https://doi.org/10.1140/epjb/e2014-50468-6
Regular Article
Low-Prandtl-number Rayleigh-Bénard convection with stress-free boundaries
1
Department of Mathematics, National Institute of
Technology, 713209
Durgapur,
India
2
Department of Physics, Indian Institute of
Technology, 721302
Kharagpur,
India
a e-mail: pinaki.math@gmail.com
Received:
10
July
2014
Received in final form:
26
September
2014
Published online:
24
November
2014
Results of direct numerical simulations on Rayleigh-Bénard convection in low-Prandtl-number convection with stress-free horizontal boundaries are presented. Simulations are done in a three dimensional rectangular simulation box of dimensions Lx × Ly × 1. Instabilities and the corresponding fluid patterns near onset of convection are investigated by varying the horizontal aspect ratio η = Ly/Lx in a range 1 ≤ η ≤ 4. Fluid patterns are complex and unsteady at the instability onset for η ≥ 2. They consist of wavy rolls, rhombic patterns and oblique wavy rolls. The patterns near onset are time periodic for η < 2. We observe periodic wavy rolls for η = 4 / 3. Homoclinic bifurcations are observed for η = 1 for 0 ≤ Pr ≤ 0.03. We observe spontaneous breaking of a single limit cycle in two and again spontaneous merging of two limit cycles into one in a simulation box with η = 1, as the reduced Rayleigh number r = Ra/Rac is raised at a fixed value of Pr. The effect of Prandtl number on the homoclinic bifurcations is also investigated. We also present a low-dimensional model, which captures the instability sequence quite accurately for η = 1.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2014