Homoclinic bifurcations in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

Abstract

We present results of direct numerical simulations on homoclinic gluing and ungluing bifurcations in a low-Prandtl-number () Rayleigh-Bénard system rotating slowly and uniformly about a vertical axis. We have performed simulations with stress-free top and bottom boundaries for several values of the Taylor number () near the instability onset. We observe a single homoclinic ungluing bifurcation, marked by the spontaneous breaking of a larger limit cycle into two limit cycles with the variation of the reduced Rayleigh number r for smaller values of . A pair of homoclinic bifurcations, instead of one bifurcation, is observed with the variation of r for slightly higher values of Ta () in the same fluid dynamical system. The variation of the bifurcation threshold with Ta is also investigated. We have also constructed a low-dimensional model which qualitatively captures the dynamics of the system near the homoclinic bifurcations for low rotation rates. The model is used to study the unfolding of bifurcations and the variation of the homoclinic bifurcation threshold with Pr.