A peculiar bifurcation transition route of thermocapillary convection in rectangular liquid layers

Transition routes of thermocapillary convection are complex and diversiform in rectangular layers. In general, three types of transition routes were observed in thermocapillary convection, including quasi-periodic bifurcations, period-doubling bifurcations and tangent bifurcations. The tangent bifurcation is a peculiar type of bifurcations, which often appears accompanied with other types of bifurcation sequences. In our experiments, a detailed research on tangent bifurcations of thermocapillary convection in rectangular liquid layers was conducted through the measurement of single-point temperature oscillation in liquid. There are different tangent bifurcation series for various of experimental conditions, including different Prandtl numbers of silicone oil and different aspect ratios. It has certain occasionality for appearance of the tangent bifurcation, mainly in the experimental condition of Prandtl number of silicone oil equal to 16 (1 cSt) or Prandtl number equal to 25 (1.5 cSt). Chaotic characteristics of bifurcations are investigated by the method of phase-space reconstruction, maximum Lyapunov exponent and permutation entropy.