Here we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity (u) in a high Reynolds number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26000. Taylor's frozen turbulence hypothesis is used to convert temporalspanwise information into a 2-D spatial spectrum which shows the contribution of streamwise (λ x ) and spanwise (λ y ) length scales to the streamwise variance at a given wall height (z). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows λ y /z ∼ (λ x /z) 1/2 behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship (λ y ∼ λ x ) as required for self-similarity and predicted by the attached eddy hypothesis.
Simulations and experiments at low Reynolds numbers have suggested that skin-friction drag generated by turbulent fluid flow over a surface can be decreased by oscillatory motion in the surface, with the amount of drag reduction predicted to decline with increasing Reynolds number. Here, we report direct measurements of substantial drag reduction achieved by using spanwise surface oscillations at high friction Reynolds numbers ($${{{\mathrm{Re}}}_{\tau }}$$
Re
τ
) up to 12,800. The drag reduction occurs via two distinct physical pathways. The first pathway, as studied previously, involves actuating the surface at frequencies comparable to those of the small-scale eddies that dominate turbulence near the surface. We show that this strategy leads to drag reduction levels up to 25% at $${{{{{{{{\mathrm{Re}}}}}}}}}_{\tau }$$
Re
τ
= 6,000, but with a power cost that exceeds any drag-reduction savings. The second pathway is new, and it involves actuation at frequencies comparable to those of the large-scale eddies farther from the surface. This alternate pathway produces drag reduction of 13% at $${{{{{{{{\mathrm{Re}}}}}}}}}_{\tau }$$
Re
τ
= 12,800. It requires significantly less power and the drag reduction grows with Reynolds number, thereby opening up potential new avenues for reducing fuel consumption by transport vehicles and increasing power generation by wind turbines.
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