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

Abstract

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.

The authors are grateful for referees' constructive remarks. Computations have been performed on NEC-SX5 supercomputers at IDRIS (Orsay, France) under research project 41474.

Notes

^a The same results are also confirmed by a higher spatial resolution of 200 × 30.