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This paper employs an input-output based approach to analyze convectivevelocities and the transport of fluctuations in turbulent channel flows. Theconvective velocity for a fluctuating quantity associated withstreamwise-spanwise wavelength pairs at each wall-normal location is obtainedthrough the maximization of the power spectral density associated with thelinearized Navier-Stokes equations with a turbulent mean profile anddelta-correlated Gaussian forcing. We first demonstrate that the meanconvective velocities computed in this manner agree well with those reportedpreviously in the literature. We then exploit the analytical framework to probethe underlying mechanisms contributing to the local convective velocity atdifferent wall-normal locations by isolating the contributions of eachspanwise-streamwise wavelength pair (flow scale). The resulting analysissuggests that the behavior of the convective velocity in the near-wall regionis influenced by large scale structures further away from the wall. Thesestructures resemble Townsend's attached eddies in the cross-plane, yet showincomplete similarity in the streamwise direction. We then investigate the roleof each linear term in the momentum equation to isolate the contribution of thepressure, mean shear, and viscous effects to the deviation of the convectivevelocity from the mean at each flow scale. Our analysis highlights the role ofthe viscous effects, particularly in regards to large channel spanningstructures whose influence extends to the near-wall region. The results of thiswork suggest the promise of an input-output approach for analyzing convectivevelocity across a range of flow scales using only the mean velocity profile.

An input-output based analysis of convective velocity in turbulent channels