Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.
Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.
复制标题
二维纳维-斯托克斯方程中超混沌开始时的拉格朗日相干结构。
作者：
R. Miranda;E. Rempel;A. Chian;N. Seehafer;B. Toledo;P. R. Muñoz
研究了具有周期边界条件和外强迫项的二维不可压Navier-Stokes方程的超混沌相变。通过改变雷诺数建立了分叉图，并识别了向超混沌(HC)的转变。在HC爆发之前，存在两个混沌吸引子和一个超混沌鞍点共存。在过渡到HC后，两个混沌吸引子与超混沌鞍子合并，产生混沌和超混沌之间的随机切换，这是能量和拟能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表征流体的混沌混合特性。在向HC转变后，流体表现出复杂的拉格朗日模式和突发期拉格朗日混沌程度的增加，这可以通过HC转变之前的超混沌鞍点来统计地预测。
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.