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Titel |
Symmetry-break, mixing, instability, and low frequency variability in a minimal Lorenz-like Model |
VerfasserIn |
V. Lucarini, K. Fraedrich |
Konferenz |
EGU General Assembly 2009
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Medientyp |
Artikel
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Sprache |
Englisch
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 11 (2009) |
Datensatznummer |
250020648
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Zusammenfassung |
Starting from the classical Saltzman 2D convection equations, we derive via a severe spectral
truncation a minimal 10 ODE system which includes the thermal effect of viscous
dissipation. Neglecting this process leads to a dynamical system which includes a decoupled
(generalized) Lorenz system. The consideration of this process breaks an important
symmetry, couples the dynamics of fast and slow variables, ensuing modifications of the
structural properties of the attractor and of the spectral features. When the relevant
nondimensional number (Eckert number Ec) is different from zero, the system is ergodic and
hyperbolic, the slow variables feature long term memory with f-3∕2 power spectra, and
the fast variables feature amplitude modulation on time scale of 1∕Ec. Increasing
the strength of the thermal-viscous feedback has a stabilizing effect, as both the
metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically
with Ec. The analyzed system features very rich dynamics: it overcomes some of
the limitations of the Lorenz system and might have prototypical value in relevant
processes in complex systems dynamics, such as the interaction between slow and
fast variables. the presence of long term memory and the associated extreme value
statistics. Analysis shows how, neglecting the coupling of slow and fast variables only
on the basis of scale analysis can be catastrophic. In fact, this leads to spurious
invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and
that cause the model losing ability in describing intrinsically multiscale processes. |
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