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Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2015

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

Abstract

The transition from the complex Rayleigh-B´enard 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-B´enard convection (θ ≈ 0◦), which is a realistic physical approximation to the ideal Rayleigh-B´enard 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.
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Dates and versions

hal-01298322 , version 1 (11-04-2016)

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Juan Felipe Torres, Daniel Henry, Atsuki Komiya, Shigenao Maruyama. Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92, pp.023031. ⟨10.1103/PhysRevE.92.023031⟩. ⟨hal-01298322⟩
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