Vorticity transports in turbulent channels under large-scale control via spanwise wall jet forcing

Vorticity transport in turbulent channels under large-scale active drag control (i.e., spanwise opposed jet forcing) is investigated via direct numerical simulation of the Navier–Stokes equation. The skin-friction coefficient is newly expressed by the volume integration average of the mean flow dissipation expressed in terms of the spanwise vorticity (Ω_z), and the turbulent transports of the spanwsie vorticity fluctuation (⁠$−v′ω′z$⁠) and of the wall-normal vorticity fluctuation (⁠$w′ω′y$⁠). Three Reynolds number cases (i.e., $Reτ=180,395$⁠, and 550) with notable drag reductions (i.e., 18%, 16%, and 15%, respectively) are examined, following the setup in Yao et al. [Phys. Rev. Fluids 2, 062601(R) (2017)]. The transports of vorticity fluctuations dominate the contributions to the frictional drag, consistent with previous results for the passive drag reduction strategy of slip-wall [Yoon et al., Phys. Fluids. 28, 081702 (2016)]. Specifically, the effect of $−v′ω′z$ is to increase drag (due to sweeping $−v′$⁠), while $w′ω′y$ decreases the drag. A triple decomposition (mean, coherent, and random) reveals the random $−v″ω′′z$ as the only term adding to drag, while the random $w″ω′′y$ and the coherent $−ṽω̃z$ and $w̃ω̃y$ transports all decrease the drag. Weighted joint probability distribution function (p.d.f.) of $v″$ and $ω′′z$ shows a transition from the first–third quadrant dominance (hence positive-correlated) near the wall to the second–fourth quadrant dominance (hence negative-correlated) away from wall. In contrast, $w″$ and $ω′′y$ are negatively correlated in the entire region. The analysis here suggests that the suppression of random spanwise-vorticity transport (⁠$v″ω′′z$⁠) is the target for more effective drag reduction under the current method.