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Analysis of the hydrostatic approximation in oceanography with compression term

Published online by Cambridge University Press:  15 April 2002

Tomás Chacón Rebollo ,
Roger Lewandowski  and
Eliseo Chacón Vera
Tomás Chacón Rebollo
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico Universidad de Sevilla, 41.080-Sevilla, Spain. (chacon@numer2.us.es)
Roger Lewandowski
Affiliation:
Modal-X, Bât. G, Université Paris X, 200 avenue de la République, 92001 Nanterre, France. (lewandow@modalx.u-paris10.fr)
Eliseo Chacón Vera
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico Universidad de Sevilla, 41.080-Sevilla, Spain. (eliseo@numer2.us.es)
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Abstract

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 the density. It therefore models a slight dependence of the density upon compression terms. We study this model as an independent mathematical object and prove an existence theorem by means of a mixed variational formulation. The proof uses a family of finite element spaces to discretize the problem coupled with a limit process that yields the solution. We finish this paper with an existence and uniqueness result for the evolutionary linear problem associated to this model. This problem includes the same additional pressure term and Coriolis force.

Keywords

Navier-Stokes equationsOceanographyCompression term.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 3 , May 2000 , pp. 525 - 537
Copyright
© EDP Sciences, SMAI, 2000

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