A framework for analyzing energy flux in turbulent channel flows is proposed which enables quantification of the drag reduction efficacy by different control methods. In contrast to the FIK [Fukagata, Iwamoto, and Kasagi, Phys. Fluids 14, L73 (2002)] and the RD [Renard and Deck, J. Fluid Mech. 790, 339 (2016)] identities, this framework expresses the skin friction coefficient in terms of the nondimensionalized dissipation rate and the work done by external excitation. We extend the energy-box analysis of Gatti et al. [J. Fluid Mech. 857, 345 (2018)] through a triple decomposition of energy flux and show how mean (${\epsilon }_M$), coherent (${\epsilon }_C$), and random turbulent (${\epsilon }_R$) dissipations contribute differently to the drag reduction and the net power saving. Three control methods, including our recently developed spanwise opposed wall-jet forcing (SOJF), the spanwise wall oscillation (SWO), and the opposed wall blowing/suction (OBS) controls, are compared at ${\text{Re}}_{\tau }\approx 200$ via direct numerical simulations (DNS). While all methods yield comparable drag reductions ($\sim 20\%$), OBS yields the maximum net power saving, followed by SOJF, and then SWO. Specifically, for SOJF control, ${\epsilon }_C$ (induced by the large-scale swirls) is much smaller than ${\epsilon }_R$ (induced mainly by the small-scale near-wall vortices) and ${\epsilon }_M$ (due to the spanwise vorticity sheet ${\mathrm{\Omega }}_z$). In contrast, for SWO control, ${\epsilon }_C$ (caused by the wall oscillation-induced ${\mathrm{\Omega }}_x$ vortex sheet)—much larger than that of SOJF—is comparable to ${\epsilon }_R$ and ${\epsilon }_M$. For OBS control, ${\epsilon }_R$ is notably suppressed without any introduction of ${\epsilon }_C$ as the energy is injected through the random velocity field. Diagnoses performed at a higher ${\text{Re}}_{\tau }$ (i.e., 2000) for SWO shows that random turbulent dissipation ${\epsilon }_R$ predominates due to the increasing near-wall vortical structures—hence their suppression should be the target for drag control at high ${\text{Re}}_{\tau }$. The analysis also suggests a promising hybrid drag control strategy by incorporating both the random (OBS) and coherent (SOJF or SWO) controls together, an issue for future exploration.

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• Structure & turbulence of boundary layers
• Turbulence