Effect of spanwise wall forcing on the separation of a turbulent temporal boundary layer under adverse pressure gradient

Spanwise wall forcing reduces skin-friction drag in turbulent flows, but its effect on flow separation under an adverse pressure gradient (APG) remains to be investigated. The temporal approach has so far been used for APG and for oscillating-wall (OW) boundary layers separately. Here, the two configurations are combined and the analysis is extended to streamwise travelling waves (STW). Direct numerical simulations of a temporally developing turbulent boundary layer are performed. Spanwise forcing is activated at Re_τ = 200, once the initial transient of the temporal boundary layer (Kozul et al., 2016) has ended. Forcing parameters are scaled with a friction velocity averaged over Re_τ = 180–500. The APG is imposed as a constant volumetric forcing in the Navier–Stokes equations, with value 7.36 × 10⁻⁴, and is activated once the transient of the spanwise forcing has ended, i.e. after four oscillation periods. OW forcing with W⁺ = 12 and T⁺ = 100 yields a drag reduction of 20–25%. Drag increase with OW has been reported only at very long periods (T⁺ ≳ 700; Quadrio et al., 2009). In the temporal configuration, such periods allow only about two forcing cycles over the simulated time, which prevents statistical convergence. STW are therefore adopted, since they access the drag-increasing regime at much shorter periods and at a tractable computational cost. The wave parameters, with A⁺ = 12, are selected from the forcing map of Quadrio et al. Periods T⁺ = 100 and 20 produce drag reduction, up to 15%, whereas T⁺ = 25 produces a drag increase of about 5%. The maximum drag increase lies near a phase speed c ≈ 0.4, lower than the value c ≈ 0.5 reported for channel flow. Separation occurs in all simulated APG cases. The results address whether spanwise forcing promotes separation and show how drag reduction and drag increase affect its onset.