We explore a reduced-order model (ROM) of plane Couette flow with a view to performing near-wall turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier–Stokes system onto a basis of controllability modes. Such ROMs were found to reproduce key aspects of turbulence dynamics in Couette flow with only a few hundred degrees of freedom, and here we use them to devise a control strategy. We consider a ROM with an extra forcing term whose structure is given by a combination of eigenfunctions of a linear viscous diffusion equation, optimised in order to minimise the total fluctuation energy. The optimisation is performed at Reynolds numbers $Re=1000, 2000, 3000$, and produces a novel control mechanism wherein the optimal forcing leads the flow to laminarisation in all cases. The forcing acts by reducing the shear in a large portion of the channel, hindering the main energy input mechanism. The forced flow possesses a new laminar solution which is linearly stable at $Re=1000$ and unstable at higher $Re$, but whose transient growth of streaky structures is substantially lower than that of laminar Couette flow, leading the flow to full laminarisation when the forcing is removed. Forcings optimised in the ROM are subsequently applied in direct numerical simulations (DNS). The same control mechanisms are observed in the DNS, where laminarisation is also achieved. We show that the ROMs provide an effective framework to design turbulence control strategies, despite the high degree of truncation, which opens up interesting possibilities for turbulence control.

Based on data from pore-resolved direct numerical simulation of turbulent flow over mono-disperse random sphere packs, we evaluate the budgets of the double-averaged turbulent kinetic energy (TKE) and the wake kinetic energy (WKE). While TKE results from temporal velocity fluctuations, WKE describes the kinetic energy in spatial variations of the time-averaged flow field. We analyse eight cases which represent sampling points within a parameter space spanned by friction Reynolds numbers $Re_\tau \in [150, 500]$ and permeability Reynolds numbers $Re_K \in [0.4, 2.8]$. A systematic exploration of the parameter space is possible by varying the ratio between flow depth and sphere diameter $h/D \in \{ 3, 5, 10 \}$. With roughness Reynolds numbers of $k_s^+ \in [20,200]$, the simulated cases lie within the transitionally or fully rough regime. Revisiting the budget equations, we identify a WKE production mechanism via viscous interaction of the flow field with solid surfaces. The scaling behaviour of different processes over $Re_K$ and $Re_\tau$ suggests that this previously unexplored mechanism has a non-negligible contribution to the WKE production. With increasing $Re_K$, progressively more WKE is transferred into TKE by wake production. A near-interface peak in the TKE production, however, primarily results from shear production and scales with interface-related scales. Conversely, further above the sediment bed, the TKE budget terms of cases with comparable $Re_\tau$ show similarity under outer-scaling. Most transport processes relocate energy in the near-interface region, whereas pressure diffusion propagates TKE and WKE into deeper regions of the sphere pack.