Transition to the chaotic state of the convective flows on a hot cone

Abstract

A transition to the chaotic state of the convective flows on a hot cone is investigated using three-dimensional numerical simulation. A wide range of the Rayleigh number from Ra =  100 to 107 for the Prandtl number of Pr =  7 and the aspect ratio of A =  0.1 is considered. Numerical results reveal a complex transition route to the chaotic state of the convective flows with a succession of Hopf, period-doubling, and quasiperiodic bifurcations; the transition to a chaotic state followed by a succession of inverse quasiperiodic and inverse period-doubling bifurcations; and a succession of period-doubling and quasiperiodic bifurcations and the transition to chaotic state again. Typical flows in the transition are characterized and analyzed using spectral analysis, the trajectory, the largest Lyapunov exponent, and the fractal dimension. Further, heat transfer in the transition is calculated, and the scaling relation is obtained.