A Characteristic Dynamic Mode Decomposition to Detect Transport-dominated Large-scale Coherent Structures in Turbulent Wall-bounded Flows
Date and Time: TBA
Speaker: Dr. Amir Shahirpour
Topic: A Characteristic Dynamic Mode Decomposition to Detect Transport-dominated Large-scale Coherent Structures in Turbulent Wall-bounded Flows
Abstract: A Characteristic DMD (CDMD) is developed to capture transport dominated energetic coherent structures in turbulent flows. It is shown that on a properly chosen frame of reference along the characteristics defined by a group velocity, a POD or DMD capture the convecting structures in a subspace defined by a minimal number of modes. To this end, a temporal sequence of state vectors from direct numerical simulations or time resolved experimental measurements are rotated in space-time such that persistent dynamical modes are found on a plane travelling along its normal in space and time. The latter serves as a new time-like coordinate and the transformed spatial coordinate will serve as a new streamwise coordinate. 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 applied to the data from direct numerical simulations and a low dimensional subspace is extracted out of turbulent pipe flow. The velocity of the reference frame matches that of the most energetic scales. 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 modes within this subspace form small angles with one another and large ones with the modes outside the subspace. 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. The remaining modes are grouped in two further subspaces distinguished by their axial length scales and degree of isotropy. 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. Inspecting the angles between each mode pair and selecting highly aligned energetic modes, a distinct separation between large and small scales emerges. 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. Given the low Reynolds number studied, the outer layer structures are not formed and the near-wall streaks are the only structures expected to exist in the flow. The captured streaks show a significant contribution to the spectrum of streamwise velocity component and very low contributions to the spectra of radial 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.