A low-Rayleigh transition into chaos for natural convection inside a horizontal annulus at Prandtl number 0.1. (November 2021) - Usman, Muhammad; Son, Jong Hyeon; Park, Il Seouk
Abstract: Instabilities in the flow of natural convection in a horizontal annulus of radius ratio 2 filled with fluid of Prandtl number 0.1 are investigated numerically. The investigation largely focuses on the very small range of Rayleigh numbers between 3, 500 and 5, 000 in which the equivalent thermal conductivity increases suddenly. Since this instability is quite uncommon and only occurs in a narrow range of Rayleigh numbers, previous studies have not concentrated on the mechanism behind it. However, the present numerical simulation with very fine increments in Rayleigh number reveals that the jump in equivalent conductivity is caused by a transition into chaos, and this transition is akin to the typical Ruelle-Takens-Newhouse and Pomeau-Manneville scenarios. As well, it is more interesting that the flow escapes out of chaos and re-stabilizes at around the Rayleigh number of 4, 800; it follows a reverse Pomeau-Manneville route. The progressions in the oscillatory pattern, power spectral density, and trajectories of equivalent conductivity in 2D and 3D phase spaces are plotted against the Rayleigh number in detail.