Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

Juan F. Torres, Daniel Henry, Atsuki Komiya, Shigenao Maruyama

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14 Citations (Scopus)


The transition from the complex Rayleigh-Bénard convection to the simple heated-from-the-sides configuration in a cubical cavity filled with a Newtonian fluid is numerically studied. The cavity is tilted by an angle θ around its lower horizontal edge and is heated and cooled from two opposite tilted sides. We first analyze the effect of a marginal inclination angle on quasi-Rayleigh-Bénard convection (θ≈0), which is a realistic physical approximation to the ideal Rayleigh-Bénard convection. We then yield the critical angles where multiple solutions that were initially found for θ≈0 disappear, eventually resulting in the single steady roll solution found in the heated-from-the-sides configuration (θ=90). We confirm the existence of critical angles during the transition θ:0→90, and we demonstrate that such angles are a consequence of either singularities or collisions of bifurcation points in the Rayleigh-number-θ parameter space. We finally derive the most important critical angles corresponding to any Newtonian fluid of Prandtl number greater than that of air.

Original languageEnglish
Article number023031
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 2015 Aug 28

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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