In this two-part paper, time-accurate solutions of the Reynolds-averaged Navier-Stokes equations are presented, which address through model problems, the response of turbulent propeller-blade boundary layers, and wakes to external-flow traveling waves. In Part 1, the Massachusetts Institute of Technology flapping-foil experiment is simulated and the results validated through comparisons with data. The physics of unsteady blade flows are shown to be complex with analogy to Stokes layers and are explicated through visualization and Fourier analysis. It is shown that convection induced steady/unsteady interaction causes deformation of the external-flow waves and is responsible for the upstream- and downstream-traveling pressure-gradient waves over the foil and in the wake, respectively. The nature of the unsteady displacement thickness suggests viscous-inviscid interaction as the mechanism for the response. In Part 2, a parametric study is undertaken to quantify the effects of frequency, foil geometry, and waveform.