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

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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.