scholarly journals AN ENERGETICALLY CONSISTENT VISCOUS SEDIMENTATION MODEL

2009 ◽  
Vol 19 (03) ◽  
pp. 477-499 ◽  
Author(s):  
JEAN DE DIEU ZABSONRÉ ◽  
CARINE LUCAS ◽  
ENRIQUE FERNÁNDEZ-NIETO
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Numerical Experiments ◽  
Water System ◽  
Two Dimensional ◽  
Sedimentation Model ◽  
Shallow Water System ◽  
Periodic Domains ◽  
The Stability

In this paper we consider a two-dimensional viscous sedimentation model which is a viscous Shallow–Water system coupled with a diffusive equation that describes the evolution of the bottom. For this model, we prove the stability of weak solutions for periodic domains and give some numerical experiments. We also discuss around various discharge quantity choices.

scholarly journals Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer shallow water system on structured meshes

2013 ◽  
Vol 80 ◽  
pp. 441-452 ◽  
Author(s):  
Marc de la Asunción ◽  
Manuel J. Castro ◽  
E.D. Fernández-Nieto ◽  
José M. Mantas ◽  
Sergio Ortega Acosta ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Two Dimensional ◽  
Shallow Water System ◽  
Structured Meshes ◽  
Gpu Implementation

Equilibrium dynamics in a forced-dissipative f-plane shallow-water system

1994 ◽  
Vol 280 ◽  
pp. 369-394 ◽  
Author(s):  
Li Yuan ◽  
Kevin Hamilton
Keyword(s):  
Energy Spectrum ◽  
Shallow Water ◽  
Gravity Waves ◽  
Water System ◽  
Water Model ◽  
Dimensional System ◽  
Linear Potential ◽  
Two Dimensional ◽  
Equilibrium Dynamics ◽  
Shallow Water System

The equilibrium dynamics in a homogeneous forced-dissipative f-plane shallow-water system is investigated through numerical simulations. In addition to classical two-dimensional turbulence, inertio-gravity waves also exist in this system. The dynamics is examined by decomposing the full flow field into a dynamically balanced potential-vortical component and a residual ‘free’ component. Here the potential-vortical component is defined as part of the flow that satisfies the gradient-wind balance equation and that contains all the linear potential vorticity of the system. The residual component is found to behave very nearly as linear inertio-gravity waves. The forcing employed is a mass and momentum source balanced so that only the large-scale potential-vortical component modes are directly excited. The dissipation is provided by a linear relaxation applied to the large scales and by an eighth-order linear hyperdiffusion. The statistical properties of the potential-vortical component in the fully developed flow were found to be very similar to those of classical two-dimensional turbulence. In particular, the energy spectrum of the potential-vortical component at scales smaller than the forcing is close to the ∼ k−3 expected for a purely two-dimensional system. Detailed analysis shows that the downscale enstrophy cascade into any wavenumber is dominated by very elongated triads involving interactions with large scales. Although not directly forced, a substantial amount of energy is found in the inertio-gravity modes and interactions among inertio-gravity modes are principally responsible for transferring energy to the small scales. The contribution of the inertio-gravity modes to the flow leads to a shallow tail at the high-wavenumber end of the total energy spectrum. For parameters roughly appropriate for the midlatitude atmosphere (notably Rossby number ∼ 0.5), the break between the roughly ∼ k−3 regime and this shallower regime occurs at scales of a few hundred km. This is similar to the observed mesoscale regime in the atmosphere. The nonlinear interactions among the inertio-gravity modes are extremely broadband in spectral space. The implications of this result for the subgrid-scale closure in the shallow-water model are discussed.

Boundary Conditions for Limited Area Models Based on the Shallow Water Equations

2013 ◽  
Vol 14 (3) ◽  
pp. 664-702 ◽  
Author(s):  
Arthur Bousquet ◽  
Madalina Petcu ◽  
Ming-Cheng Shiue ◽  
Roger Temam ◽  
Joseph Tribbia
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water System ◽  
Limited Area ◽  
Two Dimensional ◽  
One Dimensional ◽  
Shallow Water System ◽  
The Waves

AbstractA new set of boundary conditions has been derived by rigorous methods for the shallow water equations in a limited domain. The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions. The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain. The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.

On the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system

2013 ◽  
Vol 56 (3) ◽  
pp. 755-775 ◽  
Author(s):  
Chunxia Guan ◽  
Zhaoyang Yin
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Burgers Equation ◽  
Water System ◽  
Global Weak Solution ◽  
Rarefaction Waves ◽  
Global Weak Solutions ◽  
Two Component ◽  
The Cauchy Problem ◽  
Shallow Water System

AbstractIn this paper, we investigate the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system, provided the initial datau0(x)andρ0(x)have end statesu± andρ±, respectively. By perturbing the Cauchy problem of the system around rarefaction waves of the well-known Burgers equation, we obtain a global weak solution for the system under the assumptionsu− ≤ u+andρ− ≤ ρ+.

Balance regimes for the stability of a jet in anf-plane shallow water system

2007 ◽  
Vol 39 (5) ◽  
pp. 353-377 ◽  
Author(s):  
Norihiko Sugimoto ◽  
Keiichi Ishioka ◽  
Shigeo Yoden
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Shallow Water System ◽  
The Stability
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