The integral relationship on the skin friction drag (Fukagata et al., Phys. Fluids, 2002) and that on the power balance (Fukagata et al., Physica D, 2009) are introduced. As applications, a predetermined control relaminarizing a turbulent channel flow (Nakanishi et al., Int. J. Heat Fluid Flow, 2012) and a feedback control minimizing the dissipation of a flow around a circular cylinder (Naito and Fukagata, Phys. Rev. E, to appear) are introduced.
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