Suri Balachandra, Tithof Jeffrey, Grigoriev Roman O, Schatz Michael F
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA.
Phys Rev Lett. 2017 Mar 17;118(11):114501. doi: 10.1103/PhysRevLett.118.114501. Epub 2017 Mar 15.
The existence and dynamical role of particular unstable solutions (exact coherent structures) of the Navier-Stokes equation is revealed in laboratory studies of weak turbulence in a thin, electromagnetically driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.
在一个薄的、电磁驱动的流体层中弱湍流的实验室研究中，揭示了纳维 - 斯托克斯方程特定不稳定解（精确相干结构）的存在及其动力学作用。我们发现，动力学表现出众多不稳定平衡解的清晰特征，这些解是通过结合实验中的流动测量和完全解析的数值模拟计算得出的。我们通过表明湍流反复访问其状态空间邻域，证明了这些解的动力学重要性。此外，我们发现与一个这样的不稳定平衡相关的不稳定流形在相当长的一段时间内预测了实验和模拟中湍流的演化。
