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

• Published in: The International journal of heat and fluid flow Vol. 106; p. 109331
• Main Authors: Zhu, Wenkai, Chen, Xianliang, Fu, Lin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2024
• Subjects: Attached-eddy model; Boundary layer flows; Channel flows; Pipe flows; Resolvent analysis; Wall-bounded turbulence; Wall-bounded turbulence; Attached-eddy model; Pipe flows; Resolvent analysis; Channel flows; Boundary layer flows
• ISSN: 0142-727X; 1879-2278
• DOI: 10.1016/j.ijheatfluidflow.2024.109331

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. •Examination of turbulence reveals streamwise uniform amplification in perturbations.•The spectra show outer motions differ for boundary layers versus channel/pipe.•Resolvent modes of wave speeds matching mean velocity unveil self-similar structures.•Energy spectra highlight amplification of large-scale and very-large-scale motions.