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

Abstract

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 (Ωz), 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.