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A large-scale investigation of wind reversal in a square Rayleigh–Bénard cell

Published online by Cambridge University Press:  02 February 2015

Bérengère Podvin  and
Anne Sergent
Bérengère Podvin*
Affiliation:
LIMSI-CNRS, rue Von Neuman, Orsay, 91403 CEDEX, France
Anne Sergent
Affiliation:
LIMSI-CNRS, rue Von Neuman, Orsay, 91403 CEDEX, France Université Pierre et Marie Curie – Paris 6, 4 place Jussieu, 75252 CEDEX 05, Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

We consider the numerical simulation of Rayleigh–Bénard convection in a 2D square cell filled with water ( $\mathit{Pr}=4.3$ ) at a turbulent Rayleigh number of $\mathit{Ra}=5\times 10^{7}$ . We focus on the structures and dynamics of the large-scale intermittent flow. Two quasi-stable flow patterns are identified: one consists of a main diagonal roll with two corner rolls; and the other of two horizontally stacked rolls. These stable flow structures are associated with two types of events, which involve corner flow growth and pattern rotation: reversals, when the main roll rapidly switches signs; and cessations, when it disappears for longer periods. Proper orthogonal decomposition (POD) is applied independently to the velocity field and to the temperature field. In both cases, three principal modes were identified: a single-roll, large-scale circulation; a quadrupolar flow; and a double-roll, symmetry-breaking mode. The large-scale circulation is the kinetic mode with the highest energy. The most energetic temperature mode is associated with the mean temperature and corresponds to a velocity field of quadrupolar nature. The vertical heat flux is concentrated in these two modes. The reversal process is characterized by sharp fluctuations in the amplitudes of all modes. Analysis of the interaction coefficients between the spatial modes leads us to propose a three-dimensional model, based on the interaction of the large-scale circulation, the quadrupolar flow and horizontal rolls. The main dynamics and time scales of reversals and cessations are reproduced by the model in the presence of noise.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 172 - 201
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Copyright
© 2015 Cambridge University Press 

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