Mathematical and numerical modellization of large-scale oceanic waves

✍ Scribed by Aziz Belmiloudi; Françoise Brossier; Laurent Monier

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 327 KB
• Volume: 22
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(199908)22:12<967::aid-mma64>3.0.co;2-w

✦ Synopsis

Communicated by J.C. Nedelec

This paper is devoted to the theoretical and numerical study of a method which computes the variability of current and density in an oceanic domain. The equations are of Navier}Stokes type for the velocity and of transport-di!usion type for the density. They are linearized around a given mean circulation and modi"ed by physical assumptions including hydrostatic approximation. The existence and uniqueness of a solution are proved for two sets of equations: "rst the three-dimensional problem and then the two-dimensional cyclic problem derived by assuming a sinusomK dal x-dependence for the perturbation of the mean #ow. The latter corresponds to a modellization of tropical instability waves which are illustrated by the &El Nino' phenomenon. These two problems di!er from classical ones because of hydrostatic approximation, boundary conditions imposed by the oceanic domain and complex-valued functions for the cyclic case. A numerical model is developed for the two-dimensional cyclic equations. Time discretization is performed by the characteristics method; space discretization uses Q "nite elements. Numerical results are presented in a realistic case corresponding to the tropical Paci"c Ocean.