Simplified Wave Models Applicability to Shallow Mud Flows Modeled as Power-Law Fluids

Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood routing.While their use may guarantee a significant reduction of the computational effort,it is mandatory to define the conditions in which they may be confidently applied.The present paper investigates the applicability conditions of the kinematic,diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids.The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress,such as clay or kaolin suspensions,which are frequently encountered in Chinese rivers.In the framework of a linear analysis,the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one.Based on this comparison,applicability criteria for the different wave approximations for mud flood of power-law fluids are derived.The presented results provide guidelines for selecting the appropriate approximation for a given flow problem,and therefore they may represent a useful tool for engineering predictions.

Soil detachment and transport under the combined action of rainfall and runoff energy on shallow overland flow

Rainfall and runoff energy results in soil erosion. This paper presents new the concepts of rainfall and runoff energy and analyzes the relationship of rainfall energy and runoff energy with sediment transport based on the conversion theory of kinetic and potential energy using artificial rainfall and mechanical calculation. The results show that the ratio of sediment detachment in sloping fallow overland flow increases with the slope gradient,rainfall energy and runoff energy, while the sediment detachment ratio under raindrop impact are significantly higher than those under no raindrop impact. The sediment concentration increases with the slope gradient and rainfall energy; when the slope gradient and rainfall energy are constant, the sediment concentration decreases as the runoff energy increases. Rainfall disturbance coefficients have a logarithmic correlation with the rate of rainfall energy and runoff energy. On the same slope gradient,when the rainfall energy is constant, the disturbance coefficient decreases as the runoff energy increases,while when the runoff energy is constant, the disturbance coefficient increases as the rainfall energyincreases. Rainfall energy results in sediment detachment, and runoff energy is the transportation for erosion sediment. This showed that rainfall energy and runoff energy are important in the sediment detachment and transportation of shallow overland flow.

A New Wetting and Drying Method for Moving Boundary in Shallow Water Flow Models

To deal with the moving boundary hydrodynamic problems of the tidal flats in shallow water flow models, a new wetting and drying （WD） method is proposed. In the new method, a ＂predicted water depth＂ is evaluated explicitly based on the simplified shallow water equations and used to determine the status （wet or dry） together with the direction of flow. Compared with previous WD method, besides the water elevation, more factors, such as the flow velocity and the surface shear stress, are taken into account in the new method to determine the moving boundary. In addition, a formula is deduced to determine the threshold, as critical water depth, which needs to be preset before simulations. The new WD method is tested with five cases including three 1D ones and two 2D ones. The results show that the new WD method can simulate the wetting and drying process, in beth typical and practical cases, with smooth manner and achieves effective estimation of the retention volume at shallow water body.

Simulation of Wetting and Drying Processes in A Depth Integrated Shallow Water Flow Model by Slot Method

A particular porosity method named ＂slot method＂ is implemented in a depth-integrated shallow water flow model （DIVAST） to simulate wetting and drying processes. Discussed is the relationship between the shape factors of the ＂slot＂ and the preset depth used in ＂wetting-drying＂ algorithm. Two typical tests are conducted to examine the performance of the method with the effect of the shape factors of the ＂slot＂ being checked in detail in the first test. Numerical results demonstrate that： 1 ） no additional effort to improve the finite difference scheme is needed to implement ＂slot method＂ in DIVAST, and 2） ＂slot method＂ will simulate wetting and diying processes correctly if the shape factors of the ＂slot＂ being selected properly.

An Upward Shallowing Succession of Gravity Flow Deposits in the Early Cretaceous Lingshandao Formation,Western Yellow Sea

Objective Several well-exposed gravity flow deposits in the Early Cretaceous Lingshandao Formation provide a rare opportunity to study deep-water processes. The main objective of this work is to establish the spatial and temporal relationships between the various gravity flow deposits, and thus to establish their sequence stratigraphic patterns and depositional conditions.

Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion

On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.

Steady thermocapillary-buoyant convection in a shallow annular pool. Part 1:Single layer fluid

This paper examines the steady thermocapillarybuoyant convection in a shallow annular pool subjected to a radial temperature gradient. A matched asymptotic theory is used to obtain the asymptotic solutions of the flow and thermal fields in the case of small aspect ratios,which is defined as the ratio of the layer thickness to the gap width. The flow domain is divided into the core region away from the cylinder walls and two end regions near each cylinder wall. Asymptotic solutions are obtained in the core region by solving the core and end flows separately and then joining them through matched asymptotic expansions. For the system of silicon melt,the asymptotic solutions are compared with the results of numerical simulations. It is found that the two kinds of solutions have a good agreement in the core region for a small aspect ratio. With the increase of aspect ratio,the applicability of the present asymptotic solutions decreases gradually.

Three-dimensional hydrodynamic model of Xiamen waters

A semi-implicit and Eulerian - Lagrangian finite difference method for three-dimensionalshallow flow has been extended to a more complete system of equations incorporating second-moment turbulence closure model and transport equations of salinity and temperature. The simulation for flooding and drying of mudflats has been improved. The model is applied to Xiamen waters. Based on extensive survey data, water level elevation, temperature and salinity field along the eastern open boundary and at the Jiulong River inlets and runoffs are analyzed, specified and calibrated. The computed results show good agreement with the measured data, reproduce flooding, emergence of large and complex mudflat region.

On Lagrange-Projection Schemes for Shallow Water Flows Over Movable Bottom with Suspended and Bedload Transport

In the present work we aim to simulate shallow water flows over movable bottom with suspended and bedload transport.In order to numerically approximate such a system,we proceed step by step.We start by considering shallow water equations with non-constant density of the mixture water-sediment.Then,the Exner equation is included to take into account bedload sediment transport.Finally,source terms for friction,erosion and deposition processes are considered.Indeed,observe that the sediment particle could go in suspension into the water or being deposited on the bottom.For the numerical scheme,we rely on well-balanced Lagrange-projection methods.In particular,since sediment transport is generally a slow process,we aim to develop semi-implicit schemes in order to obtain fast simulations.The Lagrange-projection splitting is well-suited for such a purpose as it entails a decomposition of the(fast)acoustic waves and the(slow)material waves of the model.Hence,in subsonic regimes,an implicit approximation of the acoustic equations allows us to neglect the corresponding CFL condition and to obtain fast numerical schemes with large time step.

Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows.The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions,eddy viscosity,wind shear stresses and Coriolis forces.The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation.The dispersion of free-surface temperature is modelled by an advection-diffusion equation.Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure.Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations.In addition,the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms.We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.

Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies

This paper is devoted to a multi-mesh-scale approach for describing the dynamic behaviors of thin geophysical mass flows on complex topographies.Because the topographic surfaces are generally non-trivially curved,we introduce an appropriate local coordinate system for describing the flow behaviors in an efficient way.The complex surfaces are supposed to be composed of a finite number of triangle elements.Due to the unequal orientation of the triangular elements,the distinct flux directions add to the complexity of solving the Riemann problems at the boundaries of the triangular elements.Hence,a vertex-centered cell system is introduced for computing the evolution of the physical quantities,where the cell boundaries lie within the triangles and the conventional Riemann solvers can be applied.Consequently,there are two mesh scales:the element scale for the local topographic mapping and the vertex-centered cell scale for the evolution of the physical quantities.The final scheme is completed by employing the HLL-approach for computing the numerical flux at the interfaces.Three numerical examples and one application to a large-scale landslide are conducted to examine the performance of the proposed approach as well as to illustrate its capability in describing the shallow flows on complex topographies.

NUMERICAL SIMULATION FOR SHALLOW FLOW AND POLLUTANT DISPERSION BASED ON QUAD-TREE MESHES

A 2D depth-averaged flow-pollutant coupled model based on quad-tree meshes was established to accurately simulate flows in water areas with irregular natural boundaries in this paper. The grids were generated by recursive subdivision about seeding points. A new neighbor-finding algorithm was presented. The governing equations were discrctized in collocated conservative variables by using the finite volume method, and the normal flux of mass, momentum and pollutants across the interlace between cells were computed by a Godunov-type Flux Difference Splitting （FDS） scheme. The model was applied to simulate flow fields around a groin. The computed values are in agreement with observed data. The results indicate that quad-tree meshes have fine local resolution, high efficiency and easy local refinement. It is clear that the quad-tree grid model can offer gains in efficiency when applied to complex flow domains or strong shear flows. Finally the model is applied to flow fields and concentration fields simulation in Jiangsu Haizhou Bay. The simulated polluted area is matched well with observations. Therefore, this model can be used to predict flow and concentration fields of actual water area with irregular natural land boundaries.

Numerical simulation of shallow-water flooding using a two-dimensional finite volume model

A 2-D Finite Volume Model （FVM） is developed for shallow water flows over a complex topography with wetting and drying processes. The numerical fluxes are computed using the Harten, Lax, and van Leer （HLL） approximate Riemann solver. Second-order accuracy is achieved by employing the MUSCL reconstruction method with a slope limiter in space and an explicit two-stage Runge-Kutta method for time integration. A simple and efficient method is introduced to deal with the wetting and drying processes without any correction of the numerical flux term or the source term. In this new method, a switch of alternative schemes is used to compute the water depths at the cell interface to obtain the numerical flux. The model is verified against benchmark tests with analytical solutions and laboratory experimental data. The numerical results show that the model can simulate different types of flood waves from the ideal flood wave to cases over complex terrains. The satisfactory performance indicates an extensive application pro- spect of the present model in view of its simplicity and effectiveness.

PROBLEMS ON COMPUTING SHALLOW WATER CIRCULATION AND SIMULATING THE FLOW PAST ISLANDS IN NEARSHORE WATER

This paper continues discussing the problems of numerically solving the shallow water circulation on the basis of ref. 1, For the numerical method proposed in ref. 1, we applied a storage method with dense matrices, which abandoned usual bandwidth concept and attained the intention of saving interior storage, computing time and amount of preparing work before computing. The circulation considered the effect of small islands was successfully simulated by specially dealing with the bottom friction terms and the boundary conditions. In addition, we discussed the action of bottom friction on the dissipation of tidal energy and its effect on stability of period motion.

Coupled flood and sediment transport modelling with adaptive mesh refinement

Coupled flood and sediment transport modelling in large-scale domains has for long been hindered by the high computational cost.Adaptive mesh refinement is one of the viable ways to solving this problem without degrading the accuracy.This goal can be accomplished through mesh adaptation,e.g.,mesh coarsening and refining based on the dynamic regime of the flow and sediment transport along with bed evolution.However,previous studies in this regard have been limited to cases either without involving sediment transport or featuring flow-sediment-bed decoupling and the assumption of sediment transport capacity,which are not generally justified.Here,a coupled hydrodynamic and non-capacity sediment transport model is developed on adaptive non-uniform rectangular mesh.The proposed model is validated against experimental tests and numerical results based on the fixed meshes.It is demonstrated that the proposed model can properly capture shock waves,resolve the wetting/drying transition and reproduce morphological evolution.Compared with models based on the fixed meshes,the proposed model features great advantage in computational efficiency and holds promise for wide applications.

MODELING DAM-BREAK FLOOD OVER NATURAL RIVERS USING DISCONTINUOUS GALERKIN METHOD

A well-balanced numerical model is presented for two-dimensional, depth-averaged, shallow water flows based on the Discontinuous Galerkin （DG） method. The model is applied to simulate dam-break flood in natural rivers with wet/dry bed and complex topography. To eliminate numerical imbalance, the pressure force and bed slope terms are combined in the shallow water flow equations. For partially wet/dry elements, a treatment of the source term that preserves the well-balanced property is presented. A treatment for modeling flow over initially dry bed is presented. Numerical results show that the time step used is related to the dry bed criterion. The intercell numerical flux in the DG method is computed by the Harten-Lax-van Contact （HLLC） approximate Riemann solver. A two-dimensional slope limiting procedure is employed to prevent spurious oscillation. The robustness and accuracy of the model are demonstrated through several test cases, including dam-break flow in a channel with three bumps, laboratory dam-break tests over a triangular bump and an L-shape bend, dam-break flood in the Paute River, and the Malpasset dam-break case. Numerical results show that the model is robust and accurate to simulate dam-break flood over natural rivers with complex geometry and wet/dry beds.

Hydrodynamic modelling of flow impact on structures under extreme flow conditions

Apart from the direct threat to human lives, the flood waves as a result of the rapid catchment response to intense rainfall, breaches of flood defences, tsunamis or storm surges may induce huge impact forces on structures, causing structural damage or even failures. Most existing design codes do not properly account for these impact forces due to the limited understanding of the underlying physical processes and the lack of reliable empirical formulae or numerical approaches to quantifying them. This paper presents laboratory experiments to better understand the interaction between the extreme flow hydrodynamics and the hydraulic structures and uses the measured data to validate a numerical model. The model solves the two-dimensional shallow water equations using a finite volume Godunov-type scheme for the reliable simulation of complex flow hydrodynamics. New model components are developed for estimating the hydrostatic and hydrodynamic pressure to quantify the flow impact on structures. The model is applied to reproduce two selected experiment tests with different settings and satisfactory numerical results are obtained, which confirms its predictive capability. The model will therefore provide a potential tool for wider and more flexible field-scale applications.

Land use/cover change effects on floods with different return periods： a case study of Beijing, China

In this study, an approach integrating digital land use/cover change （LUCC） analysis, hydraulic model- ing and statistical methods was applied to quantify the effect of LUCC on floods in terms of inundation extent, flood arrival time and maximum water depth. The study took Beijing as an example and analyzed five specific floods with return periods of 20-year, 50-year, 100-year, 1000-year and 10000-year on the basis of LUCC over a nine-year period from 1996 to 2004. The analysis reveals that 1） during the period of analysis Beijing experienced unprecedented LUCC; 2） LUCC can affect inundation extent and flood arrival time, and floods with longer return periods are more influenced; 3） LUCC can affect maximum water depth and floods with shorter return periods are more influenced; and 4） LUCC is a major flood security stressor for Beijing. It warns that those cities having experienced rapid expansion during recent decades in China are in danger of more serious floods and recommends that their actual land use patterns should be carefully assessed considering flood security. This inte- grated approach is demonstrated to he a useful tool for joint assessment, planning and management of land and water.

A CONSERVATIVE COUPLED FLOW/TRANSPORT MODEL WITH ZERO MASS ERROR

A fully conservative form applied to a coupled system of two-dimensional water flow and solute motion is presented. A cell-centred finite volume method based on Roe＇s approximate Riemann solver with unstructured grids is formulated. The bed slope source terms are discretized following an upwind approach and a semi-implicit treatment is used for the friction source terms. The centered discretization of the diffusion terms is in an implicit way. It is shown that this numerical technique reproduces almost exactly the steady state of still water and enables to achieve zero numerical errors in unsteady flow over configurations with strong variations on bed slope. The model ensures a global conservation and positive values of both water level and solute concentration. Numerical results show the effectiveness of the model in solute transport over real complex geometries.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.