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February & March  2007, 18(2&3): 429-447. doi: 10.3934/dcds.2007.18.429

Numerical approximation of atmospheric-ocean models with subdivision algorithm

David Julitz 1,

1. 

Martin Luther Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, Theodor Lieser Str. 5, 06108 Halle, Germany

Received  April 2006 Revised  July 2006 Published  March 2007

The Lorenz Maas-System is a coupled atmospheric-ocean model. It contains the Maas System which models the ocean (slow variables) and the Lorenz84 System which models the atmosphere (fast variables). Both systems are coupled to each other. Recently this System was used to investigate the long term behavior of climate models with simple numerical methods (see Arnold, Imkeller and Wu [5]). In this paper we will use the established subdivision algorithm to visualize the attractor of this system. Furthermore we will investigate (also with the subdivision algorithm) some reduced versions (statistical and stochastic models) of the Lorenz Maas-System and compare the results to the original 6-dimensional system.
Keywords: random dynamical systems, averaging principle, systems with slow and fast motions, numerical approximations..
Mathematics Subject Classification: Primary: 37N10, 86-08, 86A05, 70K65, 70K70 ; Secondary:37H10, 37M0.
Citation: David Julitz. Numerical approximation of atmospheric-ocean models with subdivision algorithm. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 429-447. doi: 10.3934/dcds.2007.18.429
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