A Mathematical Model for Oceanic Circulation at "El Niño" Phenomenon
DOI:
https://doi.org/10.17268/sel.mat.2018.02.11Keywords:
Phenomenon "EL Niño", Primitive Equations, Stochastic Systems, Tropical OceanAbstract
We describe a model that interprets the circulation of the tropical ocean in the periods when the meteorological phenomenon known as "El Niño" appears; A study area is defined as being the equatorial pacific, the ocean current is described by the primitive equations, which consists of the equations of motion and temperature transport which are strongly coupled. As boundary conditions, the wind stresses on the surface of the ocean is fundamental for the warming of waters, which due to its high variability we consider it random and described by a multiplicative white noise, generating the so-called stochastic primitive equations for the circulation of the tropical ocean.
The variational formulation of the problem is presented and some estimates that allow verifying the existence of solutions of these equations.
References
Bensoussan, A, Temam, R. Equations Stochastiques du type Navier-Stokes, J. Fucntional Analysis 13, 195-222, 1973.
Constantin, P. Navier-Stokes Equations and Area of Interfaces. Commun.Math.Phys. 129,pp.241-266,1990.
Cushman and Roisin, B. Introduction to Geophysical Fluid Dynamics, Prentice-Hall, New Jersey, 1999.
Chao, Y., Halpern, D. and Perigaud, C. Sea Surface Height Variavility During 1986-1988 in the Ttropical Pacific Ocean, J. of Geophy. Reserch, vol.98, No.C4,6947-6959,1993.
Falb, P.L. Infinite-Dimensional FIltering: The Kalman-Bucy Filter in Hilbert Space, Information and Control 11, (1967), 102-137.
Langa R., J.A. Sistemas Dinámicos Estocásticos no autónomos y Sistemas Multivaluados, Bol. Soc. Esp. Mat. Apl. No. 21 (2002), 89-115.
Fleming, W.H. and Rishel, R.W. Deterministic and Stochastic Optimal Control, Springer-Verlag, Berlin, 1975.
Glatt-Holtz, N. and Ziane, M. The Stochastic Primitve Equations in Two Space Dimensions With Multiplicative Noise, Discrete and Continuous Dinamycal Systems Series B, 10(4), 2008, 801-822.
A. Gill, A. Atmosphere-Ocean Dynamics .Academic Press,Inc.1982.
Hendershot, M.C. Single Layer Models of the General Circulation of the Ocean, edited by H. Banberan, and W.Young, Springer-Verlag,New York,1987.
Haltiner, G. and Willams, R. A Numerical Predictionand Dynamic Metereology. John Wiley and Sons;Second Ed., 1979.
Jordy, A., Wang, A-P. Estimation of Transoprt at Open Boundaries With an Ensemble Kalman Filter in a Coastal Ocean Model, Ocean Modelling, 64 (2013) 56-66.
Latif, M., Maier-Reimer, E. & Olbers, D. Climate Variability Studies with a Primitive Equation Model of the Equatorial Pacific. inCoupled Ocean-Atmosphere Models, edited by J.Nihoul ,pp.63-81,Elsevier,New York,1985.
Du, L. and Zhang, T. Local and global strong solutions to the Stochastic incompressible Navier-Stokes Equation in Critical Besov Space, en Arxiv,6/12/2017 acc on 17 dic 017 https://arxiv.org/pdf/1710.11336.pdf
Marchuk, G., Dymnikov, V., Zalesny, V., Lykosov, V. and Galin, V. Numerical Simulation of a Large-Scale Atmospheric and Oceanic Circulation. in Computational Mathematics and Mathematical modelling, edited by G. Marchuk,V. Dymnikov, Mir Publishers, Moscow,pp.124-166,1985.
McCreary, Jr. & Anderson, D. Simple Models of El Niño and the Souther Oscilation.in Coupled Ocean-Atmosphere Models, edited by J.Nihoul, pp.345-370, Elsevier,New York,1985.
J-L.Lions, J-L., Temam, R. and Wang, S. On the Equations of the Large-Scale Ocean. Nonlinearity 5 pp.1007-1053,1992.
Pedlosky, J. Geophysical Fluid Dynamics, AMS,1970.
Rubio, O. Ecuaciones Diferenciales Estocásticas, Tesis de Mestro en ciencias, Universidad Nacional de Ingeniería, 1990.
Rubio, O. A Primitive equation model for the Tropical Pacific Ocean, V Americas Conferece on Differential Equations and Nonlinear Analysis, Edmonton, Canada, 2002.
Temam, R. Infinite-Dimensional Dynamical Systems in Mechanics and Phisics, Springer-Verlag,1988.
Temam, R. Navier-Stokes Equations, Nor Holland, 1977.
J. Van Neerven, Veraar, M. and Weis, L. Conditions for stochastic integrability in UMD Banach spaces. Banach spaces and their applications in analysis,2007, pp 125146.
Pancowski R. & Philander G. Parametrization of vertical mixing in Numerical Models in Tropical Oceans, J.Phys.Oceanogr.,11,1443-1451,1981.
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
