  The gradient-flow operator product expansion for QCD current correlators
including operators up to mass dimension four is calculated through NNLO. This
paves an alternative way for efficient lattice evaluations of hadronic vacuum
polarization functions. In addition, flow-time evolution equations for flowed
composite operators are derived. Their explicit form for the non-trivial
dimension-four operators of QCD is given through order $\alpha_s^3$.
