Drag control of wall-bounded turbulent flows.

Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction, enabling large-scale flow forcing without requiring instantaneous flow information. We show that the lack of drag reduction at high Re (Re$_{\mathrm{\tau }}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.25in,height=0.20in]{300720171.eps}} \label{fig1} \end{figure} $=\quad 550)$ recently reported by Canton \textit{et al. }[J. Canton \textit{et al.}, PRF (2016)] is remedied by a proper choice of the large-scale control flow, i.e. via near-wall spanwise opposed wall-jet forcing (SOWF), each wall-jet covering multiple streaks. The control method is characterized by three parameters, namely, the wall-jet amplitude A$^{\mathrm{+}}$, the spanwise wall-jet spacing $\Lambda^{\mathrm{+}}$, and the wall-jet height y$^{\mathrm{+}}_{\mathrm{c}}$ ($+$ indicates viscous scaling). We show as an example that with a choice of A$^{\mathrm{+}}\approx $.015, $\Lambda ^{\mathrm{+}}\approx $1200 and y$^{\mathrm{+}}_{\mathrm{c}} \quad =$30 (these three parameters values were found to produce maximum drag reduction for Re$_{\mathrm{\tau \thinspace }}=$ 180), the flow control definitely suppresses the wall shear stress at a series of Reynolds numbers, namely, 19{\%}, 14{\%}, and 12{\%} drag reductions at Re$_{\mathrm{\tau }}=$ 180, 395, and 550, respectively. Vortex structures ($\lambda_{\mathrm{2}})$ and flow statistics (Reynolds shear stress, rms of vorticities, kinetic energy budget, etc.) are further examined to explain the mechanism of drag reduction and increase.