Oscillatory solutions at the continuum limit of Lorenz 96 systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916437543616512 |
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| author | Qi, Di Liu, Jian-Guo |
| author_facet | Qi, Di Liu, Jian-Guo |
| contents | In this paper, we study the generation and propagation of oscillatory solutions observed in the widely used Lorenz 96 (L96) systems. First, period-two oscillations between adjacent grid points are found in the leading-order expansions of the discrete L96 system. The evolution of the envelope of period-two oscillations is described by a set of modulation equations with strictly hyperbolic structure. The modulation equations are found to be also subject to an additional reaction term dependent on the grid size, and the period-two oscillations will break down into fully chaotic dynamics when the oscillation amplitude grows large. Then, similar oscillation solutions are analyzed in the two-layer L96 model including multiscale coupling. Modulation equations for period-three oscillations are derived based on a weakly nonlinear analysis in the transition between oscillatory and nonoscillatory regions. Detailed numerical experiments are shown to confirm the analytical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Oscillatory solutions at the continuum limit of Lorenz 96 systems Qi, Di Liu, Jian-Guo Chaotic Dynamics Numerical Analysis In this paper, we study the generation and propagation of oscillatory solutions observed in the widely used Lorenz 96 (L96) systems. First, period-two oscillations between adjacent grid points are found in the leading-order expansions of the discrete L96 system. The evolution of the envelope of period-two oscillations is described by a set of modulation equations with strictly hyperbolic structure. The modulation equations are found to be also subject to an additional reaction term dependent on the grid size, and the period-two oscillations will break down into fully chaotic dynamics when the oscillation amplitude grows large. Then, similar oscillation solutions are analyzed in the two-layer L96 model including multiscale coupling. Modulation equations for period-three oscillations are derived based on a weakly nonlinear analysis in the transition between oscillatory and nonoscillatory regions. Detailed numerical experiments are shown to confirm the analytical results. |
| title | Oscillatory solutions at the continuum limit of Lorenz 96 systems |
| topic | Chaotic Dynamics Numerical Analysis |
| url | https://arxiv.org/abs/2410.10073 |