Threshold transient growth as a criterion for turbulent mean profiles

Abstract

have recently identified the ability of the streamwise-averaged streak fields U (𝑦, 𝑧, 𝑡) x in minimal channels to produce short-term transient growth as the key linear mechanism needed to sustain turbulence at 𝑅𝑒 𝜏 = 180. Here, we model this streak transient growth as a two-stage process by first selecting the dominant streak structure expected to emerge over the eddy turnover time on the turbulent mean profile 𝑈 (𝑦) x, and then examining the secondary growth on this (frozen) streak field U (𝑦, 𝑧) x. Choosing the mean streak amplitude and eddy turnover time consistent with simulations recovers the growth thresholds found by Lozano-Duran et al. (2021) for sustained turbulence. Extending this analysis to 𝑅𝑒 𝜏 = 360 and 720 suggests a Reynolds number independence of this threshold. This then indicates that the short-term growth properties of the turbulent mean profile U (𝑦, 𝑧) x are a much more plausible criterion of turbulence existence than its linear stability characteristics as originally suggested by Malkus (