Evolution to aperiodic penetrative convection in odd shaped rectangular enclosures

Abstract

The purpose of this numerical study is to analyse the character of transition from laminar to chaotic convection in a fluid layer bounded by no‐slip walls in two space dimensions for varying aspect ratio odd‐shaped enclosures consisting of two rectangular chambers, with a linking horizontal enclosure. For a medium Prandtl number fluid (Pr=7), the numerical solution of two‐dimensional Navier‐Stokes momentum and energy equations with Bousinessq approximation has been carried out. It has been found that there are finite Rayleigh numbers Ra₁, Ra₂ and Ra₃ for the onset of single, two and multiple frequency oscillatory motion at different spatial locations in the enclosure. As Ra is further increased period doubling is observed. The onset of strong chaos appears when Ra=Ra₃. This system does not revert to steady state convection at high Ra as observed by other researchers for the case of Rayleigh‐Benard convection. Moreover, the period doubling transition process is consistent with the scenario of Ruelle, Takens and Newhouse. As Ra increases, the power spectrum, and time series of various dynamical variable signals, etc. all show an increasing degree of characteristics of chaos.

Citation

Hasan, N. and Baig, F.M. (2002), "Evolution to aperiodic penetrative convection in odd shaped rectangular enclosures", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 12 No. 8, pp. 895-915. https://doi.org/10.1108/09615530210448697