Features of a blue-sky transition in an autonomous convective flow

Abstract

The nonlinear dynamics of a buoyant air flow in the gap formed by a horizontal cylindrical heat source and a concentric isothermally cooled square enclosure have been recently studied, in the limits of a two-dimensional approximation, for different values of the system aspect ratio, defined as the ratio between the cavity side length and the minimum gap width. Accurate analyses have revealed that, for low values of the aspect ratio, the dominant pattern is the swaying motion of a buoyant plume, which undergoes a period-doubling cascade for increasing values of the Rayleigh number. On the other hand, a substantially different behaviour has been preliminarily observed for higher values of the aspect ratio, since, in a thinner gap, the flow exhibits Rayleigh-Bénard-like cellular patterns above the cylinder.The aim of this communication is to describe the peculiar route to chaos which has been detected for this second type of geometry. The scenario consists in the progressive winding of a periodic limit cycle on an attractor whose topology resembles that of a French horn, which is a typical signature of the codimension-2 Shilnikov bifurcation from periodic dynamics to chaos. A similar feature, known as the blue-sky catastrophe, has never been reported so far for confined convection of pure fluids.