@phdthesis{Shahirpour2024, author = {Shahirpour, Amir}, title = {A characteristic dynamic mode decomposition to detect transport-dominated large-scale coherent structures in turbulent wall-bounded flows}, doi = {10.26127/BTUOpen-6958}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-69583}, school = {BTU Cottbus - Senftenberg}, year = {2024}, abstract = {Large-scale energetic coherent structures are detected in turbulent pipe flow at shear Reynolds number of 181. They are distinguished by having long lifetimes, living on large scales and contributing prominently to the spectral peak in premultiplied spectra of streamwise velocity component. In order to investigate these structures in the absence of small scale perturbations, they are extracted from the underlying multi-scaled and complex turbulent flow. For this purpose, data-driven methods such as Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are suitable candidates as long as the structures are stationary in space and time. Nevertheless, the transport-dominated nature of structures in wall-bounded flows poses a major problem to application of such methods. Different instances of a structure travelling with a certain group velocity in space and time will be perceived as different modes. This results in poorly decaying singular values signifying that many modes will be required to describe a single structure. To remedy this issue a Characteristic DMD (CDMD) is developed showing that on a properly chosen frame of reference along the characteristics defined by the group velocity, a POD or DMD reduce the moving structures to a few modes. Reconstruction of the candidate modes in the spatio-temporal space and transforming them back to physical space gives the low rank model of the flow. The method is initially applied to the vortex head of a compressible starting jet as it offers a distinct coherent structure and therefore, can serve as a success measure of the method. The vortex head is described with a few modes only and it is shown that the dynamics associated with the modes are detected more accurately on a moving frame. In the next step the developed method is applied to the data from Direct Numerical Simulations (DNS) and a low dimensional subspace is extracted out of highly complex turbulent pipe flow. The essential features of the flow such as spectral energy and Reynolds stresses are captured in a subspace with only 3\% of the modes. The structures living in this subspace have long lifetimes, possess wide range of length-scales and travel at group velocities close to that of the moving frame of reference. Having a significantly lower degree of freedom, the detected low rank subspace offers a more clear basis for capturing large-scale persistent structures. Aiming at separating the scales, a second spatio-temporal decomposition is applied to the low rank subspace, normal to the direction of characteristics. A secondary subspace is formed comprising of the modes with large scales using only 10\% of the new modes. Investigating the spectral and turbulent properties of the mentioned subspace, shows that it accommodates the near-wall streaks. The captured streaks show a significant contribution to the spectrum of streamwise velocity component and very low contributions to the spectra ofradial and azimuthal components. The developed CDMD proves to be an effective tool to detect and identify the large-scale coherent structures in wall-bounded turbulent flows.}, subject = {Coherent structures; Dynamische Modenzerlegung; Turbulent wall-bounded flows; Dynamic Mode Decomposition; Koh{\"a}rente Stukturen; Turbulente wandbegrenzte Str{\"o}mungen; Turbulente Str{\"o}mung; Rohrstr{\"o}mung; POD-Methode; Direkte numerische Simulation}, language = {en} }