论文标题
$ l_1 $ $基于二维动荡流中能量互动的稀疏
$l_1$-based sparsification of energy interactions in two-dimensional turbulent flows
论文作者
论文摘要
在本文中，采用促稀疏回归技术从数据相关的三维模型中的模态结构之间的模态结构之间自动识别。该方法产生了可解释的，稀疏的连接模型，这些模型以较低的计算成本重现原始动力学行为，因为需要评估的三合会相互作用更少。该方法的关键特征是，从凸优化问题的解决方案的解决方案中系统地选择了主要的交互，并且具有独特的解决方案，并且不需要对比例相互作用结构的先验假设。我们在雷诺数$ re = 2 \ times 10^4 $的二维盖驱动腔流量的模型上证明了这种方法，其中流体运动是混乱的。为了了解用于毛素投影对稀疏特性的子空间的作用，我们考虑了从两种不同的模态分解技术获得的两个模型家族。第一个使用最佳的适当正交分解模式，而第二种模式使用流量快照的离散傅立叶变换获得的单个频率振荡。我们表明，在这两种情况下，尽管没有\ textit {a-priori}的物理知识纳入了该方法，但模式层次结构之间的相关相互作用与二维湍流中规模相互作用的预期图片一致。然而，观察到相互作用模式的实质性结构变化和定量不同的稀疏性。最后，尽管该过程中未直接执行，但稀疏的模型具有出色的长期稳定性，并正确地重现了空腔中主要流动结构的时空演化。
In this paper, sparsity-promoting regression techniques are employed to automatically identify from data relevant triadic interactions between modal structures in large Galerkin-based models of two-dimensional unsteady flows. The approach produces interpretable, sparsely-connected models that reproduce the original dynamical behaviour at a much lower computational cost, as fewer triadic interactions need to be evaluated. The key feature of the approach is that dominant interactions are selected systematically from the solution of a convex optimisation problem, with a unique solution, and no a priori assumptions on the structure of scale interactions are required. We demonstrate this approach on models of two-dimensional lid-driven cavity flow at Reynolds number $Re = 2 \times 10^4$, where fluid motion is chaotic. To understand the role of the subspace utilised for the Galerkin projection on sparsity characteristics, we consider two families of models obtained from two different modal decomposition techniques. The first uses energy-optimal Proper Orthogonal Decomposition modes, while the second uses modes oscillating at a single frequency obtained from Discrete Fourier Transform of the flow snapshots. We show that, in both cases, and despite no \textit{a-priori} physical knowledge is incorporated into the approach, relevant interactions across the hierarchy of modes are identified in agreement with the expected picture of scale interactions in two-dimensional turbulence. Yet, substantial structural changes in the interaction pattern and a quantitatively different sparsity are observed. Finally, although not directly enforced in the procedure, the sparsified models have excellent long-term stability properties and correctly reproduce the spatio-temporal evolution of dominant flow structures in the cavity.
