American Institute of Mathematical Sciences

Advanced
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 - A, 2007, 18 (2&3) : 429-447. doi: 10.3934/dcds.2007.18.429
[1]

Yuri Kifer. Another proof of the averaging principle for fully coupled dynamical systems with hyperbolic fast motions. Discrete & Continuous Dynamical Systems - A, 2005, 13 (5) : 1187-1201. doi: 10.3934/dcds.2005.13.1187
[2]

Yong Xu, Bin Pei, Rong Guo. Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2257-2267. doi: 10.3934/dcdsb.2015.20.2257
[3]

Jie Xu, Yu Miao, Jicheng Liu. Strong averaging principle for slow-fast SPDEs with Poisson random measures. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2233-2256. doi: 10.3934/dcdsb.2015.20.2233
[4]

Alexandre Caboussat, Allison Leonard. Numerical solution and fast-slow decomposition of a population of weakly coupled systems. Conference Publications, 2009, 2009 (Special) : 123-132. doi: 10.3934/proc.2009.2009.123
[5]

Luca Dieci, Cinzia Elia. Smooth to discontinuous systems: A geometric and numerical method for slow-fast dynamics. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2935-2950. doi: 10.3934/dcdsb.2018112
[6]

Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1197-1212. doi: 10.3934/dcdsb.2014.19.1197
[7]

Anhui Gu. Asymptotic behavior of random lattice dynamical systems and their Wong-Zakai approximations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5737-5767. doi: 10.3934/dcdsb.2019104
[8]

Xianfeng Ma, Ercai Chen. Pre-image variational principle for bundle random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 957-972. doi: 10.3934/dcds.2009.23.957
[9]

Janusz Mierczyński. Averaging in random systems of nonnegative matrices. Conference Publications, 2015, 2015 (special) : 835-840. doi: 10.3934/proc.2015.0835
[10]

Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355
[11]

Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1
[12]

Yaofeng Su. Almost surely invariance principle for non-stationary and random intermittent dynamical systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6585-6597. doi: 10.3934/dcds.2019286
[13]

Yujun Zhu. Preimage entropy for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 829-851. doi: 10.3934/dcds.2007.18.829
[14]

Ji Li, Kening Lu, Peter W. Bates. Invariant foliations for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3639-3666. doi: 10.3934/dcds.2014.34.3639
[15]

Weigu Li, Kening Lu. Takens theorem for random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3191-3207. doi: 10.3934/dcdsb.2016093
[16]

Peng Gao. Averaging principle for stochastic Kuramoto-Sivashinsky equation with a fast oscillation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5649-5684. doi: 10.3934/dcds.2018247
[17]

Giancarlo Benettin, Anna Maria Cherubini, Francesco Fassò. Regular and chaotic motions of the fast rotating rigid body: a numerical study. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 521-540. doi: 10.3934/dcdsb.2002.2.521
[18]

Björn Schmalfuss. Attractors for nonautonomous and random dynamical systems perturbed by impulses. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 727-744. doi: 10.3934/dcds.2003.9.727
[19]

Ivan Werner. Equilibrium states and invariant measures for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 1285-1326. doi: 10.3934/dcds.2015.35.1285
[20]

Weigu Li, Kening Lu. A Siegel theorem for dynamical systems under random perturbations. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 635-642. doi: 10.3934/dcdsb.2008.9.635

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences