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| Titel |
Nonlinear feedback in a six-dimensional Lorenz model: impact of an additional heating term |
| VerfasserIn |
B.-W. Shen |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 22, no. 6 ; Nr. 22, no. 6 (2015-12-21), S.749-764 |
| Datensatznummer |
250121014
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| Publikation (Nr.) |
 copernicus.org/npg-22-749-2015.pdf |
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| Zusammenfassung |
| In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a
recent study using a five-dimensional (5-D) Lorenz model (LM), in order to
examine the impact of an additional mode and its accompanying heating term on
solution stability. The new mode added to improve the representation of the
streamfunction is referred to as a secondary streamfunction mode, while the
two additional modes, which appear in both the 6DLM and 5DLM but not in the
original LM, are referred to as secondary temperature modes. Two energy
conservation relationships of the 6DLM are first derived in the
dissipationless limit. The impact of three additional modes on solution
stability is examined by comparing numerical solutions and ensemble Lyapunov
exponents of the 6DLM and 5DLM as well as the original LM. For the onset of
chaos, the critical value of the normalized Rayleigh number (rc)
is determined to be 41.1. The critical value is larger than that in the 3DLM
(rc ~ 24.74), but slightly smaller than the one in the
5DLM (rc ~ 42.9). A stability analysis and numerical
experiments obtained using generalized LMs, with or without simplifications,
suggest the following: (1) negative nonlinear feedback in association with
the secondary temperature modes, as first identified using the 5DLM, plays a
dominant role in providing feedback for improving the solution's stability of
the 6DLM, (2) the additional heating term in association with the secondary
streamfunction mode may destabilize the solution, and (3) overall feedback
due to the secondary streamfunction mode is much smaller than the feedback
due to the secondary temperature modes; therefore, the critical Rayleigh
number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM
collectively suggest different roles for small-scale processes (i.e.,
stabilization vs. destabilization), consistent with the following statement
by Lorenz (1972): "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." The implications of this and previous work, as well as future
work, are also discussed. |
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