Numerical Modeling and Simulations for an Ocean Circulation Model of the Southern Pacific
DOI:
https://doi.org/10.17268/sel.mat.2025.02.01Keywords:
Navier-Stokes equations, Temperature model, Monolithic approach, Galerkin finite elements, El NiñoAbstract
In this work, we consider the primitive equations of an ocean circulation model for the southern pacific, which consists of the time-dependent Navier-Stokes equations in the β-plane coupled with the temperature transport equation. Specifically, the full three-dimensional equations are adopted and formulated as a monolithic system of nonstationary, nonlinear, coupled partial differential equations. The El Nino phenomenon is simulated by the action of given wind stresses on the ocean surface. We present an approximation scheme with Crank-Nicolson finite differences in time, and in space we take inf-sup stable Galerkin finite elements for the Navier-Stokes part and bilinear elements for the temperature. We solve the resulting, nonlinear monolithic discrete system by Newton's method. Numerical experiments with realistic geometry and material data are conducted, which show the practicability of our approach.
References
Clarke AJ. An Introduction to the Dynamics of El Niño and the Southern Oscillation. Academic Press; 2008.
Sarachik ES, Cane MA. The El Niño-Southern Oscillation Phenomenon. Cambridge University Press; 2010.
Cane MA. The response of an equatorial ocean to simple wind stress patterns: I. Model formulation and analytic results. Journal of Marine Research. 1979;37:233-52.
Vallis GK. Atmospheric and Oceanic Fluid Dynamics. Cambridge: Cambridge University Press; 2017.
Jin FF, Neelin JD. Modes of interannual tropical ocean–atmosphere interaction—a unfied view. Part I: Numerical results. Journal of the Atmospheric Sciences. 1993;50(21):3477-503.
Lions JL, Temam R, Wang S. On the equations of the large-scale ocean. Nonlinearity. 1992 sep;5(5):1007. Available from: https://dx.doi.org/10.1088/0951-7715/5/5/002.
Rubio O, Noriega R. A Mathematical Model for Oceanic Circulation at El Niño Phenomenon. Selecciones Matematicas. 2018 Dec; 5(02): 249-264. Available from: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2201.
Africa PC, Arndt D, Bangerth W, Blais B, Fehling M, Gassmoller R, et al. The deal.II Library, Version 9.6. Journal of Numerical Mathematics. 2024 Nov;32(4):369-80. Available from: https://www.degruyter.com/document/doi/10.1515/jnma-2024-0137/html.
Wick T. Solving Monolithic Fluid-Structure Interaction Problems in Arbitrary Lagrangian Eulerian Coordinates with the deal.II Library. Archive of Numerical Software. 2013;1:1-19. Available from: https://media.archnumsoft.org/10305/.
Hurlburt HE, Kindle JC, O’Brien JJ. A Numerical Simulation of the Onset of El Niño. Journal of Physical Oceanography. 1976;6(5):621–631. Available from: https://journals.ametsoc.org/view/journals/phoc/6/5/1520-0485_1976_006_0621_ansoto_2_0_co_2.xml.
McCreary JP, Anderson DLT. Chapter 24 Simple Models of EL Niño and the Southern Oscillation. In: Nihoul JCJ, editor. Coupled Ocean-Atmosphere Models. vol. 40 of Elsevier Oceanography Series. Elsevier; 1985. p. 345–370. Available from: https://www.sciencedirect.com/science/article/pii/S0422989408707207.
Latif M, Maier-Reimer E, Olbers DJ. Chapter 7 Climate Variability Studies with a Primitive Equation Model of the Equatorial Pacific. In: Nihoul JCJ, editor. Coupled Ocean-Atmosphere Models. vol. 40 of Elsevier Oceanography Series. Elsevier; 1985. p. 63–81. Available from: https://www.sciencedirect.com/science/article/pii/S0422989408707037.
Wick T. Multiphysics Phase-Field Fracture: Modeling, Adaptive Discretizations, and Solvers. Berlin, Boston: De Gruyter; 2020. Available from: https://www.degruyter.com/view/title/523232.
Girault V, Raviart PA. Finite Element method for the Navier-Stokes equations. Number 5 in Computer Series in Computational Mathematics. Springer-Verlag; 1986.
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