Articles | Volume 22, issue 6
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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Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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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:, 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.
Short summary
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.