Numerical calculation for bed variation in compound-meandering channel using depth integrated model without assumption of shallow water flow

In a compound meandering channel, patterns of flow structures and bed variations change with increasing water depth owing to complex momentum exchange between high-velocity flow in a main channel and low-velocity flows in flood plains. We have developed a new quasi-three-dimensional model without the shallow water assumption, i.e., hydrostatic pressure distribution; our method is known as the general bottom velocity computation (BVC) method. In this method, a set of depth-integrated equations, including depth-integrated momentum and vorticity equations, are prepared for evaluating bottom velocity and vertical velocity distributions. The objective of this study is to develop a bed variation calculation method for both single and compound meandering channels by using the BVC method coupled with a sediment transport model. This paper shows that the BVC method can reproduce the pattern change of bed variation in a compound meandering channel flow with increasing relative depth. The variation in sediment transport rate due to overbank flow is explained by experimental and computational results.     

Ekman Layer in 3D-Model of the Geodynamo

The main subject of the paper is to resolve the Ekman layer analytically and to formulate an appropriate set of 3D-geodynamo equations. The equations are formulated in the mean field approximation where the mean values of magnetic field and velocity over azimuthal direction vanish. This approach should allow the numerical calculation to be performed for small Ekman numbers, down to 10^–12 , which are usually considered to be realistic in the geodynamo. The solution of the Ekman layer is also newly interpreted and consequently a new term appears in the usual expression for the geostrophic shear. The viscous terms are neglected in the main volume of the core and their leading role is assumed just in the thin Ekman layer. The inner core is not included in these considerations and no concrete calculations of a model are presented.     

Response of the Changjiang diluted water around Jeju Island to external forcings: A modeling study of 2002 and 2006

The Changjiang diluted water (CDW) around Jeju Island between 2002 and 2006 in response to external forcings, such as wind, tidal forcing and low river discharge, is studied using a three-dimensional model. The model results suggest that wind largely determines spatial differences of CDW and the freshwater export toward Jeju Island between two years. In 2006, when northwestward wind blows during mid June to mid August, the wind-induced Ekman flow causes a broad northeastward extension of CDW and carries a significant amount of freshwater northeastward Jeju Island in August. On the other hand, in 2002 northward wind during mid July to early August drives the CDW to the southwest of Jeju Island, and thereafter the CDW is mainly advected northeastward along the Cheju Current during mid August when the wind becomes weak. Therefore, the amount of freshwater around Jeju Island increases in September, not in August. The response to tidal forcing shows that tide-induced vertical mixing tends to enhance a meander of CDW around Changjiang Bank and shift the CDW flowing into the Yellow Sea southeastward toward Jeju Island. As a result, the amount of freshwater toward Jeju Island becomes larger than that in no-tides case. The summer low river discharge as a flood control scenario has little influence on the spatial behavior of CDW around Jeju Island although the discharge contributes to the amount of freshwater around Jeju Island.     

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.     

Application of third generation shallow water wave models in a tidal environment

Wave modeling was performed in the German Bight of the North Sea during November 2002, using the spectral wave models, namely the K-model and Simulating WAves Nearshore (SWAN), both developed for applications in environments of shallow water depths. These models mainly differ with respect to their dissipation source term expressions and in exclusion or inclusion of nonlinear wave–wave interactions. The K-model uses nonlinear dissipation and bottom dissipation, and neglects quadruplet wave–wave interaction whereas, SWAN includes, besides bottom dissipation, dissipation by white-capping and depth induced wave breaking and triad wave–wave interaction. The boundary spectra were extracted from the WAM model results of a North Sea hindcast of the HIPOCAS project, wind fields, tidal current and water level variations from the results of models used in the Belawatt project. The purpose of this study was to test the performance of both wave models to see whether they were able to predict near-shore wave conditions accurately. The runs were performed with and without tidal current and level variations to determine their effect on the waves. Comparisons of model results with buoy measurements show that taking into account tides and currents improve the spectral shape especially in areas of high current speeds. Whereas SWAN performed better in terms of spectral shape, especially in case of two peaked spectra, the K-model showed better results in terms of integrated parameters.Responsible Editor: Hans Burchard     

The effect of velocity veering on sand transport in a shallow sea

This study aims at comparing and contrasting two different models for sand transport by currents in a shallow sea to illustrate the effect of velocity veering. The first model uses the Bailard-type formulation, which allows calculation of erosion/deposition rates at a fixed location on the sea floor via the divergence of horizontal sediment fluxes. The second model is a semi-analytical 2.5-dimensional model, which takes into account the time lag between erosion and deposition events and the velocity veering within the sediment-laden (nepheloid) layer caused by the Coriolis force. The velocity veering implies that the direction of the sediment flux is generally different from the direction of the surface flow. The latter model was designed for rapid, semi-analytical computations of sediment transport, using flow fields from 2-DH numerical models. The two models use a matching set of parameters to provide identical values for the bottom stress and suspended sediment load for a uniform steady current at any given surface velocity. The two models were compared in a range of sand grain sizes 50–500 m and current speeds up to 1 m s^–1 for an idealised square region (100 × 100 km) of a shelf sea of constant depth. The erosion/deposition patterns and suspension load were examined in three settings: (1) uniform steady flow, (2) straight jet, (3) meandering jet. It was found that both the rates and, in particular, the spatial distribution of the areas of erosion/deposition differ significantly between the models in cases (2) and (3). This difference can be attributed to additional flux divergence due to velocity veering. A comparison of model results with field data, collected at Long Island Shelf, supports the relevance of Coriolis-induced veering of currents on the direction of the sediment flux.Responsible Editor: Jens Kappenberg     

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.     

台湾浅滩浅海水深SAR遥感探测实例研究

本文基于浅海地形SAR遥感成像机理,提出星载SAR图像浅海水深遥感探测新技术.利用该遥感探测新技术与浅海地形SAR遥感图像,在台湾浅滩海域进行了浅海水深SAR遥感探测实例研究.SAR遥感探测水深值与实测水深值的比较结果显示,SAR遥感探测水深值的均方根误差达到2.5 m,误差小于10%.表明SAR具有探测浅海水深的能力,本文提出的浅海水深SAR遥感探测技术是收敛与可行的.     

南海北部深水盆地浅水流的地球物理特性及识别

浅水流(Shallow Water Flow,SWF)是深水环境海底浅部地层中超压的砂体流动,是对深水钻井最具破坏力的一种地质灾害,严重制约深水油气开发.为有效预测和防治浅水流,需要对浅水流地球物理特性进行研究,并在研究区内加以识别.本文借鉴国外主要深水盆地对浅水流问题的研究经验,对南海北部深水盆地潜在浅水流区域采取以属性判定、超压分析为主,振幅识别为辅的方法进行预测.精细层序地层学解释发现,南海北部深水盆地存在上新世以来的古珠江深水水道沉积体系和第四纪水道,这些水道砂体疏松未固结、孔隙度大、有效应力低、几乎表现出流体特性.基于遗传算法的混合反演方法发现,研究区存在典型的AVO响应,横波速度极低,低频特征明显,振幅强度弱,连续性较好,存在极性反转,高泊松比和高纵横波速度比.研究结果表明,南海北部陆坡具备浅水流发生的潜在条件,深水水道发育区为潜在的浅水流危险区,浅水流具有独特的地震响应特征,泊松比高达0.49,纵横波速度比约为3.5~9或更高,SWF层位对地震属性的敏感度VP/VS>AVO响应>泊松比.     

High-order finite volume WENO schemes for the shallow water equations with dry states

The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.     

基于改善水质的浅水湖泊引调水模式的评价指标

以浅水湖泊引清调水的目的为基础,结合生态水力学要求,兼考虑经济性因子,尝试性地建立了浅水湖泊调水方案评价指标体系.评价指标包括湖泊水质改善效果指标、水力条件指标和经济效益指标.以玄武湖调水模式为例,采用二维水质水量模型对玄武湖不同的引水规模、引水方式、引水口和出水口流量分配的引调水方案进行模拟计算,统计出各个评价指标的结果,综合分析评价出相对最优的引调水方案.该评价方法可推广到其它类似的浅水湖泊引清调水模式的评价中.     

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.     

Identification of wind stress on shallow water surfaces by optimal smoothing

Using the state space approach, an on-line filter procedure for combined wind stress identification and tidal flow forecasting is developed. The stochastic dynamic approach is based on the linear twodimensional shallow water equations. Using a finite difference scheme, a system representation of the model is obtained. To account for uncertainties, the system is embedded into a stochastic environment. By employing a Kalman filter, the on-line measurements of the water-level available can be used to identify and predict the shallow water flow. Because it takes a certain time before a fluctuation in the wind stress can be noticed in the water-level measurements, an optimal fixed-lag smoother is used to identify the stress.     

Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations

A total variation diminishing (TVD) modification of the MacCormack scheme is developed for simulating shallow water dynamics on a uniform Cartesian grid. Results obtained using conventional and deviatoric forms of the conservative non-linear shallow water equations (SWEs) are compared for cases where the bed has a varying topography. The comparisons demonstrate that the deviatoric form of the SWEs gives more accurate results than the conventional form, in the absence of numerical balancing of the flux-gradient and source terms. A further comparison is undertaken between the TVD-MacCormack model and an alternating direction implicit (ADI) model for cases involving steep-fronted shallow flows. It is demonstrated that the ADI model is unable to predict trans-critical flows correctly, and artificial viscosity has to be introduced to remove spurious oscillations. The TVD-MacCormack model reproduces all flow regimes accurately. Finally, the TVD-MacCormack model is used to predict a laboratory-scale dyke break undertaken at Delft University of Technology. The predictions agree closely with the experimental data, and are in excellent agreement with results from an alternative Godunov-type model.     

A unified formulation for the three-dimensional shallow water equations using orthogonal co-ordinates: theory and application

In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same for the three- and two-dimensional cases. A systematic derivation of the equations in tensor notation is presented, resulting in a unified formulation for the shallow water equations that covers all orthogonal horizontal grid types of practical interest. This includes spherical curvilinear orthogonal co-ordinate systems on the globe. Computational efficiency can be achieved in a single computer code. Furthermore, a single numerical algorithmic code implementation satisfies. All co-ordinate system specific metrics are determined as part of a computer-aided model grid design, which supports all four orthogonal grid types. Existing intuitive grid design and visual interpretation is conserved by appropriate conformal mappings, which conserve spherical orthogonality in planar representation. A spherical curvilinear co-ordinate solution of wind driven steady channel flow applying a strongly distorted grid is shown to give good agreement with a regular spherical co-ordinate model approach and the solution based on a β-plane approximation. Especially designed spherical curvilinear boundary fitted model grids are shown for typhoon surge propagation in the South China Sea and for ocean-driven flows through Malacca Straits. By using spherical curvilinear grids the number of grid points in these single model grid applications is reduced by a factor of 50–100 in comparison with regular spherical grids that have the same horizontal resolution in the area of interest. The spherical curvilinear approach combines the advantages of the various grid approaches, while the overall computational effort remains acceptable for very large model domains.     

Balancing the source terms in a SPH model for solving the shallow water equations

A shallow flow generally features complex hydrodynamics induced by complicated domain topography and geometry. A numerical scheme with well-balanced flux and source term gradients is therefore essential before a shallow flow model can be applied to simulate real-world problems. The issue of source term balancing has been exhaustively investigated in grid-based numerical approaches, e.g. discontinuous Galerkin finite element methods and finite volume Godunov-type methods. In recent years, a relatively new computational method, smooth particle hydrodynamics (SPH), has started to gain popularity in solving the shallow water equations (SWEs). However, the well-balanced problem has not been fully investigated and resolved in the context of SPH. This work aims to discuss the well-balanced problem caused by a standard SPH discretization to the SWEs with slope source terms and derive a corrected SPH algorithm that is able to preserve the solution of lake at rest. In order to enhance the shock capturing capability of the resulting SPH model, the Monotone Upwind-centered Scheme for Conservation Laws (MUSCL) is also explored and applied to enable Riemann solver based artificial viscosity. The new SPH model is validated against several idealized benchmark tests and a real-world dam-break case and promising results are obtained.     

Numerical resolution of well-balanced shallow water equations with complex source terms

This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile.     

Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations

Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of dry areas where no water is present, as standard numerical methods may fail in the presence of these areas. These equations also have still water steady state solutions in which the flux gradients are nonzero but exactly balanced by the source term. In this paper we propose a high order discontinuous Galerkin method which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation. A simple positivity-preserving limiter, valid under suitable CFL condition, will be introduced in one dimension and then extended to two dimensions with rectangular meshes. Numerical tests are performed to verify the positivity-preserving property, well-balanced property, high order accuracy, and good resolution for smooth and discontinuous solutions.     

Spring water table depth mediates within-site variation of soil temperature in groundwater-fed mires

Groundwater-dependent ecosystems represent globally rare edaphic islands of scattered distribution, often forming areas of regionally unique environmental conditions. A stable groundwater supply is a key parameter defining their ecological specificity, promoting also soil thermal buffering. Still, a limited number of studies dealt with the importance of water temperature in mire ecosystems and virtually no data exist on within-site variation in the temperature buffer effect. Three temperature dataloggers, placed in patches potentially differing in groundwater supply, were installed in each of 19 Western Carpathian spring mire sites from May 2019 to July 2020. Spring source plots statistically differed in water temperature parameters from the plots located towards the spring mire margin, which did not significantly differ from one another. At the majority of sites, the temperature values changed gradually from spring source to mire margins, fitting the pattern expected in the groundwater temperature buffering scenario. Dataloggers placed in the spring sources were the most distinctive from the others in thermal buffering parameters in conditional principal component analysis. The difference between the spring source and its margin was on average 3.25 °C for 95th percentile of the recorded water temperature data points (i.e. warm extremes) and 1.91 °C for 5th percentile (i.e. cold extremes). This suggests that if the temperature at spring source area is considered, thermal buffering within a site may mitigate mainly warm extremes. Thus, our data may provide an important baseline for predictions of possibly upcoming changes in spring mire hydrology caused by climate change. Both warming and precipitation decrease can give rise to the loss or substantial reduction of buffering effect if the contrasting parameters now recorded at the central part shift to those found towards the margins of groundwater-fed areas.