We introduce the Constant Power Input (CPI) concept to clarify how a drag reduction control a ects energy budget of a fully developed turbulent channel ows. The entire kinetic energy is decomposed into the mean and uctuating components, and the total dissipation is accordingly divided into the dissipation of the mean led and the turbulent dissipation. The CPI condition is essential in the present study, since it strictly restricts the amount of power applied to the ow system. This allows us to identify how each ow control strategy changes the energy ows between each component and the viscous dissipation. Ultimately, if we succeed in suppressing all turbulence, the turbulent dissipation should vanish and the power applied to the ow system should be dissipated only by the dissipation of the mean velocity, which should have a parabolic pro le. Our fundamental question in the present study is whether there exists unique relationship between the changes in the turbulent dissipation and the resultant drag reduction e ect. In order to provide the de nite an- swer to this question, we introduce triple decomposition of the velocity eld, and validate our approach by considering two di erent ow control strategies
