Lattice Boltzmann simulations of the transient shallow water flows

A two-dimensional lattice Boltzmann model (LBM) is presented for transient shallow water flows. The model is based on the shallow water equations coupled with the large eddy simulation model. In order to obtain accurate results efficiently, a multi-block lattice scheme is applied at the area where a local finer grid is needed for strong change in physical variables. The model is verified by applying to five cases with transient processes: (a) a tidal wave over steps; (b) a perturbation over a submerged hump; (c) partial dam break flow; (d) circular dam break flow; (e) interaction between a dam break surge and four square cylinders. The objectives of this study are to validate the two-dimensional LBM in transient flow simulation and provide the detailed transient processes in shallow water flows.     

Analytic Element Modeling of Steady Interface Flow in Multilayer Aquifers Using AnAqSim

This paper presents the analytic element modeling approach implemented in the software AnAqSim for simulating steady groundwater flow with a sharp fresh‐salt interface in multilayer (three‐dimensional) aquifer systems. Compared with numerical methods for variable‐density interface modeling, this approach allows quick model construction and can yield useful guidance about the three‐dimensional configuration of an interface even at a large scale. The approach employs subdomains and multiple layers as outlined by Fitts (2010) with the addition of discharge potentials for shallow interface flow (Strack 1989). The following simplifying assumptions are made: steady flow, a sharp interface between fresh‐ and salt water, static salt water, and no resistance to vertical flow and hydrostatic heads within each fresh water layer. A key component of this approach is a transition to a thin fixed minimum fresh water thickness mode when the fresh water thickness approaches zero. This allows the solution to converge and determine the steady interface position without a long transient simulation. The approach is checked against the widely used numerical codes SEAWAT and SWI/MODFLOW and a hypothetical application of the method to a coastal wellfield is presented.     

Multi-block lattice Boltzmann simulations of solute transport in shallow water flows

We report a two-dimensional multi-block lattice Boltzmann model for solute transport in shallow water flows, which is developed based on the advection–diffusion equation for mass transport and the shallow water equations for the flows. A weighting factor is included in the centered scheme for improved accuracy. The model is firstly verified by simulating three benchmark tests: wind-driven circulation in a dish-shaped lake, jet-forced flow in a circular basin, and flow formed by two parallel streams containing different uniform concentrations at the same constant velocity; and then it is applied to a practical wind-induced flow, Baiyangdian Lake, which is characterized by irregular geometries and complex bathymetries. The numerical results have shown that the model is able to produce accurate and detailed results for both water flows and solute transport, which is attractive, especially for flows in narrow zones of practical terrains and certain areas with largely varying pollutant concentrations.     

太湖水动力学三维数值试验研究——3.马山围垦对太湖风生流的影响

地形地决定湖泊流场的大小和结构和重要因素,它会影响湖泊水体内的物质输移与扩散和水质的分布,因而弄清马山围垦对湖流的影响有助于了解无锡市重要饮用水水源地梅梁湖的藻类“水华”和水质变化规律,本文在太湖风生流的三 数值模拟的基础上,用数值试验方法探讨了马山围垦对湖泊流场的影响,结果表明：虽然围垦对表层及底层风生流影响较小,但是对中间转层的流场影响较大,对整层平均流场影响更大,在多数风场作用下,围垦虽未对     

A lattice Boltzmann model coupled with a Large Eddy Simulation model for flows around a groyne

This present paper proposes a two-dimensional lattice Boltzmann model coupled with a Large Eddy Simulation (LES) model and applies it to flows around a non-submerged groyne in a channel. The LES of shallow water equations is efficiently performed using the Lattice Boltzmann Method (LBM) and the turbulence can be taken into account in conjunction with the Smagorinsky Sub-Grid Stress (SGS) model. The bounce-back scheme of the non-equilibrium part of the distribution function is used to determine the unknown distribution functions at inflow boundary, the zero gradient of the distribution function is set normal to outflow boundary to obtain the unknown distribution functions here and the bounce-back scheme, which states that an incoming particle towards the boundary is bounced back into fluid, is applied to the solid wall to ensure non-slip boundary conditions. The initial flow field is defined firstly and then is used to calculate the local equilibrium distributions as initial conditions of the distribution functions. These coupled models successfully predict the flow characteristics, such as circulating flow, velocity and water depth distributions. The comparisons between the simulated results and the experimental data show that the model scheme has the capacity to solve the complex flows in shallow water with reasonable accuracy and reliability.     

Characterization of a multilayer aquifer using open well dilution tests

An approach to characterization of multilayer aquifer systems using open well borehole dilution is described. The approach involves measuring observation well flow velocities while a nearby extraction well is pumped by introducing a saline tracer into observation wells and collecting dilution vs. depth profiles. Inspection of tracer profile evolution allows discrete permeable layers within the aquifer to be identified. Dilution profiles for well sections between permeable layers are then converted into vertical borehole flow velocities and their evolution, using an analytic solution to the advection-dispersion equation applied to borehole flow. The dilution approach is potentially able to measure much smaller flow velocities that would be detectable using flowmeters. Vertical flow velocity data from the observation wells are then matched to those generated using a hydraulic model of the aquifer system, "shorted" by the observation wells, to yield the hydraulic properties of the constituent layers. Observation well flow monitoring of pumping tests represents a cost-effective alternative or preliminary approach to pump testing each layer of a multilayer aquifer system separately using straddle packers or screened wells and requires no prior knowledge of permeable layer depths and thicknesses. The modification described here, of using tracer dilution rather than flowmeter logging to obtain well flow velocities, allows the approach to be extended to greater well separations, thus characterizing a larger volume of the aquifer. An example of the application of this approach to a multilayer Chalk Aquifer in Yorkshire, Northeast England, is presented.     

THREE-DIMENSIONAL NUMERICAL MODELING OF COHESIVE SEDIMENT TRANSPORT BY TIDAL CURRENT IN PEARL RIVER ESTUARV

IINTRODUCTIONEstUariesareprominentcoastalfeatUres.Estuariesareofgreateconomicssignificancetomankind.Attheseareas,manyharborsandwaterchannelshavetobebuiltforeconomicpurposes.ThedesignandconstrUctionofcoastalstrUctUresinestUariesrequireknowledgeofhydrodynamicsaswellassedimenttransportinsuchregions.ThenatUreofestuariesiscontrolledbyvariouscoastalhydrodynamicprocesses.Undertheactionofhydrodynamics,sedimentdepositionsorerosionswilloccurinestuariesornearcoastalstrUCtures.Tomaintainnavigati…     

A 3-D phase-averaged model for shallow-water flow with waves in vegetated water

A 3-D shallow-water flow model has been developed to simulate the flow in coastal vegetated waters with short waves. The model adopts the 3-D phase-averaged shallow-water flow equations with radiation stresses induced by short waves. It solves the governing equations using an implicit finite volume method based on quadtree rectangular mesh in the horizontal plane and stretching mesh in the vertical direction. The flow model is coupled with a spectral wave deformation model called CMS-Wave. The wave model solves the spectral wave-action balance equation and provides wave characteristics to the flow model. The model considers the effects of vegetation on currents and waves by including the drag and inertia forces of vegetation in the momentum equations and the wave energy loss due to vegetation resistance in the wave-action balance equation. The model has been tested using several sets of laboratory experiments, including steady flows in a straight channel with submerged vegetation and in a compound channel with vegetated floodplain and random waves through a vegetated channel and on a vegetated beach slope. The calculated water levels, current velocities, and wave heights are in general good agreement with the measured data.     

Analytical model of the mean velocity distribution in an open channel with double-layered rigid vegetation

An analytical model for predicting the vertical distribution of mean streamwise velocity in an open channel with double-layered rigid vegetation is proposed. The double-layered model was constructed in a laboratory flume with an array of steel cylinders of two heights. For each vegetation layer (i.e., the short- or tall-vegetation layer), the flow is vertically separated into a lower vegetation zone and an upper vegetation zone, and corresponding momentum equations for each zone are formulated. For the lower vegetation zone, a uniform velocity was adopted since turbulent shear is relatively small and the Reynolds stress is ignored. For the upper vegetation zone, a power series was used to solve the momentum equations. For the free-water zone, a new expression was suggested to obtain a zero velocity gradient at the water surface instead of the traditional logarithmic velocity distribution. Good agreement between the analytical predictions and experimental data demonstrated the validity of the model.     

垂直地震力作用下弹性半空间上扁壳基础的解析解

用布希涅斯克定义的弹性半空间内的垂直位移包括两项积分,除了积分号前面系数的差别之外,第一项积分是单层位势而第二项积分为双层位势。若扁壳基础是正高斯曲率的几何曲面,则壳底与半空间表面间的挤压强度就是半空间表面作用的分布垂直荷载。当越过边界时,双层势位的函数值和单层势位的法向导数值发生跳跃。利用这些性质,本文得出布希涅斯克积分的反演公式,从而避开要求解偏微分—积分方程组的巨大数学困难而易于得出解析解。以椭园抛物面扁壳为例说明本文方法的应用。     

The effects of ice cover on flow characteristics in a subarctic meandering river

The effects of ice cover on flow characteristics in meandering rivers are still not completely understood. Here, we quantify the effects of ice cover on flow velocity, the vertical and spatial flow distribution, and helical flow structure. Comparison with open‐channel low flow conditions is performed. An acoustic doppler current profiler (ADCP) is used to measure flow from up to three meander bends, depending on the year, in a small sandy meandering subarctic river (Pulmanki River) during two consecutive ice‐covered winters (2014 and 2015). Under ice, flow velocities and discharges were predominantly slower than during the preceding autumn open‐channel conditions. Velocity distribution was almost opposite to theoretical expectations. Under ice, velocities reduced when entering deeper water downstream of the apex in each meander bend. When entering the next bend, velocities increased again together with the shallower depths. The surface velocities were predominantly greater than bottom/riverbed velocities during open‐channel flow. The situation was the opposite in ice‐covered conditions, and the maximum velocities occurred in the middle layers of the water columns. High‐velocity core (HVC) locations varied under ice between consecutive cross‐sections. Whereas in ice‐free conditions the HVC was located next to the inner bank at the upstream cross‐sections, the HVC moved towards the outer bank around the apex and again followed the thalweg in the downstream cross‐sections. Two stacked counter‐rotating helical flow cells occurred under ice around the apex of symmetric and asymmetric bends: next to the outer bank, top‐ and bottom‐layer flows were towards the opposite direction to the middle layer flow. In the following winter, no clear counter‐rotating helical flow cells occurred due to the shallower depths and frictional disturbance by the ice cover. Most probably the flow depth was a limiting factor for the ice‐covered helical flow circulation, similarly, the shallow depths hinder secondary flow in open‐channel conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

准地转大洋风生环流的格子Boltzmann数值模拟

建立了求解准地转相当正压涡度方程的格子Boltzmann (LB)模型. 该模型将准地转相当正压涡度方程作为一个平流-扩散-反应方程来加以处理,在整体二阶精度下,通过Chapman_Enskog多尺度分析法,可将格子Boltzmann方程还原到相当正压涡度方程. 在不同Reynolds数、不同边界条件以及不同风应力驱动下的数值解表明,该模型正确反映了风生环流的基本结构和不同边界的耗散特征,并得到风生环流的多平衡态解等非线性特征. 此外,不同Rossby变形半径下的实验证明,小Rossby变形半径更容易激发环流的非线性模态. 通过与同等类型有限差方案的比较,表明本文的LB模型具有稳定性好、精度高等优点.     

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.     

Multilayer analytic element modeling of radial collector wells

A new multilayer approach is presented for the modeling of ground water flow to radial collector wells. The approach allows for the inclusion of all aspects of the unique boundary condition along the lateral arms of a collector well, including skin effect and internal friction losses due to flow in the arms. The hydraulic conductivity may differ between horizontal layers within the aquifer, and vertical anisotropy can be taken into account. The approach is based on the multilayer analytic element method, such that regional flow and local three-dimensional detail may be simulated simultaneously and accurately within one regional model. Horizontal flow inside a layer is computed analytically, while vertical flow is approximated with a standard finite-difference scheme. Results obtained with the proposed approach compare well to results obtained with three-dimensional analytic element solutions for flow in unconfined aquifers. The presented approach may be applied to predict the yield of a collector well in a regional setting and to compute the origin and residence time, and thus the quality, of water pumped by the collector well. As an example, the addition of three lateral arms to a collector well that already has three laterals is investigated. The new arms are added at an elevation of 2 m above the existing laterals. The yield increase of the collector well is computed as a function of the lengths of the three new arms.     

Improved bounds on linear instability of barotropic zonal flow within the shallow water equations

Here we develop mathematical results to describe the location of linear instability of a parallel mean flow within the framework of the shallow water equations; growth estimates of near neutral modes (for disturbances subcritical with respect to gravity wave speed) in the cases of non-rotating and rotating shallow water. The bottom topography is taken to be one-dimensional and the isobaths are parallel to the mean flow. In the case of a rotating fluid, the isobaths and the mean flow are assumed to be zonal. The flow is front-like: there is a monotonic increase of mean flow velocity. Our results show that for barotropic flows the location of instabilities will be a semi-ellipse region in the complex wave velocity plane, that is based on the wave-number, Froude number, and depth of the fluid layer. We also explore the instability region for the case of spatially unbounded mean velocity profiles for non-rotating shallow water.     

Numerical modelling of stratified flow: a spectral approach

A numerical formulation is developed to solve the three-dimensional hydrodynamic equations which describe flow in a stratified sea.Arbitrary continuous physically realistic variations of density and eddy viscosity can be included in the model, which is sufficiently flexible to be applicable to sea areas of any horizontal extent and depth. A continuous current profile from sea surface to sea bed, is computed with the model. A method for expanding computed current profiles in terms of vertical modes is proposed and the contribution of these modes to the current profiles is considered.The time variation of the wind-induced circulation of a stratified lake in response to a suddenly imposed and maintained wind stress is examined. Calculations show that the wind-driven surface current is modulated by the internal seiche motion of the lake.     

Structure of flow over alluvial bedforms: an experiment on linking field and laboratory methods

This paper presents results of a field study designed to examine the structure of flow over mobile and fixed bedforms in a natural stream and to compare the results with findings of previous laboratory studies within the framework of double time–space averaging approach. Measurements of turbulence were obtained in a small river in Illinois, USA, over a fine spatial grid of sampling points above a mobile sandy bedform and its artificially moulded replica. Flow structure over the artificial bedform is similar to that observed in laboratory studies, but is markedly different from the flow structure over natural bedforms. These differences are most pronounced in the roughness sublayer, whereas flow in the logarithmic layer over natural and artificial sand waves is fairly similar and exhibits spatial uniformity. The double time–space averaged distributions of turbulence statistics conform to the multilayer model of flow structure over bedforms. Mean velocity distributions indicate neither classical flow recirculation nor substantial reduction of velocities in the lee of bedform crests. However, vertical patterns of turbulence statistics over depth suggest that stacked wakes similar to those observed in laboratory studies exist above the bedforms. Thus, despite the absence of flow separation, wake development seems to be induced by the systematic influence of upstream bedforms on the vertical structure of turbulence. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

洪泽湖风生流对风场和水位变化响应特征

深入认识大型湖泊在不同风速、风向和水位下三维风生流结构特征对于湖泊污染控制、生态恢复及资源的开发利用具有重要意义.本文在构建笛卡尔坐标系下洪泽湖三维水动力模型的基础上,利用2次全湖30个点位流场监测数据验证了模型精度.基于1975-2020年长系列风场观测数据,确定了洪泽湖典型风速风向.在此基础上,模拟了16种不同风向,13种不同风速和20种不同水位工况条件下洪泽湖三维风生流结构.结果表明：水动力模型可以较好地刻画洪泽湖三维湖流变化特征.洪泽湖风生流结构随风向变化呈现出较大空间差异.风生流流速随着风速的升高呈加速上升趋势,其中表层水体流速上升幅度远高于其他水层.在2.4 m/s东风驱动下,溧河洼、成子湖和南部湖区垂向平均流速随着水位上升呈先升高后降低的趋势,3个湖区分别在12.7、12.4和12.2 m水位下流速达到最大值.