Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model

Shen, Bo-Wen

doi:https://doi.org/10.5194/npg-23-189-2016

Articles | Volume 23, issue 4

https://doi.org/10.5194/npg-23-189-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/npg-23-189-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 23, issue 4

Research article

|

08 Jul 2016

Research article |

| 08 Jul 2016

Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model

Bo-Wen Shen

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Final revised paper (published on 08 Jul 2016)
Preprint (discussion started on 24 Feb 2016)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

SC1: 'Comments on Dr. B.-W. Shen's Paper', Zdzislaw Musielak, 18 May 2016
- AC3: 'Responses to short comments', Bo-Wen Shen, 10 Jun 2016
RC1: 'comments on Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model', Anonymous Referee #1, 25 May 2016
- AC1: 'Responses to Reviewer I’s comments', Bo-Wen Shen, 10 Jun 2016
RC2: 'Review', Yonghui WU, 04 Jun 2016
- AC2: 'Responses to Reviewer II’s comments', Bo-Wen Shen, 10 Jun 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Bo-Wen Shen on behalf of the Authors (10 Jun 2016) Manuscript

ED: Publish as is (23 Jun 2016) by Jinqiao Duan

AR by Bo-Wen Shen on behalf of the Authors (23 Jun 2016)

Short summary

We construct a seven-dimensional Lorenz model (7DLM) to discuss the impact of an extended nonlinear feedback loop on solutions' stability and illustrate the hierarchical scale dependence of chaotic solutions. The 7DLM requires a much larger critical value for the Rayleigh parameter (r_c ∼ 116.9) for the onset of chaos. For chaotic solutions with r = 120, high correlation coefficients among the modes at different scales indicate hierarchical scale dependence.