Fluid dynamics equations for meandering rivers are derived from conservation laws.
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Retrieved literature confirms that fluid dynamics models for meandering rivers rely on governing equations such as the Navier-Stokes and continuity equations, which are fundamental expressions of conservation laws.
Abstract In meandering rivers, interactions between flow, sediment transport, and bed topography affect diverse processes, including bedform development and channel migration. Predicting how these interactions affect the spatial patterns and magnitudes of bed deformation in meandering rivers is essential for various river engineering and geoscience problems. Computational fluid dynamics simulations can predict river morphodynamics at fine temporal and spatial scales but have traditionally been challenged by the large scale of natural rivers. We conducted coupled large‐eddy simulation and bed morphodynamics simulations to create a unique database of hydro‐morphodynamic data sets for 42 meandering rivers with a variety of planform shapes and large‐scale geometrical features that mimic natural meanders. For each simulated river, the database includes (a) bed morphology, (b) three‐dimensional mean velocity field, and (c) bed shear stress distribution under bankfull flow conditions. The calculated morphodynamics results at dynamic equilibrium revealed the formation of scour and deposition patterns near the outer and inner banks, respectively, while the location of point bars and scour regions around the apexes of the meander bends is found to vary as a function of the radius of curvature of the bends to the width ratio. A new mechanism is proposed that explains this seemingly paradoxical finding. The high‐fidelity simulation results generated in this work provide researchers and s
Numerically simulating turbulent open-channel flows represents a formidable challenge in Computational Fluid Dynamics (CFD), particularly when addressing the interplay of transient turbulence, irregular bathymetry, and dynamic free-surface interactions inherent to natural river systems. This study advances a three-dimensional nonlinear (k-ε) turbulence model to resolve flow dynamics, velocity distributions, and mass transport mechanisms in both meandering and straight open channels. The framework leverages cylindrical coordinate systems to accommodate curvilinear geometries, enabling precise representation of intricate channel boundaries. The governing equations are discretized with the finite volume method, with pressure-velocity coupling achieved through the SIMPLE algorithm. The nonlinear (k-ε) formulation is uniquely suited to capture anisotropic turbulence effects while maintaining computational efficiency, addressing a critical gap in conventional isotropic eddy-viscosity models. Key innovations include the development of a geometrically adaptive numerical framework capable of simulating flow in meandering channels with variable curvature and width-to-depth ratios. Parametric analysis reveals that secondary circulations, driven by curvature-induced centrifugal forces and bed roughness heterogeneity, profoundly influence the velocity profiles and scalar transport. The model successfully predicts flow separation at bends, velocity-dip phenomena beneath free surfaces, and
The Ikeda, Parker, and Sawai river meandering model is reexamined using a physical approach employing an explicit equation of motion. For periodic river shapes as seen from above, a cross-stream surface elevation gradient creates a velocity shear that is responsible for the decay of small-wavelength meander bends, whereas secondary currents in the plane perpendicular to the downstream direction are responsible for the growth of large-wavelength bends. A decay length D=H/2C(f) involving the river depth H and the friction coefficient C(f) sets the scale for meandering, giving the downstream distance required for the fluid velocity profile to recover from changes in the channel curvature. Using this length scale and a time scale T, we explicitly trace the observed length scale invariance to the equations of motion, and predict similar time and velocity scale invariances. A general time-dependent nonlinear modal analysis for periodic rivers reveals that modes higher than the third mode are needed to describe upstream migration of bend apexes just before oxbow cutoff, and are important to accurate calculations of the time and sinuosity at cutoff.
Water is indispensable to life and the means by which it is conveyed is equally important. Natural rivers and manmade channels play a critical role in this respect because they are vital for water supply, navigation, transport of sediments, pollutants and nutrients. Most natural rivers typically have meandering (curved) geometries which make a direct study of their flow dynamics cumbersome. In order to reduce this complexity, natural rivers are usually idealized as open channel bends with rigid boundaries in order to gain insights into the flow dynamics. As such, this research examines the dynamics of flow in open channel bends with rigid boundaries, using computational fluid dynamics (CFD). The particular computational fluid dynamics code used in this research, discretizes the equations of fluid motion (i.e. the Navier-Stokes equations) using a finite volume scheme while tracking the free surface with the volume of fluid method. Turbulence was incorporated into the solution of the equations using large eddy simulation techniques. Even though the general aim is to improve current understanding of natural river bend physics, the specific aims of this research are threefold. These are: (1) to study the effects of radius of curvature on the flow physics of an idealized river bend; (2) to study in detail the effect of a variation in curvature length on the flow structure and dynamics of an open channel bend; and (3) examine in detail the effect of inertial forces on the flow dyna
The present work investigates how the dynamics of meandering rivers influence the formation of riparian vegetation patterns. To this aim, a model coupling river dynamics and riparian vegetation evolution was developed. Meandering dynamics were simulated with a fluid dynamical model using shallow water equations on an erodible bed. The riparian vegetation model takes into account some of the main actions caused by the river, i.e., water table oscillations, floods, and sedimentation. A logistic law and an exponential decay were used to model the increase and decrease in the biomass, respectively, consequent to river migration. The numerical simulation by the model highlights how river dynamics are able to induce typical vegetation patterns that are similar to some real riparian landscapes (some examples are shown). The results also show the role of (1) the relevant river‐vegetation interactions and (2) the temporal scales of vegetation evolution and river migration.
Meandering channels are dynamic landforms that arise as a result of fluid mechanic and sedimentary processes. Their evolution has been described by the meander-morphodynamic equations, which dictate that channel curvature and bed topography give rise to local perturbations in streamwise fluid velocity, prompting the preferential erosion and sediment deposition that constitute meander behaviour. Novel mathematical conditions are presented to guarantee unique solutions for the linearized equations in non-periodic domains with finite boundaries. With the boundary condition specification sufficient for the uniqueness proof one finds a well-posed initial-boundary-value problem amenable to standard numerical techniques for partial differential equations. This provides a pathway for improved numerical algorithms for simulations of meandering river dynamics. Previous theoretical analysis for linear stability theory in meandering dynamics has been restricted to spatially periodic systems. The present effort develops new results for linear stability theory in non-periodic systems with temporal driving at system boundaries as well as non-homogeneous initial conditions. Predictions for temporal driving at the inlets for non-periodic finite domains provide clarification for observed behaviour in laboratory flumes where driven conditions at the inlet avoids the long-term decay of all meanders observed in flumes with fixed entry conditions. Linear stability theory for finite domains confirm
Numerical modeling of vegetation effects on open channel flow can follow one of three approaches. Each approach allows a specific range of flow features to be simulated. Computational hydraulics models can be constructed to solve one-dimensional (1D) averaged flow momentum and continuity equations. These models can simulate the effects of vegetative resistance on bulk flow velocity and depth (de Saint-Venant equations). Computational fluid dynamics (CFD) models can be constructed to solve the 1D to 3D steady Reynolds-averaged-Navier-Stokes (RANS) equations. These models can resolve local flow and turbulence features of the temporally averaged turbulent flow field. Finally, unsteady RANS (URANS) and Large eddy simulation CFD models can be constructed to solve the unsteady 3D Navier-Stokes equations. These models can provide a complete description of the instantaneous unsteady 3D turbulent flow field, capturing organized large-scale unsteadiness and asymmetries (coherent structures) resulting from flow instabilities. The characterization of vegetative flow resistance in these models has and will continue to command the attention of both researchers and practitioners alike. For flow through vegetation, where the ratio of plant height K to flow depth d is greater than 0.5, resistance is generally due more to form drag of the vegetation than from bed shear. Emergent vegetation can also induce wave resistance from free surface distortion. Plant properties that affect form drag incl
This paper presents a study in the inter-comparison and validation of three-dimensional computational fluid dynamics codes which are currently used in river engineering. Finite volume codes PHOENICS, FLUENT and SSIIM; and finite element code TELEMAC3D are considered in this study. The work has been carried out by competent hydraulic modellers who are users of the codes and not involved in their development. This paper is therefore written from the perspective of independent practitioners of the techniques. In all codes, the flow calculations are performed by solving the three-dimensional continuity and Reynolds-averaged Navier–Stokes equations with the k–e turbulence model. The application of each code was carried out independently and this led to slightly different, but nonetheless valid, models. This is particularly seen in the different boundary conditions which have been applied and which arise in part from differences in the modelling approaches and methodology adopted by the different research groups and in part from the different assumptions and formulations implemented in the different codes. Similar finite volume meshes are used in the simulations with PHOENICS, FLUENT and SSIIM while in TELEMAC3D, a triangular finite element mesh is used. The ASME Journal of Fluids Engineering editorial policy is taken as a minimum framework for the control of numerical accuracy. In all cases, grid convergence is demonstrated and conventional criteria, such as Y+, are satisfied. A r
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