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arXiv 0904.2764physics.flu-dyn
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剪切流转换:盆地边界

Shear-flow transition: the basin boundary

Norman Lebovitz

摘要:

研究了常用于模拟剪切流中湍流转捩的动力系统(W97)的稳定平衡点吸引域的结构。盆地边界不仅包含一个平衡点Xlb,而且还包含一个周期轨道P,而正是后者介导了过渡。从Xlb附近开始的轨道重新层压。我们提供的证据表明,这是由于极端狭窄的区域互补盆地的吸引力在相空间的一部分XLB附近。这导致了一个建议,解释“混乱的边缘”方面更熟悉的不变集。

英文摘要:

The structure of the basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) often used to model transition to turbulence in shear flows. The basin boundary contains not only an equilibrium point Xlb but also a periodic orbit P, and it is the latter that mediates the transition. Orbits starting near Xlb relaminarize. We offer evidence that this is due to the extreme narrowness of the region complementary to basin of attraction in that part of phase space near Xlb. This leads to a proposal for interpreting the 'edge of chaos' in terms of more familiar invariant sets.

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