Net Marta, Sánchez Umbría Juan
Departament de Física, Universitat Politècnica de Catalunya. Jordi Girona Salgado 1-3, Campus Nord, Mòdul B4, 08034 Barcelona, Spain.
Phys Rev E. 2017 Feb;95(2-1):023102. doi: 10.1103/PhysRevE.95.023102. Epub 2017 Feb 2.
This study elucidates the origin of the multiplicity of stable oscillatory flows detected by time integration in tall rectangular cavities heated from the side. By using continuation techniques for periodic orbits, it is shown that initially unstable branches, arising at Hopf bifurcations of the basic steady flow, become stable after crossing Neimark-Sacker points. There are no saddle-node or pitchfork bifurcations of periodic orbits, which could have been alternative mechanisms of stabilization. According to the symmetries of the system, the orbits are either fixed cycles, which retain at any time the center symmetry of the steady flow, or symmetric cycles involving a time shift in the global invariance of the orbit. The bifurcation points along the branches of periodic flows are determined. By using time integrations, with unstable periodic solutions as initial conditions, we determine which of the bifurcations at the limits of the intervals of stable periodic orbits are sub- or supercritical.
本研究阐明了在从侧面加热的高矩形腔中通过时间积分检测到的多种稳定振荡流的起源。通过使用周期轨道的延拓技术，结果表明，在基本稳态流的霍普夫分岔处出现的初始不稳定分支，在穿过奈马克 - 萨克分岔点后变得稳定。不存在周期轨道的鞍结或叉形分岔，而这些本可能是稳定的替代机制。根据系统的对称性，轨道要么是固定周期，在任何时候都保持稳态流的中心对称性，要么是涉及轨道全局不变性中时间偏移的对称周期。确定了沿周期流分支的分岔点。通过将不稳定周期解作为初始条件进行时间积分，我们确定了稳定周期轨道区间极限处的哪些分岔是亚临界或超临界的。
