Calculation of primary and secondary flow and boundary shear stresses in a meandering channel

Turbulent flow in a meandering channel is computed with two Computational Fluid Dynamics (CFD) codes solving the Navier–Stokes equations by employing different turbulence closure approaches. The first CFD code solves the steady Reynolds-Averaged Navier–Stokes equations (RANS) using an isotropic turbulence closure. The second code is based on the concept of Large Eddy Simulation (LES). LES resolves the large-scale turbulence structures in the flow and is known to outperform RANS models in flows in which large-scale structures dominate the statistics. The results obtained from the two codes are compared with experimental data from a physical model study. Both, LES and RANS simulation, predict the primary helical flow pattern in the meander as well as the occurrence of an outer-bank secondary cell. Computed primary as well as secondary flow velocities are in reasonably good agreement with experimental data. Evidence is given that the outer-bank secondary cell in a meander bend is the residual of the main secondary cell of the previous bend. However, the RANS code, regardless of the turbulence model employed, overpredicts the size and strength of the outer-bank secondary cell. Furthermore, only LES is able to uphold the outer-bank second secondary cell beyond the bend apex until the exit of the bend as turbulence anisotropy contributes to its persistence. The presence of multiple secondary cells has important consequences for the distribution of shear stresses along the wetted perimeter of the channel, and thereby the sediment transport in meandering channels. Consequently, even though LES is expected to compute the bed-shear stresses along the wetted perimeter of the channel with a higher degree of accuracy than the RANS model, comparisons between LES and RANS computed wall shear stresses agree well. These findings are useful for practitioners who need to rely on RANS model predictions of the flow in meandering channels at field scale.     

Simulation of airflow around rain gauges: Comparison of LES with RANS models

Wind is responsible for systematic errors that affect rain gauge measurements. The authors investigate the use of computational fluid dynamics (CFD) to calculate airflow around rain gauges by applying a high-resolution large eddy simulation (LES) model to determine the flow fields around a measuring system of two rain gauges. The simulated air flow field is characterized by the presence of massive separation which induces the formation and shedding of highly unsteady eddies in the detached shear layers and wakes. Parts of these detached structures occur over the orifice of the rain gauges and may substantially affect the dynamics of the raindrops in this critical region. Non-dissipative LES methods used with fine enough meshes can successfully predict these eddies and their associated fluctuations. The authors compare statistics from LES with steady-state Reynolds averaged Navier–Stokes (RANS) simulations using the k–ε and shear stress transport k–ω turbulence models. They find that both RANS and LES models predict similar mean velocity distributions around the rain gauges. However, they determine the distribution of the resolved turbulent kinetic energy (TKE) to be strongly dependent on the RANS model used. Neither RANS model predictions of TKE are close to those of LES. The authors conclude that the failure of RANS to predict TKE is an important limitation, as TKE is needed to scale the local velocity fluctuations in stochastic models used to calculate the motion of raindrops in the flow field.     

Investigating the Behaviour of Two-Dimensional Finite Element Models of Compound Channel Flow

This paper describes results from a recent study concerning the numerical modelling of compound channel flow using two generalized two-dimensional finite element codes specifically adapted to floodplain studies: RMA-2 and TELEMAC-2D. By application to an 11 km reach of the River Culum, Devon, UK, simulations are developed to investigate the impact of numerical technique, mesh resolution and topographic parameterization on model results. The research is shown to raise a number of issues concerning the construction, calibration and validation of two-dimensional finite element models for this flow problem. © 1997 by John Wiley & Sons, Ltd.     

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.     

Investigation of three‐dimensional wind flow behaviour over coastal dune morphology under offshore winds using computational fluid dynamics (CFD) and ultrasonic anemometry

The behaviour of offshore‐directed winds over coastal dune and beach morphology was examined using a combination of modelling (3‐D computational fluid dynamics (CFD)) and field measurement. Both model simulations and field measurements showed reversal of offshore flows at the back beach and creation of an onshore sediment transport potential. The influence of flow reversals on the beach‐dune transport system and foredune growth patterns has previously received little attention. Detailed wind flow measurements were made using an extensive array of mast‐mounted, 3‐D ultrasonic anemometers (50 Hz), arranged parallel to the dominant incident wind direction. Large eddy simulation (LES) of the offshore wind flow over the dune was conducted using the open‐source CFD tool openFOAM. The computational domain included a terrain model obtained by airborne LiDAR and detailed ground DGPS measurements. The computational grid (~22 million cells) included localized mesh refinement near the complex foredune terrain to capture finer details of the dune morphology that might affect wind flows on the adjacent beach. Measured and simulated wind flow are presented and discussed. The CFD simulations offer new insights into the flow mechanics associated with offshore winds and how the terrain steering of wind flow impacts on the geomorphological behaviour of the dune system. Simulation of 3‐D wind flows over complex terrain such as dune systems, presents a valuable new tool for geomorphological research, as it enables new insights into the relationship between the wind field and the underlying topography. The results show that offshore and obliquely offshore winds result in flow reversal and onshore directed winds at distances of up to 20 m from the embryo dune toe. The potential geomorphological significance of the findings are discussed and simple calculations show that incoming offshore and obliquely offshore winds with mean velocities over 13 m s^?1 and 7 m s^?1, respectively, have the potential to create onshore‐directed winds at the back beach with mean velocities above 3.3 m s^?1. These are above the threshold of movement for dry sand and support previous conclusions about the significance of offshore winds in dune and beach budget calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

Two-dimensional numerical modeling of dam-break flows over natural terrain using a central explicit scheme

A two-dimensional (2D) numerical model has been developed to solve shallow water equations for simulation of dam-break flows. The spatial derivatives are discretized using a well-balanced explicit central upwind conservative scheme. The scheme is Riemann solver free and guarantees the positivity of the flow depth over complex topography if the Courant number is kept less than 0.25. The time integration is performed by Euler’s scheme. The model is verified against analytical results for water surface elevation and discharge for three benchmark test cases. A good agreement between analytical solutions and computed results is observed. The property of well-balancing in still water over an uneven bottom is also confirmed. The model is then validated by simulating a laboratory experiment in which a dam break flow propagates over a triangular obstacle. The model performance was found to be satisfactory. A dam break laboratory experimental test case on a frictionless horizontal bottom is also simulated for 2D validation of the model, and good agreement between simulation and the experimental data is observed. The suitability of the proposed model for real life applications is demonstrated by simulating the Malpasset dam-break event, which occurred in 1959 in France. The computed arrival time of the flood wave front and the maximum flow depths at various observation points matched well with the measurements on a 1/400 scale physical model. The overall performance indicates that this model can be applied for simulation of dam-break waves in real life cases.     

APPLICATION OF BED EVOLUTION MODELS OVER LOOSE AND RIGID AREAS

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Flow structure over square bars at intermediate submergence: Large Eddy Simulation study of bar spacing effect

Turbulent open-channel flow over 2D roughness elements is investigated numerically by Large Eddy Simulation (LES). The flow over square bars for two roughness regimes (k-type roughness and transitional roughness between d-type and k-type) at a relative submergence of H/k = 6.5 is considered, where H is the maximum water depth and k is the roughness height. The selected roughness configurations are based on laboratory experiments, which are used for validating numerical simulations. Results from the LES, in turn, complement the experiments in order to investigate the time-averaged flow properties at much higher spatial resolution. The concept of the double-averaging (DA) of the governing equations is utilized to quantify roughness effects at a range of flow properties. Double-averaged velocity profiles are analysed and the applicability of the logarithmic law for rough-wall flows of intermediate submergence is evaluated. Momentum flux components are quantified and roughness effect on their vertical distribution is assessed using an integral form of the DA-equations. The relative contributions of pressure drag and viscous friction to the overall bed shear stress are also reported.     

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.     

Low-cost inundation modelling at the reach scale with sparse data in the Lower Damodar River basin,India

Abstract

Data unavailability is the main reason for limited applications of hydrodynamic models for predicting inundation in the developing world. This paper aims to generate moderately high-resolution hybrid terrain data by merging height information from low-cost Indian Remote Sensing satellite (IRS) Cartosat-1 stereo satellite images, freely-available Shuttle Radar Topograph Mission (SRTM) digital elevation model (DEM) data, and limited surveyed channel cross-sections. The study reach is characterized by anabranching channels that are associated with channel bifurcation, loops and river islands. We compared the performance of a simple 1D–2D coupled LISFLOOD-FP model and a complex fully 2D finite element TELEMAC-2D model with the hybrid terrain data. The results show that TELEMAC-2D produced significantly improved simulated inundation with the hybrid terrain data, as compared to the SRTM DEM. LISFLOOD-FP was found unsuitable to work with the hybrid DEM in a complicated fluvial environment, as it failed to efficiently divert water in the branches from the main channel.

Editor D. Koutsoyiannis; Associate editor A. Viglione     

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.     

Water and sediment movement around a coastal headland: Portland Bill,southern UK

Numerical simulations of tidal flow and sand transport around a coastal headland (Portland Bill, southern UK) were undertaken to investigate patterns of sand transport during the development of tidally induced transient eddies. Results obtained from a 2-D finite-element hydrodynamic model (TELEMAC-2D) were combined with a sediment transport model (SEDTRANS), to simulate the sand transport processes around the headland. Simulation of the tidal flow around Portland Bill has shown the formation and evolution of tidally induced transient eddies, around the headland. During the evolution of these transient eddies, no current-induced bedload (transport) eddy is formed for either side of the headland. Net bedload sand transport direction, around a coastal headland, is the result of instantaneous gradients in bedload transport rates, during flood and ebb flows, rather than the average (residual) flow. Thus, the use of residual (water) circulation to describe patterns of sediment movement as bedload is not an appropriatedapproach. In the case study presented here, the distinct characteristics of the coastal and seabed morphology around the Isle of Portland (i.e. headland shape and the bathymetry) indicate that these parameters can be influencing tidal (flow) and sediment dispersion around the headland. Such an interpretation has broader implications and applications to headland-associated sandbanks elsewhere.Responsible Editor: Hans Burchard     

Computational fluid dynamics modeling of abutment scour under steady current using the level set method

The scour and deposition pattern around an abutment under constant discharge condition is calculated using a three dimensional (3D) Computational Fluid Dynamics (CFD) model. The Reynolds-Averaged Navier Stokes (RANS) equations are solved in three dimensions using a CFD model. The Level Set Method (LSM) is used for calculation of both free surface and bed topography. The two-equation turbulence model (k-ε and k-ω) is used to calculate the eddy viscosity in the RANS equations. The pressure term in the RANS equations on a staggered grid is modeled using the Chorin's projection method. The 5th order Weighted Essentially Non-Oscillatory (WENO) scheme discretizes the convective term of the RANS equations. The Kovacs and Parker and Dey formulations are used for the reduction in bed shear stress on the sloping bed. The model also used the sandslide algorithm which limits bed shear stress reduction during the erosion process. The numerical model solution is validated against experimental results collected at the Politecnico di Milano, Milan, Italy. Further, the numerical model is tested for performance by varying the grid sizes and key parameters like the space and time discretization schemes. The effect of varying bed porosity has been evaluated. Overall, the free surface is well represented in a realistic manner and bed topography is well predicted using the Level Set Method (LSM).     

Observations and modeling of wave-supported sediment gravity flows on the Po prodelta and comparison to prior observations from the Eel shelf

A mooring and tripod array was deployed from the fall of 2002 through the spring of 2003 on the Po prodelta to measure sediment transport processes associated with sediment delivered from the Po River. Observations on the prodelta revealed wave-supported gravity flows of high concentration mud suspensions that are dynamically and kinematically similar to those observed on the Eel shelf [Traykovski, P., Geyer, W.R., Irish, J.D., Lynch, J.F., 2000. The role of wave-induced density-driven fluid mud flows for cross-shelf transport on the Eel River continental shelf. Continental Shelf Research 20, 2113–2140]. Due to the dynamic similarity between the two sites, a simple one-dimensional (1D) across-shelf model with the appropriate bottom boundary condition was used to examine fluxes associated with this transport mechanism at both locations. To calculate the sediment concentrations associated with the wave-dominated and wave-current resuspension, a bottom boundary condition using a reference concentration was combined with an “active layer” formulation to limit the amount of sediment in suspension. Whereas the wave-supported gravity flow mechanism dominated the transport on the Eel shelf, on the Po prodelta flux due to this mechanism is equal in magnitude to transport due to wave resuspension and wind-forced mean currents in the cross-shore direction. Southward transport due to wave resuspension and wind forced mean currents move an order of magnitude more sediment along-shore than the down-slope flux associated wave-supported gravity flows.     

Effect of channel deepening on tidal flow and sediment transport—part II: muddy channels

Natural tidal channels often need deepening for navigation purposes (larger vessels). The depth increase may lead to tidal amplification, salt intrusion over longer distances, and increasing sand and mud import. Increasing fine sediment import, in turn, may start a process in which the sediment concentration progressively increases until the river becomes hyper-turbid, which may lead to increased dredging volumes and to decreased ecological values. These effects can be modeled and studied using detailed 3D models. Reliable simplified models for a first quick engineering evaluation are however lacking. In this paper, we apply both simplified and detailed 3D models to analyze the effects of channel deepening in prismatic and weakly converging tidal channels with saturated mud flow. The objective is to gain quantitative understanding of the effects of channel deepening on mud transport. We developed a simplified tidal mud model describing most relevant processes and effects in saturated mud flows with only minor horizontal transport gradients (quasi uniform conditions). The simplified model is not valid for non-saturated mud flow conditions. This model can either be used in standalone mode or in post-processing mode with computed near-bed velocities from a 3D hydrodynamic model as an input. The standalone model has been compared to various field data sets. Mud transport processes in the mouth region of muddy tidal channels can be realistically represented by the simplified model, if sufficient salinity and sediment data are available for calibration. The simulation of tidal mud transport and the behavior of an estuarine turbidity maximum (ETM) in saturated and non-saturated mud flow conditions cannot be represented by the simplified model and requires the application of a detailed 3D model.     

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.     

Comparison of two modeling approaches for groundwater–surface water interactions

An assessment of interactions between groundwater and surface water was carried out by applying two different modeling approaches to a small‐scale study area in the municipality of Havelock, Quebec. The first approach involved a commonly used sequential procedure that consists in determining the daily recharge rate using a quasi 2D infiltration model (HELP), applied in the next step as an imposed flux to a 3D finite‐element groundwater flow model. The flow model was calibrated under steady‐state and transient conditions against measured water levels. The second approach was based on a recently developed physically based, 3D fully coupled groundwater–surface water flow model (CATHY) applied to the entire flow domain in an integrated manner. Implementation, calibration, and results of the simulations for both approaches are presented and discussed. For equal annual precipitation (1038 mm/y) and evapotranspiration (556 mm/y), the second approach computed a recharge rate of 233 mm/y (8.9% higher than the first approach) and a net upward flow from the fractured aquifer (the first approach predicted a net downward flow to the rock). The simulated annual discharge was similar for the two approaches (9.6% difference). Both approaches were found to be useful in understanding the interactions between groundwater and surface water, although limitations are apparent in the sequential procedure's inability to account for surface–subsurface feedbacks, for instance near stream reaches where groundwater discharge is prevalent. The decoupled, two‐model approach provides disaggregated surface, vadose, and aquifer flows, and a simple aperçu at the different components of total discharge. The fully coupled model accounts for continuous water exchanges between the land surface, subsurface, and stream channel in a more complex manner, and produces a better match against observed data. Copyright © 2012 John Wiley & Sons, Ltd.     

An enhanced depth-averaged tidal model for morphological studies in the presence of rotary currents

A simple and efficient method to improve morphological predictions using depth-averaged tidal models is presented. The method includes the contribution of secondary flows in sediment transport using the computed flow field from a depth-averaged model. The method has been validated for a case study using the 3D POLCOMS model and ADCP data. The enhanced depth-averaged tidal model along with the SWAN wave model are applied to morphological prediction around the Lleyn Peninsula and Bardsey Island as a case study in the Irish Sea. Due to the presence of a headland in this area two asymmetrical tidal eddies are developed in which the cyclonic eddy is stronger as a result of Coriolis effects. The results show that the enhanced model can effectively predict formation of sand banks at the centre of cyclonic eddies, while the depth-averaged model, due to its inability to accommodate secondary flow, is inadequate in this respect.     

A preliminary investigation of the integration of modelled floodplain hydraulics with estimates of overbank floodplain sedimentation derived from Pb-210 and Cs-137 measurements

This paper investigates the possibility of linking finite element modelled two-dimensional hydraulics with floodplain sedimentation rates derived from radionuclide dating techniques. The TELEMAC-2D system is used to simulate the full dynamic velocity vector and water depth distributions for a 1 in 12 year flood event for the River Culm, Devon. These are compared to patterns of medium-term (30– 100 years) sedimentation rates and a degree of correlation is found to exist. This information is used to comment on the complexity of flow and sediment deposition interactions in floodplain environments and to provide a research design for the development of a more fully integrated floodplain morphodynamic model. Copyright © 1999 John Wiley & Sons, Ltd.     

Modelling dam-break flows over mobile beds using a 2D coupled approach

Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows.