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

在本文的前半部分，我们用拉格朗日框架讨论了与振荡流体相关的能量流动和转换。修正了熵振荡的讨论，包括振荡流体与固体壁面之间的热交换。该理论定性地给出了自激振荡的稳定极限。在后半部分，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系统，在低温学中称为“T - aconis振荡”，是由大温度梯度引起的气柱自发声波振荡。在适当的条件下，两种或三种不同振荡模式的稳定性曲线相互相交。在稳定性曲线的交点和重叠区域附近，我们发现三种或两种不同频率的模态可以同时被激发，并且它们之间的竞争导致混沌振荡通过两频和三频准周期两条路径。具有极限环的塔康尼斯振荡周期性地受到振幅和频率由外部控制的机械力的扰动。我们发现两个振荡模式之间的非线性耦合导致准周期性、频率锁定和在适当条件下发生混沌。确定了准周期过渡到混沌的全局和局部泛性，并与圆映射的泛性进行了比较。我们提出了一些普遍标度特性的实验证据，支持该图对热声系统的适用性。实验表明，尽管热声系统很复杂，但至少在混沌开始之前，它与简单的圆图属于相同的普适类。

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.