Chaotic Advection and the Emergence of Tori in the Küppers-Lortz State - Nonlinear Sciences > Chaotic DynamicsReportar como inadecuado




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Abstract: Motivated by the roll-switching behavior observed in rotatingRayleigh-B\-enard convection, we define a K\-uppers-Lortz K-L state as avolume-preserving flow with periodic roll switching. For an individual rollstate, the Lagrangian particle trajectories are periodic. In a system withroll-switching, the particles can exhibit three-dimensional, chaotic motion. Westudy a simple phenomenological map that models the Lagrangian dynamics in aK-L state. When the roll axes differ by $120^{\circ}$ in the plane of rotation,we show that the phase space is dominated by invariant tori if the ratio ofswitching time to roll turnover time is small. When this parameter approacheszero these tori limit onto the classical hexagonal convection patterns, and, asit gets large, the dynamics becomes fully chaotic and well-mixed. Forintermediate values, there are interlinked toroidal and poloidal structuresseparated by chaotic regions. We also compute the exit time distributions andshow that the unbounded chaotic orbits are normally diffusive. Although the mappresumes instantaneous switching between roll states, we show that thequalitative features of the flow persist when the model has smooth, overlappingtime-dependence for the roll amplitudes the Busse-Heikes model.



Autor: Paul Mullowney, Keith Julien, James D. Meiss

Fuente: https://arxiv.org/







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