Identification of transport-dominated large-scale structures in turbulent wall-bounded flows using a Characteristic DMD

大型相干结构是湍流中的有组织的运动。条理性--或连贯性--指的是空间和时间上的运动，当我们的大脑看到湍急的流动时，很容易就能发现这一点。这些结构对湍动能、弥散质量和动量有显著贡献。因此，它们在流动中会产生很大的可取或不可取的效果，如更好的混合或更大的阻力。尽管在过去的十年里有许多研究来了解它们的物理性质，以及我们用肉眼很容易就能发现它们，但科学界对于如何定义这些结构，它们的物理外观，它们的寿命有多长，以及长度尺度如何取决于雷诺数，仍然存在有限的共识。我们不知道它们以什么为食，它们的再生机制是如何工作的，它们是如何相互作用或与近壁湍流相互作用的。本研究的主要目的是从高度复杂的湍流流场中提取低维子空间，以满足我们对大型相干结构的直观理解。特别是，生活在这些子空间中的结构应该有很长的寿命，以大规模的方式生活，并以一定的群速度移动。为此，来自dns或时间分辨测量的状态向量的时间序列将被变换，以便我们在移动的参照系上找到沿其法线在空间和时间上传播的超曲面上的持久动力学模式。从技术上讲，我们在空间和时间上旋转流场，并对变换后的数据进行动态模式分解(DMD)，以捕捉具有小衰减或增长率的模式。将候选模沿法线重构到超曲面，并将它们转换回物理空间，得到了流动的低阶模型。接下来，我们以同样的方式观察下一个最大的群体的流动，并预测出这些模式。这就给出了结构的层次结构。同样，在实际中，我们的目标是分离大的相干结构、相干结构和非相干剩余部分。该方法将应用于两个正则湍流。所产生的结构将通过验证大规模相干结构在可由它们再现的预乘能谱中的足迹来对照物理证据进行测试。每个结构将分别从其寿命、时空演变、长度尺度和湍流特性方面进行研究。将每一个连贯的结构或其中一组结构作为域名系统的初始条件，将提供独特的机会，在没有小尺度特征和不稳定性的情况下观察每组结构的演变和自我可持续性。我们验证了大尺度运动是否在没有小尺度结构的情况下仍然存在，或者它们是否以后向散射为食。

Large Coherent structures are organized motions in turbulent flows. The organization – or coherence - refers to movements in space and time, which our brains easily spot when looking a turbulent flow. These structures contribute prominently to the turbulent kinetic energy and diffuse mass and momentum. Therefore, they come with large desirable or undesirable effects in the flow, like better mixture or more drag. Despite many studies in the last decade to understand their physical properties and the ease with which we spot them by the naked eye, there is still limited consensus in the scientific community on how to define these structures, what they physically look like, how long they live and how length scales depend on Reynolds numbers. We do not know what they feed on, how their regeneration mechanism works and how they interact with each other or with near wall turbulence.The main objective of this study is to extract low dimensional subspaces out of highly complex turbulent flow fields, which meet our intuitive understanding of large coherent structures. In particular the structures living in these subspaces shall have a long lifetime, live on large scales and travel with a certain group velocity. To this end, a temporal sequence of state vectors from DNS or time-resolved measurements, will be transformed such that we find a persistent dynamical mode on a hypersurface traveling along its normal in space and time on a moving frame of reference. Less technically speaking, we rotate the flow fields in space and time and carry out a Dynamic Mode Decomposition (DMD) on the transformed data, to capture the modes possessing small decay or growth rates. Reconstruction of the candidate modes along the normal to the hypersurface and transforming them back to physical space gives the low rank model of the flow. Next, we look at the flow in the same way for the next largest group with those modes projected out. This gives a hierarchy of structures. Again, in practical terms, we aim to separate large coherent structures, coherent structures, and an uncoherent remaining rest.The method will be applied to two canonical turbulent flows. The resulting structures will be tested against physical evidence, by verifying that the footprints of large-scale coherent structures in premultiplied energy spectra that can be reproduced by them. Each structure will be studied separately in terms of their lifetimes, spatiotemporal evolution, length scales and turbulent properties. Implementing each coherent structure or group of them as initial condition for a DNS, will provide the unique chance to observe evolution and self- sustainability of each set of structures, in absence of small-scale features and instabilities. We verify whether the large-scale motions survive in absence of small-scale structure or whether they feed on backscatter.