State space representation and scaling of different flow regimes in MFU plane Poiseuille flow
Résumé
This study is devoted to the structure of the phase space associated with a minimal flow unit (MFU) of plane Poiseuille flow in a numerical set-up similar to that introduced originally by Jiménéz and Moin (1991). Invariant sets such as edge states and unstable travelling waves are identified. Turbulent activity is observed to randomly switch from one wall to the opposite one. Such structures are characterised using properly designed symmetry variables. The phase space is visualised using these symmetry-based projections revealing how the invariant sets structure the turbulent dynamics. Finally, we investigate whether these invariant sets obey an inner unit scaling (as is the case for turbulent fluctuations) or an outer scaling, as implied in most investigations of exact coherent states in other wall-bounded shear flows.