Skin-friction turbulent drag reduction: a Lagrangian perspective

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Jacopo Banchetti

This work addresses the mechanism of turbulent skin-friction drag reduction obtained through spanwise forcing techniques. Lagrangian tracers in a direct numerical simulation (DNS) of a turbulent channel flow are exploited to provide for the first time unquestionable evidence of statistical changes in the flow with drag reduction. Our hope is that such changes, being so large as to be qualitatively unaffected by the subtle scaling problems that typically plague the comparison between two flows (the uncontrolled flow and the drag-reduced one) with different Reynolds number, will provide a lead to the physical understanding of the drag reduction mechanism.

In a first part of the thesis, an existing DNS code is augmented with the capability of dealing accurately and efficiently (in terms of memory requirement and computational cost) with massless particles. In a second part, a turbulent channel flow at Re_bulk = 3173 is considered with and without spanwise forcing (the purely temporal wall oscillation and the purely spatial stationary wave) to highlight the strong effect of the forcing on the trajectories of the tracers. Statistical quantities (some of which are introduced here on purpose) are used to describe such differences, and evidence is obtained for the highly reduced particle diffusion in a thin near-wall layer. The thickness of this layer is measured and compared to that of the Generalized Stokes Layer (GSL), known to bear quantitative relationship with the amount of drag reduction.

Lagrangian statistics promise to be key to understand the key physical mechanism by which the spanwise forcing interact with near-wall turbulence to yield reduced levels of friction drag.