Momentum transfer by linearised eddies in channel flows

Abstract: The presence and structure of an Orr-like inviscid mechanism is studied in fully developed, large-scale turbulent channel flow. Orr-like `bursts' are defined by the relation between the amplitude and local tilting angle of the wall-normal velocity perturbations, and extracted by means of wavelet-based filters. They span the shear-dominated region of the flow, and their sizes and lifespans are proportional to the distance from the wall in the logarithmic layer, forming a self-similar eddy hierarchy consistent with Townsend's attached-eddy model. Except for their amplitude, which has to be determined nonlinearly, linearised transient growth represents their evolution reasonably well. Conditional analysis, based on wavelet-filtered and low-pass-filtered velocity fields, reveals that bursts of opposite sign pair side-by-side to form tilted quasi-streamwise rollers, which align along the streaks of the streamwise velocity with the right sign to reinforce them, and that they preferentially cluster along pre-existing streak inhomogeneities. On the other hand, temporal analysis shows that consecutive rollers do not form simultaneously, suggesting that they incrementally trigger each other. This picture is similar to that of the streak-vortex cycle of the buffer layer, and the properties of the bursts suggest that they are different manifestations of the well-known attached Q$_2$-Q$_4$ events of the Reynolds stress.