In two-dimensional oscillatory flow above steep ripples, momentum transfer in the near-bed layer is dominated by the process of vortex formation and shedding. Here results from a cloud-in-cell (CIC) discrete-vortex model representing this phenomenon are horizontally averaged and then used to infer the behavior of a one-dimensional vertical (1DV) convective eddy viscosity. For symmetric waves, this eddy viscosity has a mean value that is consistent with empirically derived formulae based on laboratory measurements, and a second harmonic that decreases in amplitude from 3 times that of the mean value down to the size of the mean, as the ratio of orbital excursion amplitude to ripple wavelength increases. The peak value of this strongly time-varying eddy viscosity occurs at about the time of flow reversal in the free-stream, revealing the qualitatively different nature of the momentum transfer above rippled and flat beds. The general behavior of the eddy viscosity is explored, for ripples of different shape and steepness, through the vortex parameter range, and rules are proposed that allow the behavior of the new eddy viscosity to be extrapolated beyond this range toward the classical flat rough-bed limit. The simple, 1DV, convective eddy viscosity derived here may be used to represent the vortex-shedding process in large-scale practical formulations, and should lead to an improved representation of sediment transport in the rippled-bed regime.