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Averaging, slaving and balance dynamics in a simple atmospheric model

Wirosoetisno, D. and Shepherd, T. G. (2000) Averaging, slaving and balance dynamics in a simple atmospheric model. Physica D: Nonlinear Phenomena, 141 (1-2). pp. 37-53. ISSN 0167-2789

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To link to this article DOI: 10.1016/S0167-2789(00)00022-1

Abstract/Summary

We report numerical results from a study of balance dynamics using a simple model of atmospheric motion that is designed to help address the question of why balance dynamics is so stable. The non-autonomous Hamiltonian model has a chaotic slow degree of freedom (representing vortical modes) coupled to one or two linear fast oscillators (representing inertia-gravity waves). The system is said to be balanced when the fast and slow degrees of freedom are separated. We find adiabatic invariants that drift slowly in time. This drift is consistent with a random-walk behaviour at a speed which qualitatively scales, even for modest time scale separations, as the upper bound given by Neishtadt’s and Nekhoroshev’s theorems. Moreover, a similar type of scaling is observed for solutions obtained using a singular perturbation (‘slaving’) technique in resonant cases where Nekhoroshev’s theorem does not apply. We present evidence that the smaller Lyapunov exponents of the system scale exponentially as well. The results suggest that the observed stability of nearly-slow motion is a consequence of the approximate adiabatic invariance of the fast motion.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:32849
Uncontrolled Keywords:Balance dynamics; Adiabatic invariants; Nekhoroshev theorem
Publisher:Elsevier

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