To gain insight into the role of the Landau-Darrieus instability in the "flamelet" regime of turbulent premixed combustion, the propagation of unstable flames was simulated in flows with a scale much larger than the flame thickness. The simulations were performed using a method that approximates the flame as a discontinuity in the flow. The flow field through which the flame propagated was a periodic array of "square vortices." From the results of the simulations, it was determined that, although the scale at which the Landau-Darrieus instability has its maximum effect may be much smaller than the flow scale, flame wrinkles with a scale smaller than the flow scale do not develop. This has the consequence that for the flamelet regime of turbulent combustion the smallest flame wrinkling scale will most likely be determined by the flow, not the Landau-Darrieus instability. We also found that although the instability did not induce small scale wrinkling, it did have a significant effect on the mean consumption rate of the flame. For unstable flames, the flame distortions created by the vortices were much larger in amplitude than the distortions of a stable flame. This resulted in an increased consumption rate relative to a stable flame because of the increased surface area of the flame. It is suggested that in the flamelet regime of turbulent combustion the Landau-Darrieus instability will have a similar effect at least for weak to moderate flow intensities such as the ones studied here.