High-resolution large-eddy simulation is used to investigate the mean and turbulence properties of a separated flow in a channel constricted by periodically distributed hillshaped protrusions on one wall that obstruct the channel by 33% of its height and are arranged 9 hill heights apart. The geometry is a modification of an experimental configuration, the adaptation providing an extended region of post-reattachment recovery and allowing high-quality simulations to be performed at acceptable computing costs. The Reynolds number, based on the hill height and the bulk velocity above the crest is 10 595. The simulated domain is streamwise as well as spanwise periodic, extending from one hill crest to the next in the streamwise direction and over 4.5 hill heights in the spanwise direction. This arrangement minimizes uncertainties associated with boundary conditions and makes the flow an especially attractive generic test case for validating turbulence closures for statistically two-dimensional separation. The emphasis of the study is on elucidating the turbulence mechanisms associated with separation, recirculation reattachment, acceleration and wall proximity. Hence, careful attention has been paid to resolution, and a body-fitted, low-aspect-ratio, nearly orthogonal numerical grid of close to 5 million nodes has been used. Unusually, the results of two entirely independent simulations with different codes for identical flow and numerical conditions are compared and shown to agree closely. Results are included for mean velocity, Reynolds stresses, anisotropy measures, spectra and budgets for the Reynolds stresses. Moreover, an analysis of structural characteristics is undertaken on the basis of instantaneous realizations, and links to features observed in the statistical results are identified and interpreted. Among a number of interesting features, a distinct 'splatting' of eddies on the windward hill side following reattachment is observed, which generates strong spanwise fluctuations that are reflected, statistically, by the spanwise normal stress near the wall exceeding that of the streamwise stress by a substantial margin, despite the absence of spanwise strain.

Direct numerical simulations for fully developed channel flow, subjected to oscillatory spanwise wall motion, have been performed and analysed in an effort to illuminate the fundamental mechanisms responsible for the reduction in turbulent friction drag, observed to result from the spanwise wall motion. A range of statistical data are discussed, including second-moment budgets, joint-probability-density functions, enstrophy and energy-spectra maps. Structural features are also investigated by reference to the response of streak properties to the oscillatory forcing. The unsteady cross-flow straining is shown to cause major spanwise distortions in the streak nearwall structures, leading to a pronounced reduction in the wall-normal momentum exchange in the viscous sublayer, hence disrupting the turbulence contribution to the wall shear stress. The response of the streaks, in terms of their periodic reorientation in wall-parallel planes, the decline and recovery of their intensity during the cyclic actuation, and their wall-normal coherence, is shown to be closely correlated with the temporal variation of the shear-strain vector. Furthermore, a modulating 'top-to-bottom' effect, associated with large-scale outer-layer structures, is highlighted and deemed responsible for the observed reduction in the actuation efficiency as the Reynolds number is increased.

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DNS data for channel flow at Re τ = 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, streamwisevelocity 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 largescales-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.

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