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 (omega(z)), and the turbulent transports of the spanwsie vorticity fluctuation (-nu'omega'(z)) and of the wall-normal vorticity fluctuation (w'omega'(y)). Three Reynolds number cases (i.e., R e(tau)=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 -nu'omega'(z) is to increase drag (due to sweeping -nu'), while w'omega'(y) decreases the drag. A triple decomposition (mean, coherent, and random) reveals the random - nu ''omega ''(z) as the only term adding to drag, while the random w ''omega ''(y) and the coherent - nu omega 303; z and w omega(y) transports all decrease the drag. Weighted joint probability distribution function (p.d.f.) of nu '' and omega'(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 omega'(y) are negatively correlated in the entire region. The analysis here suggests that the suppression of random spanwise-vorticity transport (nu ''omega ''(z)) is the target for more effective drag reduction under the current method.

Automated summary

Investigation on vorticity transport in turbulent channels under large-scale active drag control reveals the significant contribution of vorticity fluctuations to frictional drag, with random and coherent components playing different roles in drag reduction. Analysis suggests that suppressing random spanwise-vorticity transport is crucial for more effective drag reduction.