Folded Solution Branches in Rayleigh–Bénard Convection in the Presence of Avoided Crossings of Neutral Stability Curves

Abstract

Sidewall effect on the Rayleigh–Bénard convection has been examined in a rectangular channel with finite aspect ratio, where the linear neutral stability curves avoid crossing on the Rayleigh number–aspect ratio plane. Numerical analysis shows that folded solution branches exist in the bifurcation diagram where the aspect ratio is adopted as the bifurcation parameter. To examine an origin of the fold, we formally derived amplitude equations. An analysis of the amplitude equations shows that certain nonlinear solutions, realized under the crossing of neutral stability curves, are split into two groups in the presence of the avoided crossing and that the folded branch arises.