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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Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions
TL;DR: In this paper, the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations with the Navier slip conditions on the impermeable boundary of a simply connected bounded regular domain was studied.
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On the rigid-lid approximation of shallow water Bingham
TL;DR: In this article, an initial value problem describing the motion of a Bingham fluid in a basin with a degenerate bottom topography is discussed, and the system governing such motion is obtained from the shallow water-Bingham models in the regime where the Froude number degenerates.
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Numerical study of the primitive equations in the small viscosity regime
TL;DR: In this article, the authors considered an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain and analyzed the generated boundary layer in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary.
Cosine Effect in Ocean Models
Carine Lucas,Antoine Rousseau +1 more
TL;DR: In this paper, the impact of the cosine terms of the Coriolis force on ocean dynamics is studied. But the authors focus on the traditional approximation of the force and do not consider the effect of these terms in large-scale ocean modeling.
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A Saint-Venant Model for Overland Flows with Precipitation and Recharge
TL;DR: In this article, the authors propose a one-dimensional Saint-Venant model for overland flows, including a water input-output source term modeling recharge via rainfall and infiltration (or exfiltration), and derive the model via asymptotic reduction from the two-dimensional Navier-Stokes equations under the shallow water assumption.
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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