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In many natural disasters such as overland oil spills or lava flows, physical fluid properties as density change when considering non-homogeneous spatial and time variable distributions of the temperature. This effect is even more remarkable when these flows show a non-Newtonian behaviour due to the sensitivity of their rheological properties as viscosity or yield stress to temperature. In these cases, temperature becomes a significant variable that drives the fluid behaviour, which must be solved using an energy equation coupled with the free surface flow system. Special attention is devoted to thermal source terms which must include all the heat fluid exchanges, and their modelling sometimes can govern the complete flow behaviour. Fluid density, viscosity and yield stress, also affected by temperature, must be recomputed every time step. Summarizing, this work presents a 2D free surface flow model considering density and temperature variations, which could even modify viscosity and yield stress, with heat transfer mechanisms. The model is applied to oil spill overland simulations and heating/cooling test cases are carried out to ensure the system energy balance. As conclusions, it can be said that the numerical results demonstrate the importance of the heat exchange effects and those of the density, viscosity and yield stress variations.

Rapid flows of water-sediment mixtures are probably the most challenging and unknown geophysical gravity-driven processes. The fluidized material in motion consists of a mixture of water and multiple solid phases with different specific characteristics. Modeling sediment transport involves an increasing complexity due to the variable bulk properties in the sediment-water mixture, the coupling of physical processes, and the presence of multiple layer phenomena. Two-dimensional shallow-type mathematical models are built in the context of free surface flows and are applicable to most of these geophysical surface processes. Their numerical solution in the finite volume framework is governed by the dynamical properties of the equations, the coupling between flow variables and the computational grid. The complexity of the numerical resolution of these highly unsteady flows and the computational cost of simulation tools increase considerably with the refinement of the non-structured spatial discretization, so that the computational effort required is one of the biggest challenges for the application of depth-averaged 2D models to large-scale long-term flows. Throughout this chapter, the combination of 2D mathematical models, robust numerical methods, and efficient computing kernels is addressed to develop Efficient Simulation Tools (EST’s) for environmental surface processes involving sediment transport with realistic temporal and spatial scales.

A Finite Volume (FV) numerical scheme previously designed for the hydrostatic Shallow Water Equations (SWE) is extended to compute non-hydrostatic pressure (NHP) in order to simulate dispersive waves. These waves are usually generated by landslides and are of importance in coastal alarm systems. The model is validated in 1D comparing with laboratory measurements and the results highlight the importance of including the NHP terms in the model to achieve a good agreement between numerical and experimental results.

The numerical resolution of shallow water equations (SWE) is required in many environmental problems involving free surface flow. Reduced-order models (ROMs) based on the POD allow such problems to be solved more efficiently in terms of computational cost without losing accuracy, as discussed in this work.

Elastic vessels like arteries and specially veins are prone to sharp changes in their area or external pressure. These phenomena create discontinuities due to a sudden jump on mechanical properties, which is a challenge when trying to simulate unsteady blood flow circulation. This work compares numerical methods to face this challenge in the context of a finite volume model.

15 figures, 2 tables., In this study, a 2D shallow water flow solver integrated with a water quality model is presented. The interaction between the main water quality constituents included is based on the Water Quality Analysis Simulation Program. Efficiency is achieved by computing with a combination of a Central Processing Unit (CPU) and a Graphics Processing Unit (GPU) device. This technique is intended to provide robust and accurate simulations with high computation speedups with respect to a single-core CPU in real events. The proposed numerical model is evaluated in cases that include the transport and reaction of water quality components over irregular bed topography and dry–wet fronts, verifying that the numerical solution in these situations conserves the required properties (C-property and positivity). The model can operate in any steady or unsteady form allowing an efficient assessment of the environmental impact of water flows. The field data from an unsteady river reach test case are used to show that the model is capable of predicting the measured temporal distribution of dissolved oxygen and water temperature, proving the robustness and computational efficiency of the model, even in the presence of noisy signals such as wind speed., This work was funded by the Spanish Ministry of Science and Innovation under the research project PGC2018-094341-B-I00. Additionally, Mario Morales-Hernández was partially supported by the U.S. Air Force Numerical Weather Modeling Program.

15 figures, 1 table., Coupled 1D2D models emerged as an efficient solution for a two-dimensional (2D) representation of the floodplain combined with a fast one-dimensional (1D) schematization of the main channel. At the same time, high-performance computing (HPC) has appeared as an efficient tool for model acceleration. In this work, a previously validated 1D2D Central Processing Unit (CPU) model is combined with an HPC technique for fast and accurate flood simulation. Due to the speed of 1D schemes, a hybrid CPU/GPU model that runs the 1D main channel on CPU and accelerates the 2D floodplain with a Graphics Processing Unit (GPU) is presented. Since the data transfer between sub-domains and devices (CPU/GPU) may be the main potential drawback of this architecture, the test cases are selected to carry out a careful time analysis. The results reveal the speed-up dependency on the 2D mesh, the event to be solved and the 1D discretization of the main channel. Additionally, special attention must be paid to the time step size computation shared between sub-models. In spite of the use of a hybrid CPU/GPU implementation, high speed-ups are accomplished in some cases., This work is part of the PGC2018-094341-B-I00 research project funded by the Ministry of Science and Innovation/FEDER. Additionally, Mario Morales-Hernández was partially supported by the U.S. Air Force Numerical Weather Modeling Program.

High order methods are becoming increasingly popular in shallow water flow modeling motivated by their high computational efficiency (i.e. the ratio between accuracy and computational cost). In particular, Discontinuous Galerkin (DG) schemes are very well suited for the resolution of the shallow water equations (SWE) and related models, being a competitive alternative to the traditional finite volume schemes. In this work, a novel framework for the construction of DG schemes using augmented Riemann solvers is proposed. Such solvers incorporate the source term at cell interfaces in the definition of the Riemann problem, allowing definition of two different inner states in the so-called star region. The benefits of this family of solvers lie in the exact preservation of the Rankine–Hugoniot condition at cell interfaces at the discrete level, ensuring the preservation of equilibrium solutions (i.e. the well-balanced property) without requiring extra corrections of the numerical fluxes. The semi-discrete DG operator becomes nil automatically under equilibrium conditions, provided the use of suitable quadrature rules. The proposed scheme is applied to the Burgers' equation with geometric source term and to the SWE. The numerical results evidence that the proposed scheme achieves the prescribed convergence rates and preserves the equilibrium states of relevance with machine precision.

10 figures, 3 tables., One of the reasons for the limited applicability of predictive water quality models is the lack of data from monitoring control stations that are required as input. In this context, the main novelty of the present work is the recovery of information on the state variables present in a water quality model through measured data at a target downstream location. The reconstruction of the upstream boundary condition is the goal of the present work. For this purpose, an adjoint-state method is developed to find the sensitivities of the functional with respect to variations on the upstream boundary conditions of the model. The resolution of both forward and backward problems ensures strong, accurate and reliable solutions in both steady state and unsteady scenarios. The different cases demonstrate that the method is able to reconstruct any observed distribution with little computational effort, including the heat balance with all its external inputs., This work is part of the PGC2018-094341-B-I00 research project funded by the Ministry of Science and Innovation/FEDER. Additionally, Mario Morales-Hernández was partially supported by the U.S. Air Force Numerical Weather Modeling Program.

Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for river and channel flows. Taking into account that most channels and rivers include junctions with other branches, the objective of this study is to explore the adjoint technique on a channel network to reconstruct the upstream boundary condition of the convection-reaction equation. For this purpose, the one-dimensional shallow water equations and the transport equation for a reactive solute are considered. The control is formulated through the gradient-descent technique supplied with a first-order iterative process. Both the physical and the adjoint equations are supplied with suitable internal boundary conditions at the junction and are numerically solved using a finite volume upwind scheme. The results reveal that the adjoint technique is capable of reconstructing the inlet solute concentration boundary condition in an acceptable number of iterations for both steady state and transient configurations using a downstream measurement location. It was also observed that the reconstruction of the boundary condition tends to be less effective the further away the measurement station is from the target.

A Laser Profilometry Technique was upgraded to detect underwater bed level evolution with a laser and a single camera for highly transient laboratory experiments. While being very simple, the proposed procedure achieves a similar performance as that met by more complex and expensive methods. This technique was applied to a dam-break test case over a mobile bed in a channel with a 90° bend, for which water and bed levels were both continuously recorded at five different places. Photogrammetry was then used to reconstruct the final topography, whose main features could be explained thanks to the analysis of only a few linear bed profiles appropriately chosen. This cheap, simple, flexible and yet accurate method thus proves to be an interesting alternative to more complex methods for morphodynamics investigations in the case of fast transient flows.

In this work, a one-dimensional (1D) finite volume numerical model for the unsteady simulation of the flow hydrodynamics and water quality is developed. The water dynamics is formulated with the 1D shallow water equations, and the water quality evolution is described by the Water Quality Analysis Simulation Program (WASP) model, allowing us to interpret and predict the transport and fate of various biochemical substances along any river reach. This combined system is solved with an explicit finite volume scheme based on Roe's linearization for the advection component of both the flow and the solute transport equations. The proposed model is able to consider temporal variations in tributaries and abstractions occurring in the river basin. This feature is transcendent in order to predict the chemical composition of natural water bodies during winter and summer periods, leading to an improvement in the agreement between computed and observed water quality evolutions. The combined model has been evaluated using literature tests in a steady state and a real-field case of the Ebro river (Spain), characterized by a marked unsteady regime. In the real case, we found that the water temperature was very sensitive to both the solar radiation and the average air temperature, requiring a careful calibration of these parameters. The numerical results are also demonstrated to be reasonably accurate, conservative and robust in real-scale field cases, showing that the model is able to predict the evolution of quality parameters as well as hydrodynamic variables in complex scenarios.

A novel implementation of the reduced-order model (ROM) of 1D advection-diffusion equation by means of a modified Proper Orthogonal Decomposition (POD) method is presented. This modified method is based on a coordinate transformation (CT-POD) that allows prediction beyond a training time horizon for advection dominated equations.

A one-dimensional (1D) numerical model for the simulation of oil spills in coastal flows is studied. A two-layer eulerian model is implemented. The main advantage of this model is the capability of solving the evolution of the oil layer, computing the oil depth and the velocity field.

Finite-depth sediment layers are common in natural water bodies. The presence of underlying bedrock strata covered by erodible bed layers is ubiquitous in rivers and estuaries. In the last years, the development of models based on the non-capacity sediment transport assumption, also called non-equilibrium assumption, has offered a new theoretical background to deal with complex non-erodible bed configurations and the associated numerical problems. Bedload non-capacity sediment transport models consider that the actual solid transport state can be different from the equilibrium state and depending on the temporal evolution of the flow. The treatment of finite-depth erodible bed layers, i.e. partially erodible beds, in bedload models based on the equilibrium approach has usually been made using numerical fixes, which correct the unphysical results obtained in some cases. Generally, the presence of a finite-depth erodible layer implies the introduction of a kind of non-equilibrium condition in the bedload transport state. Nevertheless, this common natural bed configuration has not been previously considered in the development of numerical models. In this work, a finite volume model (FVM) for bedload transport based on non-capacity approach and dealing with finite-depth erodible layers is proposed. New expressions for the actual bedload transport rate and the net exchange flux through the static-moving bed layers interface are used to develop a numerical scheme which solves the coupled shallow water and non-capacity bedload transport system of equations. The reconstruction of the intermediate states for the local Riemann problem at each intercell edge is designed to correctly model the presence of non-erodible strata, avoiding the appearance of unphysical results in the approximate solution without reducing the time step. The new coupled scheme is tested against laboratory benchmarking experiments in order to demonstrate its stability and accuracy, pointing out the properties of both equilibrium and non-equilibrium formulations., This work was partially funded by the MINECO/FEDER under research project CGL2015-66114-R and by Diputacion General de Aragon, DGA, through Fondo Europeo de Desarrollo Regional, FEDER.

En las últimas décadas, la simulación de diferentes procesos hidráulicos/hidrológicos ha constituido una herramienta de gran utilidad tanto en la prevención de riesgos como en la gestión de sus consecuencias. La predicción de caudales, calados y manchas de inundación para distintos episodios de ondas de avenida permite valorar la situación con antelación y proporciona información útil a la hora de tomar medidas de contención como, por ejemplo, la colocación óptima de diques para evitar o paliar daños. En este trabajo, se describe la aplicación de un modelo distribuido de simulación hidráulica basado en las ecuaciones 2D de aguas poco profundas a la simulación de ondas de avenida en un tramo urbano del río Ginel (Fuentes de Ebro). Mediante este modelo, se pueden obtener resultados de calado de agua y velocidad en cualquier punto del dominio de cálculo. El código está diseñado para aprovechar la potencia de las tarjetas gráficas (GPU) de última generación, proporcionando una simulación ágil y precisa y constituya el motor de cálculo del programa RiverFlow2D. Los resultados obtenidos permiten valorar las consecuencias de varias riadas con períodos de retorno de hasta 500 años.

In the past decade, shallow water solvers have dramatically improved both in terms of accuracy and computational power. New mathematical models and numerical schemes have been systematically verified against 1D exact solutions and laboratory experiments. Despite the two-dimensional nature of some of these benchmark tests, none of them reports complete 2D water depth fields, but only a few profiles are measured and reported in the best case. This work reports a new benchmarking dataset for validation of shallow water solvers, in which two-dimensional transient water depth measurements are available for complex steady and transient laboratory flume experiments, ranging from transcritical steady flow to dam-break flows around obstacles and complex beds. The transient water surface was measured using a commercial-grade RGB-D sensing device which allows to capture a succession of color-coded point clouds at a high frequency. These experimental measurements are compared with 2D shallow water simulations carried out with an extensively tested finite volume solver. Results asses the suitability of this dataset to perform as benchmark tests, identifying potential limitations of current and future models.

Numerical simulation of flows that consider interaction between overland and drainage networks has become a practical tool to prevent and mitigate flood situations in urban environments, especially when dealing with intense storm events, where the limited capacity of the sewer systems can be a trigger for flooding. Additionally, in order to prevent any kind of pollutant dispersion through the drainage network, it is very interesting to have a certain monitorization or control over the quality of the water that flows in both domains. In this sense, the addition of a pollutant transport component to both surface and sewer hydraulic models would benefit the global analysis of the combined water flow. On the other hand, when considering a realistic large domain with complex topography or streets structure, a fine spatial discretization is mandatory. Hence the number of grid cells is usually very large and, therefore, it is necessary to use parallelization techniques for the calculation, the use of Graphic Processing Units (GPU) being one of the most efficient due to the leveraging of thousands of processors within a single device. In this work, an efficient GPU-based 2D shallow water flow solver (RiverFlow2D-GPU) is fully coupled with EPA’s Storm Water Management Model (SWMM). Both models are able to develop a transient water quality analysis taking into account several pollutants. The coupled model, referred to as RiverFlow2D-GPU UD (Urban Drainge) is applied to three real-world cases, covering the most common hydraulic situations in urban hydrology/hydraulics. A UK Environmental Agency test case is used as model validation, showing a good agreement between RiverFlow2D-GPU UD and the rest of the numerical models considered. The efficiency of the model is proven in two more complex domains, leading to a &gt, 100x faster simulations compared with the traditional CPU computation.

19 figures, 3 tables.-- © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/, Steady shallow flows past an open channel lateral cavity can induce the excitation of an eigenmode of a gravity standing wave inside the cavity, called seiche, which may be coupled with the shedding of vortices at the opening of the cavity. The presence of the seiche is of fundamental interest as it enhances the mass exchange between the main channel and the cavity. Measurements of the time evolution of the water surface are not often found in the literature for this type of flows. In this work, an experimental and numerical study of a shallow flow past a channel lateral cavity is carried out. The main novelty is the use of a pioneering non-intrusive experimental technique to measure the water surface at the channel-cavity region. This optical technique offers high resolution 2D data in time and space of the water surface evolution, allowing to determine the relevant features of the seiche oscillation. Such data are supplemented with Particle Image Velocimetry measurements. Furthermore, the experiments are numerically reproduced using a high-resolution depth-averaged URANS shallow water model, under the assumption that shallow water turbulence is mainly horizontal. The experimental and numerical results are analyzed in the frequency domain. High-resolution two-dimensional amplitude oscillation maps of the seiche phenomenon, as well as velocity fields, are presented. The high quality of the experimental data reported in this work makes this data set a suitable benchmark for numerical simulation models in order to evaluate their performance in the resolution of turbulent resonant shallow flows., This work was funded by the Spanish Ministry of Science and Innovation under the research project PGC2018-094341-B-I00 (Navas-Montilla, Martínez-Aranda, García-Palacín and García-Navarro). This work has also been partially funded by Gobierno de Aragón through Fondo Social Europeo: Feder 20142020 “Construyendo Europa desde Aragón”. Navas-Montilla, Martínez-Aranda, García-Palacín and García-Navarro acknowledge the support of the Regional Government of Aragón to the Computational Fluid Mechanics Group (T32_20R). A. Lozano acknowledges the support of the Regional Government of Aragón to the Fluid Mechanics for a Clean Energy Research Group (T01-17R).

25 figures.-- Supplementary information available., An important feature of the two-layer shallow flow model is that the resulting system of equations cannot be expressed in conservation-law form. Here, the HLLS and ARoe solvers, derived initially for systems of conservation laws, are reformulated and applied to the two-layer shallow flows in a great variety of problems. Their resulting extension and combination allows us to overcome the loss of the hyperbolic character, ensuring energy or exactly balanced property, guarantees positivity of the solution, and provides a correct drying/wetting advance front without requiring tuning parameters. As a result, in those cases where the rich description of internal and external waves cannot be provided by the ARoe solver, HLLS is applied. Variable density is considered in each layer as a result of a bulk density driven by the mixture of different constituents. A wide variety of test cases is presented confirming the properties of this combination, including exactly balanced scenarios in subcritical and subcritical-transcritical scenarios, dam-break problems over bed variations and wet/dry fronts, non-hyperbolic conditions, transcritical exchange flow with loss of hyperbolicity. Despite the complexity of the test cases presented here, accurate and stable simulations are guaranteed, ensuring positivity of the solution without decreasing the time step., This work was funded by the Spanish Ministry of Science and Innovation under the research project PGC2018-094341-B-I00. This work has also been partially funded by Gobierno de Aragón through Fondo Social Europeo: Feder 2014–2020 Construyendo Europa desde Aragón.

32 figures, 7 tables., Culverts allow roads to safely traverse small streams or drainage ditches, and their proper design is critical to ensure a safe and reliable transportation network. A correct modelization of these hydraulic structures becomes crucial in the assessment of flood footprints or discharge peak estimation in a risk evaluation plan. The question of how to include culverts comes up frequently when assembling a hydraulic model that requires the presence of as many singular elements as possible. In this work, three different culvert integrations with the surface domain are studied and compared in the context of a 2D shallow water (SW) model. All of them are based on the Federal Highway Administration (FHWA) formulation for the culvert discharge estimation but differ in complexity and in the interaction with the numerical model for surface flow, some of them as internal boundary conditions. Several steady and unsteady validation test cases are presented and the numerical results are compared with the predictions from HEC-RAS 1D and HY-8 software. The culvert area, shape and their sensitivity to the 2D computational mesh is also analyzed., The present work was partially funded by the Aragón Government through the Fondo Social Europeo. It has also been supported by the Research Project PGC2018-094341-B-I00 funded by the Spanish Ministry of Science, Innovation and Universities (MICINN). Additionally, Mario Morales-Hernández was partially supported by the U.S. Air Force Numerical Weather Modeling Program.

15 figure, 3 tables., In this work, a novel 2D depth-integrated numerical model for highly sediment-laden shallow flows over non-uniform erodible beds is presented, including variable density and exchange between the bed layer and the water–sediment mixture flow. The system of equations is formed by the 2D conservation equations for the mass and momentum of the mixture, the mass conservation equation for the different sediment size-classes transported in the flow and the bed evolution equation. The depth-averaged mixture density varies according to the volumetric concentration of the different sediment size-classes that can be incorporated from the bed to the flow and transported as suspended materials. The rheological behaviour of the flow is directly controlled by the properties of the mixture. A new x-split augmented Roe (xA-Roe) scheme is derived to solve the coupled flow and suspended solid-phase equations in both structured and unstructured meshes. The numerical scheme is defined to properly include density variations and momentum source terms, retaining a well-balanced flux formulation in steady states and the correct treatment of the wet–dry fronts. The numerical scheme is assessed with steady and transient cases involving highly sediment-laden flows, demonstrating its accuracy, stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes., This work was partially funded by the MINECO/FEDER under research project PGC2018-094341-B-I00 and by Diputacion General de Aragon, DGA, through Fondo Europeo de Desarrollo Regional, FEDER.

20 figures, 3 tables., The two-layer problem is defined as the coexistence of two immiscible fluids, separated by an interface surface. Under the shallow-flow hypothesis, 1D models are based on a four equations system accounting for the mass and momentum conservation in each fluid layer. Mathematically, the system of conservation laws modelling 1D two-layer flows has the important drawback of loss of hyperbolicity, causing that numerical schemes based on the eigenvalues of the Jacobian become unstable. In this work, well-balanced FORCE scheme is proposed for 1D two-layer shallow flows. The FORCE scheme combines the first-order Lax–Friedrichs flux and the second-order Lax–Wendroff flux. The scheme is supplemented with a hydrostatic reconstruction procedure in order to ensure the well-balanced behaviour of the model for steady flows even under wet–dry conditions. Additionally, a method to obtain high-accuracy numerical solutions for two-layer steady flows including friction dissipation is proposed to design reference benchmark tests for model validation. The enhanced FORCE scheme is faced to lake-at-rest benchmarking tests and steady flow cases including friction, demonstrating its well-balanced character. Furthermore, the numerical results obtained for highly unsteady two-layer dambreaks are used to analyse the robustness and accuracy of the model under a wide range of flow conditions., This work was developed under a CSIC-JAE grant in the framework of the project PGC2018-094341-B-I00, which is funded by MINECO/FEDER and by Diputacion General de Aragon, DGA, through Fondo Europeo de Desarrollo Regional, FEDER.

In this work, numerical solvers based on extensions of the Roe and HLL schemes are adapted to deal with test cases involving extreme collapsing conditions in elastic vessels. To achieve this goal, the system is transformed to provide a conservation–law form, allowing to define Rankine–Hugoniot conditions. The approximate solvers allow to describe the inner states of the solution. Therefore, source term fixes can be used to prevent unphysical values of vessel area and, at the same time, the eigenvalues of the system control stability. Numerical solvers of different order are tested using a wide variety of Riemann problems, including extreme vessel collapse and blockage. In all cases, the robustness of the approximate solvers presented here is checked using first and third order methods in time and space, using the WENO reconstruction scheme in combination with the TVDRK3 method., This project has been funded with support from the Dextera A.S. company.

The study of resonant shallow flows past a lateral cavity is of great relevance due to their interest in civil and environmental engineering [1]. Such flows exhibit the presence of a standing gravity wave, called seiche, which is coupled with the shedding of vortices at the opening of the cavity. A complete understanding of such phenomenon is necessary as it may determine the mass exchange between the main channel and the cavity [2]. A better insight into this phenomenon helps to improve the design and implementation of innovative river bank restoration techniques. An experimental study of the resonant flow in a laboratory flume with a single lateral cavity is herein presented. Five different flow configurations at a fixed Froude number (Fr=0.8) are considered. The main novelty of the present work is the use of a pioneering non-intrusive experimental technique [3] to measure the water surface at the channel-cavity region. This optical technique offers high resolution 2D data in time and space of the water surface evolution, allowing to determine the relevant features of the seiche oscillation, i.e. spatial distribution of oscillation nodes and anti-nodes, oscillation modes and amplitude of the oscillation. Such data are supplemented with Particle Image Velocimetry measurements to perform a more detailed study of the resonance phenomenon. High-resolution two-dimensional amplitude oscillation maps of the seiche phenomenon are presented for the experimental water depth. Experimental velocity fields inside the cavity are presented and confirm the inherent coupling between the unstable shear layer at the opening of the cavity and the gravity standing wave. The high quality of the experimental data reported in this work makes this data set a suitable benchmark for numerical simulation models in order to evaluate their performance in the resolution of turbulent resonant shallow flows.[1] C. Juez, M. Thalmann, A. J. Schleiss & M. J. Franca, Morphological resilience to flow fluctuations of fine sediment deposits in bank lateral cavities, Advances in Water Resources, 115 (2018) 44-59.[2] I. Kimura & T. Hosoda, Fundamental properties of flows in open channels with dead zone, Journal of Hydraulic Engineering 123 (1997) 98-107.[3] S. Martínez-Aranda, J. Fernández-Pato, D. Caviedes-Voullième, I. García-Palacín & P. García-Navarro, Towards transient experimental water surfaces: a new benchmark dataset for 2D shallow water solvers, Advances in water resources, 121 (2018) 130-149.

Steady shallow flows past an open channel lateral cavity have been widely studied in the last years due to their engineering and environmental relevance, e.g. for river restoration purposes [1]. Such flows can induce the excitation of an eigenmode of a gravity standing wave inside the cavity, called seiche, which may be coupled with the shedding of vortices at the opening of the cavity. A complete understanding of such phenomenon is necessary as it may determine the mass exchange between the main channel and the cavity [2]. A numerical study of the resonant flow in a channel with a single lateral cavity is herein presented. Five different flow configurations at a fixed Froude number (Fr=0.8), measured in the laboratory [3], are used as a benchmark. Such experiments are reproduced using a high-order 2D depth-averaged URANS model based on the shallow water equations, assuming that shallow water turbulence is mainly horizontal [4]. The large-scale horizontal vortices are resolved by the model, whereas the effect of the small-scale turbulence is accounted for by means of a turbulence model. Water surface elevation and velocity measurements are used for comparison with the numerical results. A detailed comparison of the seiche amplitude distribution in the cavity-channel area is presented, showing a good agreement between the numerical results and the observations. Frequency analysis techniques are used to extract the relevant features of the flow. It is evidenced that the proposed model is able to reproduce the observed spatial distribution of oscillation nodes and anti-nodes, as well as the time-averaged flow field. The coupling mechanism between the gravity wave inside the cavity and the unstable shear layer at the opening of the cavity is also accurately captured. [1] C. Juez, M. Thalmann, A. J. Schleiss & M. J. Franca, Morphological resilience to flow fluctuations of fine sediment deposits in bank lateral cavities, Advances in Water Resources, 115 (2018) 44-59.[2] I. Kimura & T. Hosoda, Fundamental properties of flows in open channels with dead zone, Journal of Hydraulic Engineering 123 (1997) 98-107.[3] S. Martínez-Aranda, J. Fernández-Pato, D. Caviedes-Voullième, I. García-Palacín & P. García-Navarro, Towards transient experimental water surfaces: a new benchmark dataset for 2D shallow water solvers, Advances in water resources, 121 (2018) 130-149.[4] A. Navas-Montilla, C. Juez, M.J. Franca & J. Murillo, Depth-averaged unsteady RANS simulation of resonant shallow flows in lateral cavities using augmented WENO-ADER schemes, Journal of Computational Physics, 24 (2019) 203-217.