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

David Gérard-Varet

Journées équations aux dérivées partielles (2003)

  • page 1-15
  • ISSN: 0752-0360

Abstract

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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 layers.

How to cite

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Gérard-Varet, David. "Convergence of the rotating fluids system in a domain with rough boundaries." Journées équations aux dérivées partielles (2003): 1-15. <http://eudml.org/doc/93450>.

@article{Gérard2003,
abstract = {We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size $\epsilon $. We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as $\epsilon $ 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 layers.},
author = {Gérard-Varet, David},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-15},
publisher = {Université de Nantes},
title = {Convergence of the rotating fluids system in a domain with rough boundaries},
url = {http://eudml.org/doc/93450},
year = {2003},
}

TY - JOUR
AU - Gérard-Varet, David
TI - Convergence of the rotating fluids system in a domain with rough boundaries
JO - Journées équations aux dérivées partielles
PY - 2003
PB - Université de Nantes
SP - 1
EP - 15
AB - We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size $\epsilon $. We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as $\epsilon $ 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 layers.
LA - eng
UR - http://eudml.org/doc/93450
ER -

References

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