Solutions multiples et bifurcations des écoulements bidimensionnels de convection naturelle dans une cavité annulaire horizontaleMultiple solutions and bifurcations of two-dimensional natural convection flows in a horizontal annulus

A critical review of buoyancy-induced flow transitions in horizontal annuli

“…Detail of the bifurcation diagram near the imperfect transcritical bifurcation for the case Pr ¼ 0:7, R ¼ 1:2, as reported by Petrone et al[39]. The continuous and dashed lines indicate a stable and an unstable solution branch, respectively.Rothmayer and Fant[51] issued a stability condition relating the normalized gap spacing, H=r i , and the critical Grashof number, based on the inner radius Gr ri;c :…”

“…Mizushima et al [38] were the first to attempt a rigorous determination of the behaviour of the system near the bifurcation point, confirming that the dual solutions were due to an imperfect transcritical bifurcation. Petrone et al [39,40], performed a stability analysis of numerically obtained steady-state solutions, and concluded that, in the limit R/1, the imperfect transcritical bifurcation closes into the pitchfork bifurcation typical of the onset of RayleigheBénard convection, leading once again to the threshold value, Ra H;c ¼ 1708. In Fig.…”

“…In Fig. 7, a detail of the bifurcation diagram near the imperfect bifurcation is shown, for the case R ¼ 1:2 and Pr ¼ 0:7 [39].…”