A shallow water model conserving energy and potential enstrophy in the presence of boundaries

2009 ◽  
Vol 67 (6) ◽  
pp. 779-814 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model ◽  
Potential Enstrophy

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.

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 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 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.

Diffusion Experiments with a Global Discontinuous Galerkin Shallow-Water Model

2009 ◽  
Vol 137 (10) ◽  
pp. 3339-3350 ◽  
Author(s):  
Ramachandran D. Nair
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Water Model ◽  
Order System ◽  
Small Scale ◽  
Shallow Water Model ◽  
First Order ◽  
Advection Diffusion Equation ◽  
Diffusion Scheme ◽  
Cubed Sphere

Abstract A second-order diffusion scheme is developed for the discontinuous Galerkin (DG) global shallow-water model. The shallow-water equations are discretized on the cubed sphere tiled with quadrilateral elements relying on a nonorthogonal curvilinear coordinate system. In the viscous shallow-water model the diffusion terms (viscous fluxes) are approximated with two different approaches: 1) the element-wise localized discretization without considering the interelement contributions and 2) the discretization based on the local discontinuous Galerkin (LDG) method. In the LDG formulation the advection–diffusion equation is solved as a first-order system. All of the curvature terms resulting from the cubed-sphere geometry are incorporated into the first-order system. The effectiveness of each diffusion scheme is studied using the standard shallow-water test cases. The approach of element-wise localized discretization of the diffusion term is easy to implement but found to be less effective, and with relatively high diffusion coefficients, it can adversely affect the solution. The shallow-water tests show that the LDG scheme converges monotonically and that the rate of convergence is dependent on the coefficient of diffusion. Also the LDG scheme successfully eliminates small-scale noise, and the simulated results are smooth and comparable to the reference solution.

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