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Lagrangian chaos in confined two-dimensional oscillatory convection

Published online by Cambridge University Press:  27 October 2014

L. Oteski ,
Y. Duguet  and
L. R. Pastur
L. Oteski*
Affiliation:
CNRS, Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur (LIMSI), F-91403 Orsay, France University Paris-Sud, F-91405 Orsay, France
Y. Duguet
Affiliation:
CNRS, Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur (LIMSI), F-91403 Orsay, France
L. R. Pastur
Affiliation:
CNRS, Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur (LIMSI), F-91403 Orsay, France University Paris-Sud, F-91405 Orsay, France
*
†Email address for correspondence: [email protected]
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Abstract

The chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially heated cavity with aspect ratio 2 and Prandtl number 0.71 for Rayleigh numbers around the first Hopf bifurcation. A scattering approach reveals different zones depending on whether the statistics of return times exhibit exponential or algebraic decay. Melnikov functions are computed and predict the appearance of the main mixing regions via the break-up of the homoclinic and heteroclinic orbits. The non-hyperbolic regions are characterised by a larger number of Kolmogorov–Arnold–Moser (KAM) tori. Based on the numerical extraction of many unstable periodic orbits (UPOs) and their stable/unstable manifolds, we suggest a coarse-graining procedure to estimate numerically the spatial fraction of chaos inside the cavity as a function of the Rayleigh number. Mixing is almost complete before the first transition to quasi-periodicity takes place. The algebraic mixing rate is estimated for tracers released from a localised source near the hot wall.

JFM classification

Mixing: Chaotic advection Convection: Convection in cavities Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 759 , 25 November 2014 , pp. 489 - 519
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Copyright
© 2014 Cambridge University Press 

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