Resolvent analysis of turbulent channel flow with manipulated mean velocity profile

Abstract

Using the resolvent analysis, we investigate how the near-wall mode primarily responsible for the friction drag is amplified or suppressed depending on the shape of the mean velocity profile of a turbulent channel flow. Following the recent finding by Kühnen et al. (2018), who modified the mean velocity profile to be flatter and attained significant drag reduction, we introduce two types of artificially flattened turbulent mean velocity profiles: one is based on the turbulent viscosity model proposed by Reynolds and Tiederman (1967), and the other is based on the mean velocity profile of laminar flow. A special care is taken so that both the bulk and friction Reynolds numbers are unchanged, whereby only the effect of change in the mean velocity profile can be studied. These mean velocity profiles are used as the base flow in the resolvent analysis, and the response of the wavenumber-frequency mode corresponding to the near-wall coherent structure is assessed via the change in the singular value (i.e., amplification rate). The flatness of the modified mean velocity profiles is quantified by three different measures. In general, the flatter mean velocity profiles are found to result in significant suppression of near-wall mode. Further, increasing the mean velocity gradient in the very vicinity of the wall is found to have a significant importance for the suppression of near-wall mode through mitigation of the critical layer.

Turbulent Drag Reduction by Streamwise Traveling Waves of Wall-Normal Forcing

“…The input-output analysis of phase-averaged flows can be a useful tool for understanding turbulence suppression mechanisms, as summarized by Jovanović (2021). Apart from spanwise wall oscillation, tangential injection of momentum to flatten the mean velocity profile (Kühnen et al 2018) can also be categorized into Strategy IIb, as such flattening of the mean velocity profile is found via resolvent analysis to reduce the amplification of near-wall modes (Uekusa et al 2020).…”