Abstract
The drag-reduction mechanism of spanwise wall oscillation in a turbulent channel was investigated as an extension of the work of Yakeno et al. [“Modification of quasi-streamwise vortical structure in a drag-reduced turbulent channel flow with spanwise wall oscillation,” Phys. Fluids 26, 085109 (2014)] at a low Reynolds number. Flow instability was evaluated by computing the transient energy growth under an oscillating base flow which governed the generation of a near-wall streak structure. Oscillation affected the optimal energy growth of the streak mode, whose characteristics were reasonably consistent with those in a direct numerical simulation. The optimal growth of the tilted-streak mode was enhanced with a thicker Stokes layer under longer oscillation periods, while that of the original streak mode was weakened. The transition of the optimal perturbation under oscillation showed that the spanwise Stokes layer shear contributed considerably more to modification than the spanwise velocity did. A new drag-reduction performance estimation model was suggested using the acceleration of the spanwise velocity shear based on streak formation modification under oscillation, which restrains energy transfer to streamwise vortices via a tilting delay due to oscillation. This simple model worked well even under long oscillation periods and was theoretically consistent with that of Yakeno et al. based on the change in the Reynolds shear stress due to a streamwise vortex at a low Reynolds number.
Highlights
Direct numerical simulation (DNS) of the Navier–Stokes equations has made it possible to analyze the dynamics of flows in great detail and to control the corresponding turbulence,1–5 and this approach has benefited from technological developments in computational fluid dynamics (CFD)
The time step is Dt ð1⁄4 DtÃuÃs2=ÃÞ 1⁄4 0:15, and the maximum growth rate, GmaxðsÞ, is computed as the maximum eigenvalue, kj, for each target time, s, based on Eq [16]. This program was validated by comparison with the results reported by Butler and Farrell49 for the case of laminar Poiseuille flow and those by Pujals et al.55 for turbulent channel flow
The energy growth rate was computed by the direct stability analysis with turbulent viscosity in the perturbation equation, with the Stokes layer in the spanwise direction and the turbulent mean velocity in the streamwise direction as the unsteady base flow
Summary
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