立方体中における高プラントル流体の自然対流 : 疑似スペクトル法による数値実験

概要

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Thermal convection of fluids heated from below occurs when the Rayleigh number becomes greater than a critical value. In general, convection gradually evolves to complex, often time-dependent, states as the Rayleigh number increases. The process involves various forms of transition, such as from one convecting pattern to another, steady to time dependent and simply periodic to chaotic oscillation. The present research focuses on an evolution process of infinite Pr convection in a cubical geometry with stress-free boundary conditions. The numerical computations have been carried out up to Ra = 2×10^5 using an efficient scheme based on the pseudospectral method. With increasing Ra, a convecting pattern starts losing its symmetries at about Ra = 7×10^4, but does not evolve to time-dependent states. Effects of truncation number on the numerical accuracy are also investigated. For example, a truncation number of N = 12 is adequate at Ra = 10^4, while N = 16 is needed at Ra = 10^5. The Nusselt number appears to grow at a rate of Ra^<1/3> when Ra exceeds 10^4, suggesting the formation of distinct thermal boundary layers.
社団法人日本機械学会の論文
1990-09-25