Duty-cycle modulation of the self-sustaining process by spanwise wall oscillation

Abstract: Direct Numerical Simulation of turbulent channel flow at friction Reynolds number around 200 is performed with spanwise wall actuation to achieve drag reduction. A quasi-square-wave waveform, featuring impulsive transitions and constant-velocity plateaus, separates the actuation cycle into distinct Reversal and Displacement Phases, thereby permitting direct observation of the underlying physics. Phase-resolved analysis reveals that the actuation modulates the self-sustaining process (SSP): during the Reversal Phase, the Stokes strain passes through zero, the SSP resumes, and streaks regenerate; during the Displacement Phase, sustained Stokes strain diverts wall-normal vorticity spanwise via vortex tilting, depleting SSP precursors and suppressing streaks. A stochastic enstrophy-budget analysis confirms this mechanism at the governing-equation level: competition between mean-shear production of wall-normal enstrophy and Stokes-driven spanwise diversion, drawing from a shared reservoir, reflects directed, phase-opposed switching. The quasi-square wave improves the gross drag-reduction margin by 2.5 percentage points over the optimal sinusoidal baseline, solely via temporal Stokes-strain redistribution, and the waveform renders duty-cycle switching directly observable, thus elucidating the causal chain of drag reduction.