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Forthcoming events in this series
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The Quasi-biennial and Tropospheric Biennial oscillations as synchronized chaos? - insights from observations and the laboratory
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The fluid dynamics of green buildings
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On the emergence of PV staircases and jets in planetary atmospheres
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Heavy gas dispersion over complex terrain
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Bayesian 4DVAR: An extension to weak constraint 4DVAR data assimilation
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Impact of flux adjustments on the Atlantic Meridional Overturning Circulation in a GCM
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Origin of our Solar system: new ideas gleaned from the Cassini-Huygens mission to Saturn and Titan and the MESSENGER mission to Mercury
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Climate mitigation by carbon dioxide sequestration
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Mixing, jet sharpening and angular momentum in shallow atmospheres
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Complete solutions of the fundamental fluid mechanics equations sets: generalization of the famous Stokes problem on oscillating plane on 2D and 3D cases (analytic, numeric visualization and experiment)
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The southern hemisphere westerlies during the last glacial maximum
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Long term memory and 1/f-scaling in climate observations and models (TBC)
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Symmetry breaking, mixing, instability, and low-frequency variability in a minimal Lorenz-like system
Abstract
Starting from the classical Saltzman two-dimensional 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 and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number) Ec is different from zero, an additional time scale of O(Ec^(?1)) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/ f^(3/2) power spectra, and the fast variables feature amplitude modulation. 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. This 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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The alpha model - an energy conserving turbulence closure
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