Rayleigh-Bénard对流同宿分岔附近的斑图动力学
Pattern dynamics near homoclinic bifurcation in Rayleigh-Bénard convection
摘要：
本文首次报道了扩展耗散系统中逆同宿分支附近的斑图动力学。我们观察到，在三维Rayleigh-Bénard对流的直接数值模拟中，当Rayleigh数提高到临界值以上时，两组相互垂直的振荡交叉辊竞争到两组可能的振荡交叉辊中的一组的自发破裂。横滚模式的时间周期发散，并在分叉点附近表现出标度行为。这是一个例子，从非局部到局部模式动力学附近的逆同宿分岔。我们还提出了一个简单的四模式模型，捕捉模式动态相当不错。
英文摘要：
We report for the first time the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-Bénard convection, a spontaneous breaking of a competition of two mutually perpendicular sets of oscillating cross rolls to one of two possible sets of oscillating cross rolls as the Rayleigh number is raised above a critical value. The time period of the cross-roll patterns diverges, and shows scaling behavior near the bifurcation point. This is an example of a transition from nonlocal to local pattern dynamics near an inverse homoclinic bifurcation. We also present a simple four-mode model that captures the pattern dynamics quite well.
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