Appearance of quasiperiodicity within a period doubling route to chaos of a swaying thermal plume

The birth, evolution and disappearance of quasiperiodic dynamics in buoyancy-driven flow arising from an enclosed horizontal cylinder are analysed here, by numerical means, in the limit of the 2D approximation. The governing equations are solved on orthogonal Cartesian grids, giving special treatment to the internal, non-aligned boundaries. Thanks to the adoption of a high level of re finement of the Rayleigh number range, quasiperiodicity was observed to emerge from a periodic limit cycle (P1), and to turn into its omologous orbit with doubled period (P2), eventually evolving into a classical period-doubling route to chaos, for further increases of the Rayleigh number. The present study gives a deeper insight to what appears to be an imperfect period doubling bifurcation through a quasiperiodic T2-torus. The approach used is based on the classical tools for time series analysis. The distribution of the power spectral densities is used to search for and characterise the existence of relations between the frequencies of the P1, T2 and P2 dynamics. The topology of the orbits, as well as their evolution within the quasiperiodic window, are analysed with the aid of phase space representation and Poincar è maps.