Understanding the Performance of an Unstructured-Mesh Global Shallow Water Model on Kinetic Energy Spectra and Nonlinear Vorticity Dynamics

Abstract The effects of moisture on the energetics of a statistically stationary, baroclinically unstable jet representing the midlatitude atmosphere are examined using a two-layer, β-plane shallow-water model. Flow is driven by a relaxation of the interface between the two layers to a baroclinically unstable profile. Moisture is input to the lower layer by evaporation. When supersaturation occurs, precipitation is triggered and the related latent heat release drives a mass transfer between the two layers. A comparison between dry and moist reference atmospheres shows that precipitation reduces eddy kinetic energy. This is related to the meridional distribution of precipitation, which occurs on the poleward side of the jet (where the interface field is raised). This latitudinal structure of precipitation is related to a correlation between poleward flow and ascent, which is analyzed using a shallow-water analog to the ω equation. The precipitation effect on the energy budget is predominately due to zonal- and time-averaged terms. Because of this, dry simulations in which the thermal forcing is modified to mimic the effect of zonally averaged precipitation are carried out and compared with their precipitating counterparts. These simulations show a similar reduction of baroclinic eddy kinetic energy; however, the barotropic eddy kinetic energy response shows a larger difference.

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Available Potential Energy in Density Coordinates

Journal of Physical Oceanography ◽

10.1175/jpo-d-17-0272.1 ◽

2018 ◽

Vol 48 (8) ◽

pp. 1867-1883 ◽

Cited By ~ 1

Author(s):

Alain Colin de Verdière ◽

Thierry Huck ◽

Souren Pogossian ◽

Michel Ollitrault

Keyword(s):

Kinetic Energy ◽

Potential Energy ◽

Shallow Water ◽

Ocean Circulation ◽

World Ocean ◽

Water Model ◽

Shallow Water Model ◽

Available Potential Energy ◽

Vertical Displacements ◽

World Ocean Atlas

AbstractThe vertically integrated potential energy of an incompressible stratified fluid formulated in density coordinates can be simply written as a weighted vertical sum of the squares of the vertical displacements of density surfaces, a general expression valid for arbitrary displacements. The sum of this form of potential energy and kinetic energy is then a conserved quantity for the multilayer shallow water model. The formulation in density coordinates is a natural one to find the Lorenz reference state of available potential energy (APE). We describe the method to compute the APE of an ocean state and provide two applications. The first is the classical double-gyre, wind-driven circulation simulated by a shallow water model at high resolution. We show that the eddy kinetic and eddy potential energies are localized in regions of large gradients of mean APE. These large gradients surround an APE minimum found between the two gyres. The second is the time-mean World Ocean Circulation reconstructed from hydrography (World Ocean Atlas) and reference velocities at 1000 db from the Argo float program to obtain an absolute circulation. The total available potential energy exceeds the total mean kinetic energy of the World Ocean by three orders of magnitude, pointing out the very small Burger number of the circulation. The Gulf Stream, the Kuroshio, the Agulhas retroflection, and the confluence regions are four examples that confirm the shallow water model results that large gradients of mean available potential energy can be used as predictors for the presence of high eddy kinetic energy (obtained here from satellite altimetry).

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

Physics of Fluids ◽

10.1063/5.0027831 ◽

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

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Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽

10.3390/w13162152 ◽

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.

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

Water ◽

10.3390/w13152054 ◽

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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Localized vortices in a nonlinear shallow water model: examples and numerical experiments

Journal of Physics Conference Series ◽

10.1088/1742-6596/722/1/012038 ◽

2016 ◽

Vol 722 ◽

pp. 012038

Author(s):

S A Beisel ◽

A A Tolchennikov

Keyword(s):

Shallow Water ◽

Numerical Experiments ◽

Water Model ◽

Shallow Water Model

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Diffusion Experiments with a Global Discontinuous Galerkin Shallow-Water Model

Monthly Weather Review ◽

10.1175/2009mwr2843.1 ◽

2009 ◽

Vol 137 (10) ◽

pp. 3339-3350 ◽

Cited By ~ 25

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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