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

在这项工作的前半部分，我们使用拉格朗日框架讨论与振荡流体有关的能量流动和转换。修正了熵振荡的讨论，包括振荡流体与固壁之间的换热讨论。该理论定性地给出了自激振动的稳定性极限。在后半部分，我们报道了在热声系统中观察到的强非线性现象的实验结果。引起人们兴趣的流体动力学系统，在低温中被称为“T aconis振荡”，它是由大的温度梯度引起的气柱的自发声振荡。在适当的条件下，两个或三个不同振荡模式的稳定性曲线相交。在重叠区和稳定性曲线的交点附近，我们发现可以同时激发三个或两个频率不相称的不同模，它们之间的竞争导致了两条路径、两个频率和三个频率准周期的混沌振荡。具有极限环的Taconis振动被外部控制的幅度和频率的机械力周期性地摄动。我们发现，在适当的条件下，两个振动模之间的非线性耦合导致了准周期、频率锁定和混沌的开始。确定了准周期向混沌转变的全局普适性和局部普适性，并与圆映射普适性进行了比较。我们给出了一些普遍标度性质的实验证据，以支持MAP对热声系统的适用性。实验表明，尽管热声系统很复杂，但它与简单圆映象属于同一普适类，至少在混沌开始时是这样。

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.