Stability analyses of Longitudinal Rolls of Poiseuille-Rayleigh-Bénard Flows in Air-Filled Channels of Finite Transversal Extension

• Published in: Numerical heat transfer. Part A, Applications Applications, 2006-07, Vol.50 (5), p.467-490
• Main Authors: Xin, Shihe, Nicolas, Xavier, Quéré, Patrick Le
• Format: Article
• Language: English
• Subjects: Buoyancy-driven instability; Chemical vapor deposition (including plasma-enhanced cvd, mocvd, etc.); Cross-disciplinary physics: materials science; rheology; Engineering Sciences; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fluids mechanics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Materials science; Mechanics; Methods of deposition of films and coatings; film growth and epitaxy; Physics; Thermics
• ISSN: 1040-7782; 1521-0634
• DOI: 10.1080/10407780600620079

Time-stepping, steady-state solving and continuation methods are used to investigate the onset and stability of longitudinal rolls of Poiseuille-Rayleigh-Bénard flows in air-filled channels of finite transversal extension. In a channel of transversal aspect ratio 10, three solution branches of steady longitudinal rolls are discovered. Those with 9 and 10 rolls are linked to supercritical pitchfork bifurcations of the base flow, while that with 11 rolls seems to be an isolated branch. All three branches of longitudinal rolls are found to be unstable with respect to wavy oscillatory perturbations, and nonlinear studies show that the coresponding Hopf bifurcations are supercritical.