Studies on mathematical aspect of the onset of thermal convection and chaotic mixing

研究了矩形水平或倾斜容器内流体热对流的开始。在这里，容器的所有壁面都具有良好的导热性能，外部温度场呈线性向上递减。通过数值分析，阐明了临界瑞利数Rc和最不稳定模式的流动结构与容器的高宽比和倾角的关系。此外，还阐明了流体颗粒在最不稳定模式速度场中的轨迹特征。

Onset of thermal convection of a fluid in a rectangular horizontal or inclined container is examined. Here all the walls of container are of perfect thermal conductance, and external temperature field is linearly decreasing upward. By a numerical analysis, the dependences of critical Rayleigh number Rc and the flow structure of most unstable mode on the aspect ratios and inclination angles of container are clarified. Moreover, the characteristics of trajectories of fluid particles in the velocity field of most unstable mode are clarified.