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Zbl 0978.76101
Chacón Rebollo, Tomás; Lewandowski, Roger; Chacón Vera, Eliseo
Analysis of the hydrostatic approximation in oceanography with compression term. (English)
[J] M2AN, Math. Model. Numer. Anal. 34, No.3, 525-537 (2000); erratum ibid. 34, No.5, 1117 (2000). ISSN 0764-583X; ISSN 1290-3841/e

Summary: The hydrostatic approximation of the incompressible three-dimensional 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 equation of state 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.

MSC 2000:: *76U05 Rotating fluids
76M10 Finite element methods
86A05 Hydrology, hydrography, oceanography
35Q35 Other equations arising in fluid mechanics

Keywords: hydrostatic approximation; Navier-Stokes equations; oceanography; Coriolis force; additional pressure term; existence theorem; mixed variational formulation; finite element spaces; uniqueness; evolutionary linear problem

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