School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
IST Austria, 3400 Klosterneuburg, Austria.
Phys Rev E. 2018 Aug;98(2-1):023105. doi: 10.1103/PhysRevE.98.023105.
Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.
最近的研究表明，纳维-斯托克斯方程的不稳定、非混沌解可能为流体湍流提供深刻的见解。在本文中，我们提出了一个实验和数值相结合的研究，探索不稳定平衡解及其不变流形在弱湍流动、电磁驱动的浅层流体层中的动力学作用。通过识别当湍流演化减缓时的瞬间，我们计算了一个现实二维流动模型的 31 个不稳定平衡点。我们通过表明它们被湍流流动密切访问来证明这些不稳定平衡点的动力学相关性。我们还通过验证它们被从不稳定平衡点的邻域出发的、在状态空间中长距离离开的湍流轨迹所遮蔽来证明不稳定流形的动力学相关性。
