Mathematical and numerical modellization of large-scale oceanic waves. (English) Zbl 0938.35137
To model the title problem, the authors consider linearized Navier-Stokes equations in hydrostatic and Boussinesq approximations. The existence and uniqueness of the solution are proved for the three-dimensional problem and for the two-dimensional cyclic problem which describes the “El-Nino” phenomenon. The cyclic equations are also solved numerically in a realistic situation corresponding to the tropical region of the Pacific Ocean. The numerical algorithm uses the method of characteristics for time discretization and \(Q_1\) finite elements for space discretization. The results are in good agreement with physical observations.
Reviewer: O.Titow (Berlin)
MSC:
35Q35 | PDEs in connection with fluid mechanics |
76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
86A05 | Hydrology, hydrography, oceanography |
76M10 | Finite element methods applied to problems in fluid mechanics |
35B50 | Maximum principles in context of PDEs |
35K55 | Nonlinear parabolic equations |
Keywords:
hydrostatic approximation; Boussinesq approximation; \(Q_1\) finite element; El-Nino phenomenon; linearized Navier-Stokes equations; existence; uniqueness; three-dimensional problem; two-dimensional cyclic problem; method of characteristicsReferences:
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