DOT),wavelet filter is proposed to reduce short-wavelength and noise signals in DOT. The surface geostrophic currents calculated from the DOT models filtered by wavelet filter in global and Kuroshio regions show more detailed information than those from the DOT models filtered by Gaussian filter. Based on a satellite gravity field model (CG01C) and a gravity field model (EGM96),combining an altimetry-derived mean sea surface height model (KMSS04),two mean DOT models are estimated. The short-wavelength and noise signals of these two DOT models are removed by using wavelet filter,and the DOT models asso-ciated global mean surface geostrophic current fields are calculated separately. Comparison of the surface geostrophic currents from CG01C and EGM96 model in global,Kuroshio and equatorial Pacific regions with that from oceanography,and comparison of influences of the two gravity models errors on the precision of the surface geostrophic currents velocity show that the accuracy of CG01C model has been greatly improved over pre-existing models at long wavelengths. At large and middle scale,the surface geostrophic current from satellite gravity and satellite altimetry agrees well with that from oceanography,which indicates that ocean currents detected by satellite measurement have reached relatively high precision.     

Managing reservoir sedimentation by venting turbidity currents:A review

Reservoir sedimentation is an issue that dam operators are increasingly facing as dams are aging. Not only does it reduce a reservoir's capacity but it also affects its outlet structures such as bottom outlets and powerhouse intakes. Sedimentation may also impoverish downstream ecosystems. For these reasons, several strategies for sediment management are being investigated and applied worldwide. Among these methods, venting of turbidity currents reaching the dam can be very beneficial and economical. This measure helps in preserving a certain continuity of sediment transport in rivers obstructed by dams. However, several practical but also theoretical challenges hamper this technique, rendering its use less common and its aspects rela-tively unknown. The present paper aims to gather the actual state-of-the-art concerning turbidity currents venting and to present an outlook for future development and research in this field.     

Flux-Corrected Transport with MT3DMS for Positive Solution of Transport with Full-Tensor Dispersion

Solute transport is usually modeled by the advection-dispersion-reaction equation. In the standard approach, mechanical dispersion is a tensor with principal directions parallel and perpendicular to the flow vector. Since realistic scenarios include nonuniform and unsteady flow fields, the governing equation has full tensor mechanical dispersion. When conventional grid-based numerical methods are used, approximation of the cross terms arising from the off-diagonal terms cause nonphysical solution with oscillations. As an example, for the common scenario of contaminant input into a domain with zero initial concentration, the cross-dispersion terms can result in negative concentrations that can wreak havoc in reactive transport applications. To address this issue, we use the well-known flux-corrected-transport (FCT) technique for a standard finite volume method. Although FCT has most often been used to eliminate oscillations resulting from discretization of the advection term for explicit time stepping, we show that it can be adapted for full-tensor dispersion and implicit time stepping. Unlike other approaches based on new discretization techniques (e.g., mimetic finite difference, nonlinear finite volume), FCT has the advantage of being flexible and widely applicable. Implementation of FCT requires solving an additional system of equations at each time step, using a modified “low order” matrix and a modified right-hand-side vector. To demonstrate the flexibility of FCT, we have modified the well-known and widely used groundwater solute transport simulator, MT3DMS. We apply the new simulator, MT3DMS-FCT, to several benchmark problems that suffer from negative concentrations when using MT3DMS. The new results are mass conservative and strictly nonnegative.