Journal ArticleDOI
A shallow water model with eddy viscosity for basins with varying bottom topography
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In this article, the authors introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model and prove the global regularity of the resulting model.Abstract:
The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.read more
Citations
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The one-dimensional shallow water equations with transparent boundary conditions
TL;DR: In this paper, the authors address the question of the local in time well-posedness of the one-dimensional shallow water on an interval, these equations being supplemented with suitable boundary conditions.
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An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
TL;DR: In this paper, an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x is studied.
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Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems
TL;DR: In this paper, the authors derived the non-hydrostatic Saint-Venant system for shallow waters including friction and viscosity from the free surface Navier-Stokes system, leading to two formulations of growing complexity depending on the level of approximation chosen for the fluid pressure.
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New Developments and Cosine Effect in the Viscous Shallow Water and Quasi-geostrophic Equations
Carine Lucas,Antoine Rousseau +1 more
TL;DR: The viscous Shallow Water Equations and Quasi-Geostrophic Equations are considered and some new terms, related to the Coriolis force, are revealed thanks to a rigorous asymptotic analysis.
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Mathematical analysis of a saint-venant model with variable temperature
Vincent Giovangigli,Binh Tran +1 more
TL;DR: In this article, the authors investigated the mathematical properties of a Saint-Venant model with an energy equation and with temperature-dependent transport coefficients and derived a symmetric conservative formulation of the system.
References
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Book
An Introduction to Fluid Dynamics
TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Book
Navier-Stokes Equations: Theory and Numerical Analysis
TL;DR: This paper presents thediscretization of the Navier-Stokes Equations: General Stability and Convergence Theorems, and describes the development of the Curl Operator and its application to the Steady-State Naviers' Equations.
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