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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2017-56
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
09 Oct 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).
Wave propagation in the Lorenz-96 model
Dirk L. Van Kekem and Alef E. Sterk Johann Bernoulli Institute for Mathematics and Computer Sc ience, University of Groningen, PO Box 407, 9700 AK Groningen, the Netherlands
Abstract. In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter n and the forcing parameter F. For F > 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with n, but its period tends to a finite limit as n → ∞. For F < 0 and odd n the first bifurcation is a supercritical Hopf bifurcation, and in this case the period of the traveling wave also grows linearly with n. For F < 0 and even n a Hopf bifurcation is preceded by either one or two pitchfork bifurcations. This bifurcation sequence leads to standing waves, and their spatiotemporal properties depend on whether n has remainder 2 or 0 upon division by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values n and F.

Citation: Van Kekem, D. L. and Sterk, A. E.: Wave propagation in the Lorenz-96 model, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2017-56, in review, 2017.
Dirk L. Van Kekem and Alef E. Sterk
Dirk L. Van Kekem and Alef E. Sterk
Dirk L. Van Kekem and Alef E. Sterk

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Short summary
In this paper we investigate the spatiotemporal properties of waves in the Lorenz-96 model. In particular, we explain how these properties are related to the presence of Hopf and pitchfork bifurcations. We also explain bifurcation scenarios by which multiple stable waves can coexist for the same parameter values.
In this paper we investigate the spatiotemporal properties of waves in the Lorenz-96 model. In...
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