  We study the high-frequency limit of non-autonomous gradient flows in metric
spaces of energy functionals comprising an explicitly time-dependent
perturbation term which might oscillate in a rapid way, but fulfills a certain
Lipschitz condition. On grounds of the existence results by Ferreira and
Guevara (2015) on non-autonomous gradient flows (which we also extend to the
framework of geodesically non-convex energies), we prove that the associated
solution curves converge to a solution of the time-averaged evolution equation
in the limit of infinite frequency. Under the additional assumption of
dynamical geodesic $\lambda$-convexity of the energy, we obtain an explicit
rate of convergence. In the non-convex case, we specifically investigate
nonlinear drift-diffusion equations with time-dependent drift which are
gradient flows with respect to the $L^2$-Wasserstein distance. We prove that a
family of weak solutions obtained as a limit of the Minimizing Movement scheme
exhibits the above-mentioned behaviour in the high-frequency limit.
