A model based on Hirano-Exner equations for two-dimensional transient flows over heterogeneous erodible beds

In order to study the morphological evolution of river beds composed of heterogeneous material, the interaction among the different grain sizes must be taken into account. In this paper, these equations are combined with the two-dimensional shallow water equations to describe the flow field. The resulting system of equations can be solved in two ways: (i) in a coupled way, solving flow and sediment equations simultaneously at a given time-step or (ii) in an uncoupled manner by first solving the flow field and using the magnitudes obtained at each time-step to update the channel morphology (bed and surface composition). The coupled strategy is preferable when dealing with strong and quick interactions between the flow field, the bed evolution and the different particle sizes present on the bed surface. A number of numerical difficulties arise from solving the fully coupled system of equations. These problems are reduced by means of a weakly-coupled strategy to numerically estimate the wave celerities containing the information of the bed and the grain sizes present on the bed. Hence, a two-dimensional numerical scheme able to simulate in a self-stable way the unsteady morphological evolution of channels formed by cohesionless grain size mixtures is presented. The coupling technique is simplified without decreasing the number of waves involved in the numerical scheme but by simplifying their definitions. The numerical results are satisfactorily tested with synthetic cases and against experimental data.     

Impacts of boundary layer parameterization schemes and air-sea coupling on WRF simulation of the East Asian summer monsoon

The planetary boundary layer(PBL)scheme in the regional climate model(RCM)has a significant impact on the interactions and exchanges of moisture,momentum,and energy between land,ocean,and atmosphere;however,its uncertainty will cause large systematic biases of RCM.Based on the four different PBL schemes(YSU,ACM2,Boulac,and MYJ)in Weather Research and Forecasting(WRF)model,the impacts of these schemes on the simulation of circulation and precipitation during the East Asian summer monsoon(EASM)are investigated.The simulated results of the two local turbulent kinetic energy(TKE)schemes,Boulac and MYJ,are more consistent with the observations than those in the two nonlocal closure schemes,YSU and ACM2.The former simulate more reasonable low-level southwesterly flow over East China and west pacific subtropical high(WPSH)than the latter.As to the modeling of summer monsoon precipitation,both the spatial distributions and temporal evolutions from Boulac and MYJ are also better than those in YSU and ACM2 schemes.In addition,through the comparison between YSU and Boulac experiments,the differences from the results of EASM simulation are more obvious over the oceanic area.In the experiments with the nonlocal schemes YSU and ACM2,the boundary layer mixing processes are much stronger,which lead to produce more sea surface latent heat flux and enhanced convection,and finally induce the overestimated precipitation and corresponding deviation of monsoon circulation.With the further study,it is found that the absence of air-sea interaction in WRF may amplify the biases caused by PBL scheme over the ocean.Consequently,there is a reduced latent heat flux over the sea surface and even more reasonable EASM simulation,if an ocean model coupled into WRF.     

Structure of numerically simulated katabatic and anabatic flows along steep slopes

Direct numerical simulation (DNS) is applied to investigate properties of katabatic and anabatic flows along thermally perturbed (in terms of surface buoyancy flux) sloping surfaces in the absence of rotation. Numerical experiments are conducted for homogeneous surface forcings over infinite planar slopes. The simulated flows are the turbulent analogs of the Prandtl (1942) one-dimensional laminar slope flow. The simulated flows achieve quasi-steady periodic regimes at large times, with turbulent fluctuations being modified by persistent low-frequency oscillatory motions with frequency equal to the product of the ambient buoyancy frequency and the sine of the slope angle. These oscillatory wave-type motions result from interactions between turbulence and ambient stable stratification despite the temporal constancy of the surface buoyant forcing. The structure of the mean-flow fields and turbulence statistics in simulated slope flows is analyzed. An integral dynamic similarity constraint for steady slope/wall flows forced by surface buoyancy flux is derived and quantitatively verified against the DNS data.     

Curvilinear immersed boundary method for simulating coupled flow and bed morphodynamic interactions due to sediment transport phenomena

The fluid-structure interaction curvilinear immersed boundary (FSI-CURVIB) numerical method of Borazjani et al. [3] is extended to simulate coupled flow and sediment transport phenomena in turbulent open-channel flows. The mobile channel bed is discretized with an unstructured triangular mesh and is treated as a sharp-interface immersed boundary embedded in a background curvilinear mesh used to discretize the general channel outline. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations closed with the k − ω turbulence model are solved numerically on a hybrid staggered/non-staggered grid using a second-order accurate fractional step method. The bed deformation is calculated by solving the sediment continuity equation in the bed-load layer using an unstructured, finite-volume formulation that is consistent with the CURVIB framework. Both the first-order upwind and the higher-order hybrid GAMMA schemes [12] are implemented to discretize the bed-load flux gradients and their relative accuracy is evaluated through a systematic grid refinement study. The GAMMA scheme is employed in conjunction with a sand-slide algorithm for limiting the bed slope at locations where the material angle of repose condition is violated. The flow and bed deformation equations are coupled using the partitioned loose-coupling FSI-CURVIB approach [3]. The hydrodynamic module of the method is validated by applying it to simulate the flow in an 180° open-channel bend with fixed bed. To demonstrate the ability of the model to simulate bed morphodynamics and evaluate its accuracy, we apply it to calculate turbulent flow through two mobile-bed open channels, with 90° and 135° bends, respectively, for which experimental measurements are available.     

Evaluating the dual‐boundary forcing concept in subsurface–land surface interactions of the hydrological cycle

Subsurface and land surface processes (e.g. groundwater flow, evapotranspiration) of the hydrological cycle are connected via complex feedback mechanisms, which are difficult to analyze and quantify. In this study, the dual‐boundary forcing concept that reveals space–time coherence between groundwater dynamics and land surface processes is evaluated. The underlying hypothesis is that a simplified representation of groundwater dynamics may alter the variability of land surface processes, which may eventually affect the prognostic capability of a numerical model. A coupled subsurface–land surface model ParFlow.CLM is applied over the Rur catchment, Germany, and the mass and energy fluxes of the coupled water and energy cycles are simulated over three consecutive years considering three different lower boundary conditions (dynamic, constant, and free‐drainage) based on groundwater dynamics to substantiate the aforementioned hypothesis. Continuous wavelet transform technique is applied to analyze scale‐dependent variability of the simulated mass and energy fluxes. The results show clear differences in temporal variability of latent heat flux simulated by the model configurations with different lower boundary conditions at monthly to multi‐month time scales (~32–91 days) especially under soil moisture limited conditions. The results also suggest that temporal variability of latent heat flux is affected at even smaller time scales (~1–3 days) if a simple gravity drainage lower boundary condition is considered in the coupled model. This study demonstrates the importance of a physically consistent representation of groundwater dynamics in a numerical model, which may be important to consider in local weather prediction models and water resources assessments, e.g. drought prediction. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of slow atmospheric turbulent flows induced by lithospheric sources

The paper presents the results of numerical experiments with a simplified nonstationary model of turbulent flow of viscous compressible gas for two classes of flows comparable in scale with the height of the troposphere. In the first experiment, the possibility for light tropospheric gases to reach the tropopause during their intense release from the lithosphere is explored on the example of methane, and the gas volumes required for this are estimated. In the second experiment, interaction of the wind flow with orographic heterogeneities is studied, and the development of the intense eddy process is demonstrated.     

From rainfall to spring discharge: Coupling conduit flow,subsurface matrix flow and surface flow in karst systems using a discrete–continuum model

Physics-based distributed models for simulating flow in karst systems are generally based on the discrete–continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete–continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit–matrix coupling is based on the Peaceman’s well-index such that simulated exchange fluxes across the conduit–matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface–subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples.     

沙漠-绿洲陆-气相互作用和绿洲效应的数值模拟

本文利用一个已发展的陆面过程参数化方案与大气边界层模式耦合,模拟了半干旱区绿洲戈壁非均匀下垫面的陆面过程及其与大气边界层的相互作用,给出了“绿洲效应”这一自然现象垂直剖面上更为清晰、准确和细致的结构特征.数值模拟的结果与早前的许多观测实验结论相吻合,即“绿洲效应”具有明显的“冷岛效应”和“湿岛效应”;它表现为在绿洲区域比戈壁沙漠区域环境温度低、湿度大、湍流动能输送弱,具有下沉气流而导致与周围戈壁沙漠区域产生水平输送环流.而更加细致地研究这些现象对于深入了解绿洲气候的形成和绿洲的维持机理具有重要的意义.     

Coupling water flow and solute transport into a physically-based surface-subsurface hydrological model

A distributed-parameter physically-based solute transport model using a novel approach to describe surface-subsurface interactions is coupled to an existing flow model. In the integrated model the same surface routing and mass transport equations are used for both hillslope and channel processes, but with different parametrizations for these two cases. For the subsurface an advanced time-splitting procedure is used to solve the advection-dispersion equation for transport and a standard finite element scheme is used to solve Richards equation for flow. The surface-subsurface interactions are resolved using a mass balance-based surface boundary condition switching algorithm that partitions water and solute into actual fluxes across the land surface and changes in water and mass storage. The time stepping strategy allows the different time scales that characterize surface and subsurface water and solute dynamics to be efficiently and accurately captured. The model features and performance are demonstrated in a series of numerical experiments of hillslope drainage and runoff generation.     

Experiment and simulation of turbulent flow in local scour around a spur dyke

The turbulent flow in the local scour hole around a single non-submerged spur dyke is investigated with both experimental and numerical methods. The experiments are conducted under clear-water scour regime with an impermeable spur dyke. The scour geometry and flow velocities are measured in details with a high-resolution laser displacement meter, electro-magnetic velocimetries and PIV （Particle image velocimetry）. A 3D non-linear k-ε model is developed to simulate the complex local flow field around the scour area. The numerical model is formulated using FVM （Finite volume method） on a collocated unstructured mesh, capable of resolving complex geometries and boundaries. It is found that the simulation results are reasonably consistent with those of the experimental measurements. Based on the study results, the nature of the flow structure around a spur dyke with local scour hole is analyzed.     

High-resolution numerical simulation of turbulence in natural waterways

We develop an efficient and versatile numerical model for carrying out high-resolution simulations of turbulent flows in natural meandering streams with arbitrarily complex bathymetry. The numerical model solves the 3D, unsteady, incompressible Navier-Stokes and continuity equations in generalized curvilinear coordinates. The method can handle the arbitrary geometrical complexity of natural streams using the sharp-interface curvilinear immersed boundary (CURVIB) method of Ge and Sotiropoulos (2007) [1]. The governing equations are discretized with three-point, central, second-order accurate finite-difference formulas and integrated in time using an efficient, second-order accurate fractional step method. To enable efficient simulations on grids with tens of millions of grid nodes in long and shallow domains typical of natural streams, the algebraic multigrid (AMG) method is used to solve the Poisson equation for the pressure coupled with a matrix-free Krylov solver for the momentum equations. Depending on the desired level of resolution and available computational resources, the numerical model can either simulate, via direct numerical simulation (DNS), large-eddy simulation (LES), or unsteady Reynolds-averaged Navier-Stokes (URANS) modeling. The potential of the model as a powerful tool for simulating energetic coherent structures in turbulent flows in natural river reaches is demonstrated by applying it to carry out LES and URANS in a 50-m long natural meandering stream at resolution sufficiently fine to capture vortex shedding from centimeter-scale roughness elements on the bed. The accuracy of the simulations is demonstrated by comparisons with experimental data and the relative performance of the LES and URANS models is also discussed.     

Indirect air–sea interactions simulated with a coupled turbulence-resolving model

A turbulence-resolving parallelized atmospheric large-eddy simulation model (PALM) has been applied to study turbulent interactions between the humid atmospheric boundary layer (ABL) and the salt water oceanic mixed layer (OML). The most energetic three-dimensional turbulent eddies in the ABL–OML system (convective cells) were explicitly resolved in these simulations. This study considers a case of shear-free convection in the coupled ABL–OML system. The ABL–OML coupling scheme used the turbulent fluxes at the bottom of the ABL as upper boundary conditions for the OML and the sea surface temperature at the top of the OML as lower boundary conditions for the ABL. The analysis of the numerical experiment confirms that the ABL–OML interactions involve both the traditional direct coupling mechanism and much less studied indirect coupling mechanism (Garrett Dyn Atmos Ocean 23:19–34, 1996). The direct coupling refers to a common flux-gradient representation of the air–sea exchange, which is controlled by the temperature difference across the air–water interface. The indirect coupling refers to thermal instability of the Rayleigh–Benard convection, which is controlled by the temperature difference across the entire mixed layer through formation of the large convective eddies or cells. The indirect coupling mechanism in these simulations explained up to 45 % of the ABL–OML co-variability on the turbulent scales. Despite relatively small amplitude of the sea surface temperature fluctuations, persistence of the OML cells organizes the ABL convective cells. Water downdrafts in the OML cells tend to be collocated with air updrafts in the ABL cells. The study concludes that the convective structures in the ABL and the OML are co-organized. The OML convection controls the air–sea turbulent exchange in the quasi-equilibrium convective ABL–OML system.     

Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow

This numerical investigation was carried out to advance mechanistic understanding of sediment transport under sheet flow conditions. An Euler–Euler coupled two-phase flow model was developed to simulate fluid–sediment oscillatory sheet flow. Since the concentration of sediment particles is high in such flows, the kinematics of the fluid and sediment phases are strongly coupled. This model includes interaction forces, intergranular stresses and turbulent stress closure. Each phase was modeled via the Reynolds-Averaged Navier–Stokes equations, with interphase momentum conservation accounting for the interaction between the phases. The generation and transformation of turbulence was modeled using the two-equation k–ε$k''–''\epsilon$ turbulence model. Concentration and sediment flux profiles were compared with experimental data for sheet flow conditions considering both symmetric and asymmetric oscillatory flows. Sediment and fluid velocity variations, concentration profiles, sediment flux and turbulence parameters of wave-generated sheet flow were studied numerically with a focus on sediment transport characteristics. In all applications, the model predictions compared well with the experimental data. Unlike previous investigations in which the flow is driven by a horizontal pressure gradient, the present model solves the Navier–Stokes equations under propagating waves. The model’s ability to predict sediment transport under oscillatory sheet flow conditions underscores its potential for understanding the evolution of beach morphology.     

A penalty finite difference model for Navier-Stokes flow problem in sedimentation basins

An explicit finite difference solution procedure for the 2D, unsteady, turbulent and incompressible Navier-Stokes flow problem is developed. The innovative feature of the numerical model is the use of a penalty function technique. To illustrate the effectiveness of the model, two numerically predicted flow patterns for laboratory size sedimentation tanks are compared to actual experimental results. The predicted flow pattern shows a satisfactory match with experimental data.     

Mean and turbulent flow fields in a simulated ice‐covered channel with a gravel bed: some laboratory observations

Northern rivers experience freeze‐up over the winter, creating asymmetric under‐ice flows. Field and laboratory measurements of under‐ice flows typically exhibit flow asymmetry and its characteristics depend on the presence of roughness elements on the ice cover underside. In this study, flume experiments of flows under a simulated ice cover are presented. Open water conditions and simulated rough ice‐covered flows are discussed. Mean flow and turbulent flow statistics were obtained from an Acoustic Doppler Velocimeter (ADV) above a gravel‐bed surface. A central region of faster flow develops in the middle portion of the flow with the addition of a rough cover. The turbulent flow characteristics are unambiguously different when simulated ice covered conditions are used. Two distinct boundary layers (near the bed and in the vicinity of the ice cover, near the water surface) are clearly identified, each being characterized by high turbulent intensity levels. Detailed profile measurements of Reynolds stresses and turbulent kinetic energy indicate that the turbulence structure is strongly influenced by the presence of an ice cover and its roughness characteristics. In general, for y/d > 0·4 (where y is height above bed and d is local flow depth), the addition of cover and its roughening tends to generate higher turbulent kinetic energy values in comparison to open water flows and Reynolds stresses become increasingly negative due to increased turbulence levels in the vicinity of the rough ice cover. The high negative Reynolds stresses not only indicate high turbulence levels created by the rough ice cover but also coherent flow structures where quadrants one and three dominate. Copyright © 2012 John Wiley & Sons, Ltd.     

Process-based interpretation of tracer tests in carbonate aquifers

A tracer test in a carbonate aquifer is analyzed using the method of moments and two analytical advection-dispersion models (ADMs) as well as a numerical model. The numerical model is a coupled continuum-pipe flow and transport model that accounts for two different flow components in karstified carbonate aquifers, i.e., rapid and often turbulent conduit flow and Darcian flow in the fissured porous rock. All techniques employed provide reasonable fits to the tracer breakthrough curve (TBC) measured at a spring. The resulting parameter estimates are compared to investigate how each conceptual model of flow and transport processes that forms the basis of the analyses affects the interpretation of the tracer test. Numerical modeling results suggest that the method of moments and the analytical ADMs tend to overestimate the conduit volume because part of the water discharged at the spring is wrongly attributed to the conduit system if flow in the fissured porous rock is ignored. In addition, numerical modeling suggests that mixing of the two flow components accounts for part of the dispersion apparent in the measured TBC, while the remaining part can be attributed to Taylor dispersion. These processes, however, cannot reasonably explain the tail of the TBC. Instead, retention in immobile-fluid regions as included in a nonequilibrium ADM provides a possible explanation.     

Modelling thin film flow with erosion and deposition

A model is developed for the laminar flow of a thin film mixture made of water and particles over a surface with roughness of the same order as the film height. Particle erosion and deposition are also considered and modelled with two separate equations which are coupled to the fluid flow. This leads to a self-regulated erosion/deposition model, not requiring an explicit value for the transport capacity of the flow, this parameter appears analytically in the model. This approach is tested against a standard model for the erosion/deposition process. Algorithms are also developed to evaluate the required non-standard roughness parameters from experimental measurements and a numerical test of the model is carried out.     

Distribution characteristics of inertial sediment particles in the turbulent boundary layer of an open channel flow determined using Vorono? analysis

This paper presents the numerical investigation of the distribution of inertial sediment particles in the turbulent boundary layer of an open channel flow with the particle Stokes number ranging from 0.6 to 20.4. The methodology is a combination of three numerical approaches, i.e. direct numerical simulation of turbulent flow, the point-particle immersed boundary method, and the discrete particle method. By applying the Vorono? analysis, the preferential concentration characteristics of sediment particles were investigated quantitatively. It was found that the normalized area of the Vorono? cells follows a log-normal particle distribution. The inertial sediment particles distributed unevenly in the turbulent boundary layer and the unevenness, governed by the particle Stokes number, was more significant as the particle Stokes number approaches unity. The inertial sediment particles in the turbulent boundary layer accumulated preferentially in streamwise-aligned streaky structures and this pattern was less significant with increasing particle Stokes number.     

Distribution characteristics of inertial sediment particles in the turbulent boundary layer of an open channel flow determined using Voronoi analysis

This paper presents the numerical investigation of the distribution of inertial sediment particles in the turbulent boundary layer of an open channel flow with the particle Stokes number ranging from 0.6 to 20.4. The methodology is a combination of three numerical approaches, i.e. direct numerical simulation of turbulent flow, the point-particle immersed boundary method, and the discrete particle method. By applying the Vorono analysis, the preferential concentration characteristics of sediment particles were investigated quantitatively. It was found that the normalized area of the Voronoi cells follows a lognormal particle distribution. The inertial sediment particles distributed unevenly in the turbulent boundary layer and the unevenness, governed by the particle Stokes number, was more significant as the particle Stokes number approaches unity. The inertial sediment particles in the turbulent boundary layer accumulated preferentially in streamwise-aligned streaky structures and this pattern was less significant with increasing particle Stokes number.