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| Titel |
Lyapunov, Floquet, and singular vectors for baroclinic waves |
| VerfasserIn |
R. M. Samelson |
| 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 ; 8, no. 6 ; Nr. 8, no. 6, S.439-448 |
| Datensatznummer |
250005888
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| Publikation (Nr.) |
 copernicus.org/npg-8-439-2001.pdf |
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| Zusammenfassung |
| The dynamics of the
growth of linear disturbances to a chaotic basic state is analyzed in an
asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In
this model, an ordinary differential equation for the wave amplitude is
coupled to a partial differential equation for the zonal flow correction.
The leading Lyapunov vector is nearly parallel to the leading Floquet
vector f1
of the lowest-order unstable periodic orbit over most of the attractor.
Departures of the Lyapunov vector from this orientation are primarily
rotations of the vector in an approximate tangent plane to the large-scale
attractor structure. Exponential growth and decay rates of the Lyapunov
vector during individual Poincaré section returns are an order of
magnitude larger than the Lyapunov exponent l ≈
0.016. Relatively large deviations of the Lyapunov vector from parallel to
f1
are generally associated with relatively large transient decays. The
transient growth and decay of the Lyapunov vector is well described by the
transient growth and decay of the leading Floquet vectors of the set of
unstable periodic orbits associated with the attractor. Each of these
vectors is also nearly parallel to f1.
The dynamical splitting of the complete sets of Floquet vectors for the
higher-order cycles follows the previous results on the lowest-order
cycle, with the vectors divided into wave-dynamical and decaying zonal
flow modes. Singular vectors and singular values also generally follow
this split. The primary difference between the leading Lyapunov and
singular vectors is the contribution of decaying, inviscidly-damped
wave-dynamical structures to the singular vectors. |
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