title: Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure.
abstract: 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.
authors.affiliation: Mechanical Systems Laboratory, Corporate Research & Development Center, Toshiba Corporation, 1, Komukai-Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan.
authors.forename: Juan F
authors.initials: JF
authors.lastname: Torres
authors.affiliation: Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS/Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France.
authors.forename: Daniel
authors.initials: D
authors.lastname: Henry
authors.affiliation: Institute of Fluid Science, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan.
authors.forename: Atsuki
authors.initials: A
authors.lastname: Komiya
authors.affiliation: Institute of Fluid Science, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan.
authors.forename: Shigenao
authors.initials: S
authors.lastname: Maruyama