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This work investigates the modal and non-modal stability characteristics of a plane Poiseuille flow modified by stationary streamwise-distributed Stokes Layer generated by a sinusoidal spanwise forcing applied at the walls. This type of forcing, which is known to possess significant capabilities in terms of turbulent skin-friction drag reduction, is shown here to improve the temporal stability of the Poiseuille flow too.
The analytical difficulties of the extended Orr–Sommerfeld problem, where streamwise homogeneity is lost owing to the spanwise base flow, are overcome by a formulation which exploits the sinusoidal waveform of the wall forcing. The numerical code, preliminary validated via selected Direct Numerical Simulations, is then used to carry out a massive study that carefully explores the discretization as well as the physical parameters.
At Re = 2000, it is found that wall-based spanwise forcing is capable to increase the negative real part of the least-stable eigenvalue by more than 200\%, and to decrease the maximum transient growth of perturbations by more than 70\%. These figures are highly Re-dependent and improve with increasing Re.