scholarly journals Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs

2019 ◽  
Vol 67 (4) ◽  
pp. 322-328 ◽  
Author(s):  
Jaromír Říha ◽  
David Duchan ◽  
Zbyněk Zachoval ◽  
Sébastien Erpicum ◽  
Pierre Archambeau ◽  
...  
Keyword(s):  
Shallow Water ◽  
Flow Direction ◽  
Near Field ◽  
Water Model ◽  
Shallow Water Model ◽  
Study Results ◽  
Trapezoidal Profile ◽  
Shallow Water Models ◽  
The Difference ◽  
Flow Configurations

Abstract Shallow-water models are standard for simulating flow in river systems during floods, including in the near-field of sudden changes in the topography, where vertical flow contraction occurs such as in case of channel overbanking, side spillways or levee overtopping. In the case of stagnant inundation and for frontal flow, the flow configurations are close to the flow over a broad-crested weir with the trapezoidal profile in the flow direction (i.e. inclined upstream and downstream slopes). In this study, results of shallow-water numerical modelling were compared with seven sets of previous experimental observations of flow over a frontal broad-crested weir, to assess the effect of vertical contraction and surface roughness on the accuracy of the computational results. Three different upstream slopes of the broad-crested weir (V:H = 1:Z1 = 1:1, 1:2, 1:3) and three roughness scenarios were tested. The results indicate that, for smooth surface, numerical simulations overestimate by about 2 to 5% the weir discharge coefficient. In case of a rough surface, the difference between computations and observations reach up to 10%, for high relative roughness. When taking into account mentioned the differences, the shallow-water model may be applied for a range of engineering purposes.

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals Controlling the Computational Modes of the Arbitrarily Structured C Grid

2012 ◽  
Vol 140 (10) ◽  
pp. 3220-3234 ◽  
Author(s):  
Hilary Weller
Keyword(s):  
Shallow Water ◽  
Flow Direction ◽  
Water Model ◽  
Test Cases ◽  
Continuous Linear ◽  
Shallow Water Model ◽  
Advection Schemes ◽  
Water Test ◽  
Better Than ◽  
Potential Enstrophy

Abstract The arbitrarily structured C grid, Thuburn–Ringler–Skamarock–Klemp (TRiSK), is being used in the Model for Prediction Across Scales (MPAS) and is being considered by the Met Office for their next dynamical core. However, the hexagonal C grid supports a branch of spurious Rossby modes, which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilized transport (CLUST), a blend between centered and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed that gives further discrimination between schemes than using potential enstrophy alone. Indeed, some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude–longitude grids of the sphere for various shallow-water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result, TRiSK appears to perform better than a spectral shallow-water model.

Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Variational Principles ◽  
Mean Field ◽  
Tangent Plane ◽  
Primitive Equations ◽  
Water Model ◽  
Shallow Water Model ◽  
Shallow Water Models ◽  
Rotating Shallow Water

In this chapter, one- and two-layer versions of the rotating shallow-water model on the tangent plane to the rotating, and on the whole rotating sphere, are derived from primitive equations by vertical averaging and columnar motion (mean-field) hypothesis. Main properties of the models including conservation laws and wave-vortex dichotomy are established. Potential vorticity conservation is derived, and the properties of inertia–gravity waves are exhibited. The model is then reformulated in Lagrangian coordinates, variational principles for its one- and two-layer version are established, and conservation laws are reinterpreted in these terms.

CONSERVATION LAWS FOR ONE-DIMENSIONAL SHALLOW WATER MODELS FOR ONE AND TWO-LAYER FLOWS

2006 ◽  
Vol 16 (01) ◽  
pp. 119-137 ◽  
Author(s):  
RICARDO BARROS
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Shallow Water Model ◽  
Frobenius Problem ◽  
One Dimensional ◽  
Shallow Water Models ◽  
The One ◽  
Open Question

A full set of conservation laws for the two-layer shallow water equations is presented for the one-dimensional case. We prove that all the conservation laws are linear combination of the equations for the conservation of mass and velocity (in each layer), total momentum and total energy.This result generalizes that of Montgomery and Moodie that found the same conserved quantities by restricting their search to the multinomials expressions in the layer variables. Though the question of whether or not there are only a finite number of these quantities is left as an open question by the authors. Our work puts an end to this: in fact, no more conservation laws are admitted for the two-layer shallow water equations. The key mathematical ingredient of the method proposed leading to the result is the Frobenius problem. Moreover, we present a full set of conservation laws for the classical one-dimensional shallow water model with topography, by using the same techniques.

Shallow-water analysis of gravity-current flows past isolated obstacles

2009 ◽  
Vol 635 ◽  
pp. 415-438 ◽  
Author(s):  
E. GONZALEZ-JUEZ ◽  
E. MEIBURG
Keyword(s):  
Shallow Water ◽  
Gravity Current ◽  
Water Model ◽  
Shallow Water Model ◽  
Shallow Water Theory ◽  
Front Speed ◽  
Model Predictions ◽  
Shallow Water Models ◽  
Simulation Results ◽  
Current Flows

The flow of a partial-depth lock-exchange gravity current past an isolated bottom-mounted obstacle is studied by means of two-dimensional direct numerical simulations and steady shallow-water theory. The simulations indicate that the flux of the current downstream of the obstacle is approximately constant in space and time. This information is employed to extend the shallow-water models of Rottman et al. (J. Hazard. Mater., vol. 11, 1985, pp. 325–340) and Lane-Serff, Beal & Hadfield (J. Fluid Mech., vol. 292, 1995, pp. 39–53), in order to predict the height and front speed of the downstream current as functions of the upstream Froude number and the ratio of obstacle to current height. The model predictions are found to agree closely with the simulation results. In addition, the shallow-water model provides an estimate for the maximum drag that lies within 10% of the simulation results for obstacles much larger than the boundary-layer thickness.

scholarly journals Towards district scale flood simulations using conventional and anisotropic porosity shallow water models with high-resolution topographic information

2018 ◽  
pp. 90-98
Author(s):  
Ilhan Özgen ◽  
Morgan Abily ◽  
Jiaheng Zhao ◽  
Dongfang Liang ◽  
Philippe Gourbesville ◽  
...  
Keyword(s):  
High Resolution ◽  
Shallow Water ◽  
Large Deviation ◽  
Computational Cost ◽  
Water Model ◽  
Shallow Water Model ◽  
Data Set ◽  
Shallow Water Models ◽  
Urban Catchments ◽  
Water Models

Current topographic survey technology provides high-resolution (HR) datasets for urban environments. Incorporating this HR information in models aiming to provide flood risk assessment is desirable because the flood wave propagation is depending on the urban topographic features, i.e. buildings, bridges and street networks. Conceptual, numerical and practical challenges arise from the application of shallow water models to HR urban flood modeling. For instance, numerical challenges are occurrence of wet-dry fronts, geometric discontinuities in the urban environment and discontinuous solutions, i.e. shock waves. These challenges can be overcome by using a Godunov-type scheme. However, the computational cost of this type of schemes is high, such that HR two-dimensional shallow water simulations with practical relevance have to be run on supercomputers. The porous shallow water model is an alternative approach that aims to reduce computational cost by using a coarse resolution and accounting for unresolved processes by means of the porosity terms. Usually, a speedup between two and three orders of magnitude in comparison to HR simulations can be obtained. This study reports preliminary results of a practical test case concerning pluvial flooding in a district of the city of Nice, France, caused by the intense rainfall event on October 3rd, 2015. HR topography data set on a 1 m resolution is available for the district, whereby street features of infra-metric dimensions have been included. A reference solution is calculated by a HR shallow water model on a 1 m by 1 m structured computational grid. The porous shallow water model is run on a 10 m by 10 m grid and the influence of the drag source term is studied. The model results show a large deviation, which is caused by the poor meshing strategy of the porous shallow water (AP) model. The study also summarizes practical challenges that arise during the application of the AP and HR models to a large urban catchment. The main difficulty is to obtain a good mesh. In smaller scale investigations, the mesh is currently constructed by hand such that the cell edges align with buildings. This approach is not feasible for large scale urban catchments with a large number of buildings. Future steps that have to be taken, such as a strategy for automatic mesh generation, are reported on.

scholarly journals A Grid Convergence Study for the Integral Porosity Shallow Water Model on Unstructured Triangular Meshes

10.29007/mspj ◽  
2018 ◽  
Author(s):  
Ilhan Özgen-Xian ◽  
Dongfang Liang ◽  
Reinhard Hinkelmann
Keyword(s):  
Shallow Water ◽  
Hydraulic Jump ◽  
Water Model ◽  
Shallow Water Model ◽  
Flow Conditions ◽  
High Frequency Oscillations ◽  
Grid Convergence ◽  
Shallow Water Models ◽  
Convergence Study ◽  
Porosity Model

The integral porosity shallow water model (IP) is a modified form of the depth-averaged shallow water flow model, which utilizes porosities to account for unresolved sub-grid-scale topography such as buildings to enable fast urban flooding simulations. Existing research has repeatedly pointed out that the IP model is inherently oversensitive to the mesh de- sign. This paper presents a detailed grid convergence study of the IP model for simulating a laboratory experiment on the interaction between a dam-break wave and an obstacle in a channel, which is featured by the highly complex non-hydrostatic flow with a backwards- propagating hydraulic jump. We compare three different mesh refinement techniques with up to six levels of refinement: (1) uniform, (2) manual, (3) locally coarsened. For this investigated case, the modeling error due to the shallow water assumptions is more sig- nificant than that due to the porosity treatment. Neither a conventional shallow water model, nor the integral porosity model is able to predict the measured data well owning to non-hydrostatic flow conditions and a backwards propagating hydraulic jump. We show that the integral porosity model results converge to the conventional shallow water model results at locations that are not affected by these non-hydrostatic flow conditions. We conclude that, when the obstacle density is low, high-frequency oscillations may appear in the domain owing to Ka ́rma ́n vortex shedding. These cannot be captured accurately by the integral porosity shallow water model, unless high resolutions similar to those in the conventional shallow water models are used. However, the benefit of the porosity model is lost by using high resolutions.

The instability of vertically curved fronts in a two-layer shallow water model

2020 ◽  
Vol 32 (12) ◽  
pp. 124117
Author(s):  
M. W. Harris ◽  
F. J. Poulin ◽  
K. G. Lamb
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model

scholarly journals Development of a Practical Model for Predicting Soil Salinity in a Salt Marsh in the Arakawa River Estuary

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2054
Author(s):  
Naoki Kuroda ◽  
Katsuhide Yokoyama ◽  
Tadaharu Ishikawa
Keyword(s):  
Salt Marsh ◽  
Hydraulic Conductivity ◽  
Shallow Water ◽  
Soil Salinity ◽  
River Estuary ◽  
Flow Simulation ◽  
Design Tool ◽  
Water Model ◽  
Shallow Water Model ◽  
Practical Model

Our group has studied the spatiotemporal variation of soil and water salinity in an artificial salt marsh along the Arakawa River estuary and developed a practical model for predicting soil salinity. The salinity of the salt marsh and the water level of a nearby channel were measured once a month for 13 consecutive months. The vertical profile of the soil salinity in the salt marsh was measured once monthly over the same period. A numerical flow simulation adopting the shallow water model faithfully reproduced the salinity variation in the salt marsh. Further, we developed a soil salinity model to estimate the soil salinity in a salt marsh in Arakawa River. The vertical distribution of the soil salinity in the salt marsh was uniform and changed at almost the same time. The hydraulic conductivity of the soil, moreover, was high. The uniform distribution of salinity and high hydraulic conductivity could be explained by the vertical and horizontal transport of salinity through channels burrowed in the soil by organisms. By combining the shallow water model and the soil salinity model, the soil salinity of the salt marsh was well reproduced. The above results suggest that a stable brackish ecotone can be created in an artificial salt marsh using our numerical model as a design tool.

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