Surfing the edge: using feedback control to find nonlinear solutions
Surfing the edge: using feedback control to find nonlinear solutions
复制标题
冲浪边缘：使用反馈控制寻找非线性解决方案
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
M. Wolfrum
中科院分区：
文献类型：
--
作者：
A. Willis;Y. Duguet;O. Omel’chenko;M. Wolfrum
许多过渡的壁面剪切流的特征是在状态空间中层流和湍流共存。在过去的十年中，探测两个吸引子之间的边缘边界导致了不可压缩Navier-Stokes方程新（不稳定）解的数值发现。然而，用于计算边缘状态的迭代二分法对于大型系统来说可能变得过于昂贵。在这里，我们提出了一个简单的反馈控制策略，以稳定边缘状态，从而加快了几个数量级的数值识别。该方法被示出为几种配置的圆柱管流。行波解被识别为边缘状态，并且可以在仅一个短的数值运行中被快速地隔离。一个新的分支的解决方案也被确定。当边缘状态是周期轨道或混沌状态时，反馈控制并不精确地收敛到不受控系统的解，但在单次运行中仍然使动力学非常接近原始边缘流形。我们讨论了这种新方法的速度和简单性所提供的机会，以探测状态空间和参数空间的结构。
Many transitional wall-bounded shear flows are characterised by the coexistence in state space of laminar and turbulent regimes. Probing the edge boundary between the two attractors has led in the last decade to the numerical discovery of new (unstable) solutions to the incompressible Navier–Stokes equations. However, the iterative bisection method used to compute edge states can become prohibitively costly for large systems. Here we suggest a simple feedback control strategy to stabilise edge states, hence accelerating their numerical identification by several orders of magnitude. The method is illustrated for several configurations of cylindrical pipe flow. Travelling waves solutions are identified as edge states, and can be isolated rapidly in only one short numerical run. A new branch of solutions is also identified. When the edge state is a periodic orbit or chaotic state, the feedback control does not converge precisely to solutions of the uncontrolled system, but nevertheless brings the dynamics very close to the original edge manifold in a single run. We discuss the opportunities offered by the speed and simplicity of this new method to probe the structure of both state space and parameter space.
影响因子：
8.6
作者：
J. Sieber;O. Omel’chenko;M. Wolfrum
通讯作者：
J. Sieber;O. Omel’chenko;M. Wolfrum
优化能量增长作为寻找精确相干结构的工具
影响因子：
2.7
作者：
Olvera D
通讯作者：
Olvera D
影响因子：
3.7
作者：
Chandler, Gary J.;Kerswell, Rich R.
通讯作者：
Kerswell, Rich R.