  This study computes the optimal normal actuation on the surface of a NACA0012
airfoil at an angle of attack of 15{\deg} and a Reynolds number of Re = 1000,
using costs defined for minimal drag and maximal lift. To allow for a general
actuation profile, non-zero actuation is permissible on both the suction and
pressure surfaces. This approach of optimal actuation along the full airfoil
surface augments most other studies that have focused on parametrically varied
open-loop control restricted to the suction surface. The gradient-based
optimization procedure requires the gradient of the cost functional with
respect to the design variables, which is determined using the adjoint of the
governing equations. The optimal actuation profile for the two performance aims
are compared. Where possible, similarities with commonly considered open-loop
actuation in the form of backward traveling waves on the suction surface have
been highlighted. In addition, the key spatial locations on the airfoil surface
for the two optimal control strategies have been compared to earlier works
where actuation has been limited to a sub-domain of the airfoil surface. The
flow features emerging from the optimal actuation variations, and their
consequent influence on the instantaneous aerodynamic coefficients, have been
analyzed. To complement our findings with normal actuation, we also provide in
the appendix: results for a more general form of actuation with independent x
and y components, and for a different optimization window to assess the effect
of this window parameter on the actuation profile and the flow features.
