多孔介质中的双稳热对流

对矩形横截面多孔介质中热对流的复杂分岔行为──二次分岔进行研究．使用Ｌｉａｐｕｎｏｖ－Ｓｃｈｍｉｄｔ约化并充分利用问题本身的对称性，研究了于最低的两个不同临界Ｒａｙｌｅｉｇｈ数处从平凡的静态传热解产生的热对流主分岔解之间的相互作用；揭示了主分岔解的二次分岔并给出了主分岔解及二次分岔解的渐近展开．稳定性分析表明从第二临界Ｒａｙｌｅｉｇｈ数产生的主分岔解经二次分岔后由不稳定变得稳定，从而与由最小临界Ｒａｙｌｅｉｇｈ数产生的主分岔解组成双稳定热对流．文中理论分析可较恰当地解释已有的数值模拟结果．

BISTABLE STATES OF THERMAL CONVECTIONAL FLOW IN POROUS MEDIA

The behaviour of bifurcations for thermal convectional flow in porous media, with respect to two parameters: bifurcational Rayleigh number and auxiliary aspect ratio of rectangular porous media, is studied. Attention is focused on those values of the aspect ratio at which, the two lowest critical Rayleigh numbers are near each other. We found the secondary bifurcation of the thermal convectional flow by means of the Liapunov-Schmidt reduction, and give the asymptotical expansions of the primary and secondary branches of these steady solutions. The analysis of stabilities indicates that the primary branch bifurcated from the secondary critical point becomes stable from unstable if the secondary bifurcation point is stridden. Thus this branch and the stable primary branch developed from the first critical point form bistable states of thermal convectional flow.