Stability analyses of longitudinal rolls of poiseuille-Rayleigh- bénard flows in air-filled channels of finite transversal extension

S. Xin (1, 2) , Xavier Nicolas (3, 4) , P. Le Quere (1)

1 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur
2 CETHIL - Centre de Thermique de Lyon
3 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
4 LETEM - Laboratoire d'Etudes des Transferts d'Energie et de Matière

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.

Mots clés: Stability analysis; Poiseuille; Rayleigh-Bénard; mixed convection; thermoconvective rolls; longitudinal rolls; wavy rolls; transition; linear stability; finite aspect ratio; laminar flow; channel flow

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Thermique [physics.class-ph]; Thermique [physics.class-ph]

S. Xin, Xavier Nicolas, P. Le Quere. Stability analyses of longitudinal rolls of poiseuille-Rayleigh- bénard flows in air-filled channels of finite transversal extension. Numerical Heat Transfer, Part A Applications, 2006, 50 (5), pp.467-490. ⟨10.1080/10407780600620079⟩. ⟨hal-00694581⟩