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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 22, issue 6
Nonlin. Processes Geophys., 22, 749–764, 2015
https://doi.org/10.5194/npg-22-749-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 22, 749–764, 2015
https://doi.org/10.5194/npg-22-749-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 21 Dec 2015

Research article | 21 Dec 2015

Nonlinear feedback in a six-dimensional Lorenz model: impact of an additional heating term

B.-W. Shen

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Cited articles

Anthes, R.: Turning the tables on chaos: is the atmosphere more predictable than we assume?, UCAR Magazine, available at: https://www2.ucar.edu/atmosnews/opinion/turning-tables-chaos-atmosphere-more-predictable-we-assume-0, last access: 14 December 2015, 2011.
Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J. M.: Lyapunov Characteristic Exponents fro Smooth Dynamical Systems and for Hamiltonian Systems; A method for computing all of them. Part 1: Theory, Meccanica, 15, 9–20, 1980.
Blender, R. and Lucarini, V.: Nambu representation of an extended Lorenz model with viscous heating, Physica D, 243, 86–91, 2013.
Chen, Z.-M. and Price, W. G.: On the relation between Raleigh-Benard convection and Lorenz system, Chaos Soliton. Fract., 28, 571–578, 2006.
Christiansen, F. and Rugh, H.: Computing Lyapunov spectra with continuous Gram–Schmid orthonormalization, Nonlinearity, 10, 1063–1072, 1997.
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While the negative nonlinear feedback associated with two new modes in the 5DLM can stabilize solutions, additional resolved heating processes by a third mode in the 6DLM can destabilize solutions. The findings support the view of Lorenz (1972) on the role of small-scale processes: if the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.
While the negative nonlinear feedback associated with two new modes in the 5DLM can stabilize...
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