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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 |
2198-5634
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics Discussions ; 2, no. 2 ; Nr. 2, no. 2 (2015-03-17), S.475-512 |
| Datensatznummer |
250115154
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| Publikation (Nr.) |
 copernicus.org/npgd-2-475-2015.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 steamfunction is referred to as
a secondary streamfunction mode, while the two additional modes,
that 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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