On the influence of outer large-scale structures on near-wall turbulence in channel flow

Direct Numerical Simulation (DNS) data for channel flow at 1025 are used to analyse the interaction between large outer scales in the log-law region – referred to as super-streaks – and the small-scale, streaky, streamwise-velocity fluctuations in the viscosity-affected near-wall layer. The study is inspired by extensive experimental investigations by Mathis, Marusic, and Hutchins, culminating in a predictive model that describes, in a supposedly universal manner, the “footprinting” and “modulating” effects of the outer structures on the small-scale near-wall motions. The approach used herein is based on the examination of joint PDFs for the small-scale fluctuations, conditioned on regions of large-scale footprints. The large and small scales are separated by means of the Huang-Hilbert empirical-mode decomposition, the validity of which is demonstrated by way of pre-multiplied energy spectra, correlation maps, and energy profiles for both scales. Observations derived from the PDFs then form the basis of assessing the validity of the assumptions underlying the model. Although the present observations support some elements of the model, the results imply that modulation by negative and positive large-scale fluctuations differ greatly – an asymmetric response that is not compatible with the model. The study is thus extended to examining the validity of an alternative proposal, which is based on the assumption that a universal description of the small-scale response to the large-scale motions has to rely on the velocity fluctuations being scaled with the large-scales-modified local friction velocity, rather than with the mean value. This proposal is partially supported by the present analysis. Finally, an alternative, new phenomenological model is proposed and examined.