Stability limit for a self-excited oscillation due to thermoacoustic effect.

在前半部分，我们讨论了能量流动和转换与振荡流体使用的拉格朗日框架。修正了熵振荡的讨论，包括振荡流体与固壁之间的热交换。利用该理论定性地给出了自激振荡的稳定极限。在后半部分中，我们报告了在热声系统中观察到的强非线性现象的实验结果。引起我们兴趣的流体动力学系统，在低温学中被称为“T aconis振荡”，是由大的温度梯度引起的气体柱的自发声振荡。在适当的条件下，两个或三个不同振荡模式的稳定性曲线会相交。在重叠区域和稳定性曲线的交点附近，可以同时激发出三个或两个不同的无公度频率的模，它们之间的竞争通过两条途径，即双频准周期和三频准周期，导致混沌振荡.具有极限环的Taconis振荡被具有振幅和频率的外部控制的机械力周期性地扰动。我们发现，两个振荡模式之间的非线性耦合导致准周期，频率锁定和混沌的发病适当的条件。确定了拟周期向混沌过渡的全局和局部普适性，并与圆映射普适性进行了比较。我们提出了一些实验证据，有利于普遍的标度特性的适用性的地图热声系统。实验表明，热声系统属于相同的普适类的简单圆映射，至少到混沌的开始，尽管系统的复杂性。

In the first half of this work we discuss about energy flows and conversions associated with oscillating fluid using the Lagrange frame. Discussion of entropy oscillations is corrected including that of heat exchange between oscillating fluid and solid wall. Stability limit for a self-excited oscillation is qualitatively given by this theory. In the latter half we report experimental results of strongly nonlinear phenomena observed in a thermoacoustic system. The hydrodynamic system attracting our interest, called "T aconis oscillation" in cryogenics, is a spontaneous acoustic oscillation of a gas column induced by large temperature gradients. Stability curves for two or three diferent oscillatory modes intersect with each other for proper conditions. Near the overlapped region and the intersection of the stability curves we find that three or two different modes with incommensurate frequencies can be excited simultaneously, and that competition between them leads to chaotic oscillations through two routes, two-frequency and three-frequency quasiperiodicities. Taconis oscillation with a limit cycle is periodically perturbed by a mechanical force with the amplitude and frequency externally controlled. We find that nonlinear coupling between two oscillating modes leads to quasiperiodicities, frequency-lockings and the onset of chaos for suitable conditions. The global and local universal properties for the quasiperiodic transition to chaos are determined and compared with the circle map universality. We present some experimental evidence for universal scaling properties in favor of the applicability of the map to thermoacoustic systems. The experiment demonstrates that the thermoacoustic system belongs to the same universality class as the simple circle map, at least up to the onset of chaos, in spite of the complexity of the system.