  The application of drag-control strategies on canonical wall-bounded
turbulence, such as periodic channel and zero- or adverse-pressure-gradient
boundary layers, raises the question of how to describe control effects
consistently for different reference cases. We employ the RD identity (Renard &
Deck, J. Fluid Mech., 790, 2016, pp. 339-367) to decompose the mean friction
drag and investigate the control effects of uniform blowing and suction applied
to a NACA4412 airfoil at chord Reynolds numbers Re_c=200,000 and 400,000. The
connection of the drag reduction/increase by using blowing/suction with the
turbulence statistics (including viscous dissipation, turbulence-kinetic-energy
production, and spatial growth of the flow) across the boundary layer,
subjected to adverse or favorable pressure gradients, are examined. We found
that the peaks of the statistics associated with the friction-drag generation
exhibit good scaling in either inner or outer units throughout the boundary
layer. They are also independent of the Reynolds number, control scheme, and
intensity of the blowing/suction. The small- and large-scale structures are
separated with an adaptive scale-decomposition method, i.e. empirical mode
decomposition (EMD), aiming to analyze the scale-specific contribution of
turbulent motions to friction-drag generation. Results unveil that blowing on
the suction side of the airfoil is able to enhance the contribution of
large-scale motions and to suppress that of small-scales; on the other hand,
suction behaves contrarily. The contributions related to cross-scale
interactions remain almost unchanged with different control strategies.
