B121 熱対流における固有値の反発

概要

論文の詳細を見る
Linear stability analysis gives infinite number of eigenvalues for instability problems in continuous media. For the onset of thermal convection in a rectangular cavity heated from below, a number of Rayleigh numbers are obtained as solutions of an eigenvalue problem, each of which corresponds to different instability modes. The Rayleigh numbers give the critical value above which the each mode becomes unstable and the value changes with the change of the aspect ratio of the cavity. The curves of the critical values of the Rayleigh number plotted against the aspect ratio are called neutral curves. The neutral curves intersect each other for infinitely extended fluid layer, but do not intersect for finite lengths of rectangular cavity. The origin of non-intersections (repulsions) of the eigenvalues are explored by considering partially non-slip side boundaries and by applying an purturbation analysis, which is formulated in double expansions of the aspect ratio and a parameter which manifest the magnitude of non-slip condition at the side bounaries.
日本流体力学会の論文
2000-07-25