Forecasting Fluid Flows Using the Geometry of Turbulence
Forecasting Fluid Flows Using the Geometry of Turbulence
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DOI：
10.1103/physrevlett.118.114501
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发表时间：
2017-03-15
影响因子：
8.6
通讯作者：
Schatz, Michael F.
中科院分区：
文献类型：
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作者：
Suri, Balachandra;Tithof, Jeffrey;Schatz, Michael F.
在稀薄的电磁驱动流体层的弱湍流的实验室研究中揭示了Navier-Stokes方程的特殊不稳定解（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许多不稳定平衡解的明确特征，这些解是使用实验中的流量测量和完全解决的数值模拟相结合计算的。我们通过展示湍流反复访问其状态空间邻域来证明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联的不稳定流形在实验和模拟中预测了相当长一段时间内湍流的演变。
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.