scholarly journals A numerical shallow-water model for gravity currents for a wide range of density differences

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Hiroyuki A. Shimizu ◽  
Takehiro Koyaguchi ◽  
Yujiro J. Suzuki
Keyword(s):  
Shallow Water ◽  
Gravity Currents ◽  
Water Model ◽  
Shallow Water Model ◽  
Wide Range

scholarly journals A Shallow Water Model for Convective Self-Aggregation

2020 ◽  
Author(s):  
Da Yang
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Wave Pattern ◽  
Water Model ◽  
Shallow Water Model ◽  
Modeling Framework ◽  
Convective Storms ◽  
Wide Range ◽  
Self Aggregation

AbstractRandomly distributed convective storms can self-aggregate in the absence of large-scale forcings. Here we present a 1D shallow water model to study the convective self-aggregation. This model simulates the dynamics of the planetary boundary layer and represents convection as a triggered process. Once triggered, convection lasts for finite time and occupies finite length. We show that the model can successfully simulate self-aggregation, and that the results are robust to a wide range of parameter values. In the simulations, convection excites gravity waves. The gravity waves then form a standing wave pattern, separating the domain into convectively active and inactive regions. We analyze the available potential energy (APE) budget and show that convection generates APE, providing energy for self-aggregation. By performing dimensional analysis, we develop a scaling theory for the size of convective aggregation, which is set by the gravity wave speed, damping timescale, and number density of convective storms. This paper provides a simple modeling framework to further study convective self-aggregation.

A two-layer, shallow-water model for 3D gravity currents

2012 ◽  
Vol 50 (2) ◽  
pp. 208-217 ◽  
Author(s):  
Michele La Rocca ◽  
Claudia Adduce ◽  
Giampiero Sciortino ◽  
Allen Bateman Pinzon ◽  
Maria Antonietta Boniforti
Keyword(s):  
Shallow Water ◽  
Gravity Currents ◽  
Water Model ◽  
Shallow Water Model ◽  
3D Gravity

Centrifugal, barotropic and baroclinic instabilities of isolated ageostrophic anticyclones in the two-layer rotating shallow water model and their nonlinear saturation

2014 ◽  
Vol 762 ◽  
pp. 5-34 ◽  
Author(s):  
Noé Lahaye ◽  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Initial Conditions ◽  
Vertical Shear ◽  
Water Model ◽  
Shallow Water Model ◽  
Nonlinear Saturation ◽  
Centrifugal Instability ◽  
Wide Range ◽  
Nonlinear Mechanism ◽  
Rotating Shallow Water

AbstractInstabilities of isolated anticyclonic vortices in the two-layer rotating shallow water model are studied at Rossby numbers up to two, with the main goal to understand the interplay between the classical centrifugal instability and other ageostrophic instabilities. We find that different types of instabilities with low azimuthal wavenumbers exist, and may compete. In a wide range of parameters, an asymmetric version of the standard centrifugal instability has larger growth rate than the latter. The dependence of the instabilities on the parameters of the flow, i.e. Rossby and Burger numbers, vertical shear and the ratios of the layers’ thicknesses and densities, is investigated. The zones of dominance of each instability are determined in the parameter space. Nonlinear saturation of these instabilities is then studied with the help of a high-resolution finite-volume numerical scheme, by using the unstable modes identified from the linear stability analysis as initial conditions. Differences in nonlinear development of the competing centrifugal and ageostrophic barotropic instabilities are evidenced. A nonlinear mechanism of axial symmetry breaking during the saturation of the centrifugal instability is displayed.

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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