University of Brasília (UnB), Faculty UnB-Gama, and Plasma Physics Laboratory, Institute of Physics, Brasília, DF 70910-900, Brazil.
Chaos. 2013 Sep;23(3):033107. doi: 10.1063/1.4811297.
We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.
我们研究了具有周期边界条件和外部强迫项的二维不可压缩纳维-斯托克斯方程中的超混沌转变。通过改变雷诺数构建分岔图，并确定超混沌（HC）的转变。在 HC 发生之前，存在两个混沌吸引子和一个超混沌鞍的共存。HC 发生后，两个混沌吸引子与超混沌鞍合并，导致混沌和超混沌之间的随机切换，这是能量和涡度时间序列中间歇性爆发的原因。通过检测拉格朗日相干结构来描述流的混沌混合特性。HC 发生后，流显示出复杂的拉格朗日模式，并且在爆发期间的拉格朗日混沌水平增加，这可以通过 HC 转变之前的超混沌鞍进行统计预测。
