Etikyala S, Sujith R I
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Chaos. 2017 Feb;27(2):023106. doi: 10.1063/1.4975822.
In this paper, we report on the existence of the phenomenon of change of criticality in a horizontal Rijke tube, a prototypical thermoacoustic system. In the experiments, the phenomenon is shown to occur as the criticality of the Hopf bifurcation changes with varying air flow rates in the system. The dynamics of a nonlinear system exhibiting Hopf bifurcation can be described using a Stuart-Landau equation (SLE) in the vicinity of the bifurcation point. The criticality of Hopf bifurcations can be determined by the Landau constant of the Stuart-Landau equation, which represents the effect of nonlinearities in the system. We propose an SLE to model the bifurcations seen in the horizontal Rijke tube. We identify a rescaled version of Strouhal number as the Landau constant, which determines the criticality of the bifurcation in the present study.
在本文中，我们报告了在一个典型的热声系统——水平瑞利管中存在临界性变化现象。在实验中，该现象表现为随着系统中空气流速的变化，霍普夫分岔的临界性发生改变。在分岔点附近，呈现霍普夫分岔的非线性系统的动力学可以用斯图尔特 - 朗道方程（SLE）来描述。霍普夫分岔的临界性可由斯图尔特 - 朗道方程的朗道常数确定，该常数代表了系统中非线性的影响。我们提出一个斯图尔特 - 朗道方程来对水平瑞利管中观察到的分岔进行建模。我们确定了斯特劳哈尔数的一个重新标度版本作为朗道常数，它决定了本研究中该分岔的临界性。
