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A new two-dimensional shallow water model including pressure effects and slow varying bottom topography

Stefania Ferrari, Fausto Saleri (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...

A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography

Stefania Ferrari, Fausto Saleri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...

Analysis of the hydrostatic approximation in oceanography with compression term

Tomás Chacón Rebollo, Roger Lewandowski, Eliseo Chacón Vera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...

Analysis of the hydrostatic approximation in oceanography with compression term

Tomás Chacón Rebollo, Roger Lewandowski, Eliseo Chacón Vera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...

Convergence of the rotating fluids system in a domain with rough boundaries

David Gérard-Varet (2003)

Journées équations aux dérivées partielles

We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size ϵ . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as ϵ goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with the classical...

Ekman boundary layers in rotating fluids

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L 2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.

Ekman boundary layers in rotating fluids

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.

Estimates based on scale separation for geophysical flows.

François Jauberteau, Roger Temam (2002)

RACSAM

The objective of this work is to obtain theoretical estimates on the large and small scales for geophysical flows. Firstly, we consider the shallow water problem in the one-dimensional case, then in the two-dimensional case. Finally we consider geophysical flows under the hydrostatic hypothesis and the Boussinesq approximation. Scale separation is based on Fourier series, with N models in each spatial direction, and the choice of a cut-off level N1 < N to define large and small scales. We...

Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Reinhard Farwig (2005)

Banach Center Publications

Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved L q -estimates of second order derivatives uniformly in the angular and translational velocities, ω and...

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