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

TL;DR

This study introduces an input-output framework to analyze convective velocities in turbulent channel flows, revealing how large-scale structures and viscous effects influence local flow behavior across different scales.

Contribution

It develops a novel input-output based analytical method to compute and interpret convective velocities in turbulent flows using only mean velocity profiles.

Findings

Convective velocities align with previous literature.

Large-scale structures influence near-wall convective velocities.

Viscous effects significantly impact large flow structures.

Abstract

This paper employs an input-output based approach to analyze convective velocities and the transport of fluctuations in turbulent channel flows. The convective velocity for a fluctuating quantity associated with streamwise-spanwise wavelength pairs at each wall-normal location is obtained through the maximization of the power spectral density associated with the linearized Navier-Stokes equations with a turbulent mean profile and delta-correlated Gaussian forcing. We first demonstrate that the mean convective velocities computed in this manner agree well with those reported previously in the literature. We then exploit the analytical framework to probe the underlying mechanisms contributing to the local convective velocity at different wall-normal locations by isolating the contributions of each spanwise-streamwise wavelength pair (flow scale). The resulting analysis suggests that the behavior of the convective velocity in the near-wall region is influenced by large scale structures further away from the wall. These structures resemble Townsend's attached eddies in the cross-plane, yet show incomplete similarity in the streamwise direction. We then investigate the role of each linear term in the momentum equation to isolate the contribution of the pressure, mean shear, and viscous effects to the deviation of the convective velocity from the mean at each flow scale. Our analysis highlights the role of the viscous effects, particularly in regards to large channel spanning structures whose influence extends to the near-wall region. The results of this work suggest the promise of an input-output approach for analyzing convective velocity across a range of flow scales using only the mean velocity profile.