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Standing Swells Surveyed Showing Surprisingly Stable Solutions for the Lorenz '96 Model

Computational Story Lab, Department of Mathematics and Statistics, Vermont Complex Systems Center, Vermont Advanced Computing Core, University of Vermont, Burlington, Vermont, USA

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Lewis Mitchell

Computational Story Lab, Department of Mathematics and Statistics, Vermont Complex Systems Center, Vermont Advanced Computing Core, University of Vermont, Burlington, Vermont, USA

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Peter Sheridan Dodds

Computational Story Lab, Department of Mathematics and Statistics, Vermont Complex Systems Center, Vermont Advanced Computing Core, University of Vermont, Burlington, Vermont, USA

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, and

Christopher M. Danforth

Computational Story Lab, Department of Mathematics and Statistics, Vermont Complex Systems Center, Vermont Advanced Computing Core, University of Vermont, Burlington, Vermont, USA

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https://doi.org/10.1142/S0218127414300274Cited by:12 (Source: Crossref)

Abstract

The Lorenz '96 model is an adjustable dimension system of ODEs exhibiting chaotic behavior representative of the dynamics observed in the Earth's atmosphere. In the present study, we characterize statistical properties of the chaotic dynamics while varying the degrees of freedom and the forcing. Tuning the dimensionality of the system, we find regions of parameter space with surprising stability in the form of standing waves traveling amongst the slow oscillators. The boundaries of these stable regions fluctuate regularly with the number of slow oscillators. These results demonstrate hidden order in the Lorenz '96 system, strengthening the evidence for its role as a hallmark representative of nonlinear dynamical behavior.

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