Drag reduction and transient growth of a streak in a spanwise wall-oscillatory turbulent channel flow

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.