Analysis of some oceanography physics problems by the Galerkin’s method

Orenga, Pierre; Chatelon, François Joseph; Fluixa, Charles

doi:10.1007/978-3-642-60603-8_4

Cited by 2 publications

(1 citation statement)

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“…The authors use the equations that describe the three-dimensional flow of geophysical fluids presented in [7,8]. These equations are obtained by conserving the different state variables, including momentum, temperature, salinity and mass.…”

Section: Geophysical Fluid Equationsmentioning

confidence: 99%

Resolution to a three-dimensional physical oceanographic problem using the non-linear Galerkin method

Martino

Orenga

1999

Int. J. Numer. Meth. Fluids

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This paper presents the numerical results concerning the adaptation of the non‐linear Galerkin method to three‐dimensional geophysical fluid equations. This method was developed by Marion and Temam to solve the Navier–Stokes two‐dimensional equations. It allows a substantial decrease in calculation costs due to the application of an appropriate treatment to each mode based on its position in the spectrum. The large scales involved in the study of geophysical flow require that the earth's rotational effects and the existence of a high degree of stratification be taken into account. These phenomena play an important role in the distribution of the energy spectrum. It is shown here that the non‐linear Galerkin method is very well‐suited to the treatment of these phenomena. First, the method for the particular situation of a rigid‐lid with a flat bottom is validated, for which the functional basis used is particularly well‐adapted. Then the more general case of a domain exhibiting variable bathymetry is presented, which necessitates the use of the transformation σ, thus providing a study domain with a cylindrical configuration. Copyright © 1999 John Wiley & Sons, Ltd.

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Section: Geophysical Fluid Equationsmentioning

confidence: 99%