Resolvent analyses of incompressible turbulent channel, pipe and boundary-layer flows

This work investigates the linear responses of turbulent mean flow to harmonic forcing in incompressible channel, pipe, and zero-pressure-gradient boundary-layer flows. Employing established universal relations, the mean flow and associated eddy viscosity at Reτ=8000 are obtained. This research reveals that the most amplified perturbations in all three flows are streamwise uniform, corresponding to streamwise streaks originating from streamwise vortices. With the low-rank nature of the resolvent analysis, the streamwise energy density subject to harmonic forcings in a broad parameter space is examined. The greatest energy amplification occurs near the critical wall-normal location where the turbulent mean velocity matches the wave speed, aligning with Taylor's frozen-turbulence hypothesis. Analysis centered on resolvent modes, where wave speeds match the mean velocity, uncovers that the coherent structures related to these modes are geometrically self-similar. The spanwise dimensions of these structures are proportional to their distance from the wall, thereby providing robust evidence supporting the attached-eddy model. Furthermore, the constructed premultiplied energy spectra based on the linear operator can identify large-scale motions and very-large-scale motions in wall-bounded turbulent flows, suggesting their capacity to be amplified by the mean flow.