The influence of a periodic multiscale transient flow on isothermal-flame propagation is examined computationally. It is found that the increase in flame surface area, and hence the burning speed, due to wrinkling by the flow depends quadratically (linearly) on the intensity of the flow-field velocity fluctuations at low (high) intensities, while the dependence is consistent with a 4/3 power law for an intermediate range of intensities, consistent with results from earlier studies of flame propagation in weakly exothermic turbulent flows. Particular contributions of this work are elucidation of (a) the quantitative extent of the burning-speed enhancement for low and moderate intensities, (b) the influence of the multiscale character of the excitation flow and (c) the stabilization of flame surface-area growth after the initial period of unbounded growth revealed in earlier work. The effect of multiple excitation-flow scales on surface-area enhancement is found to be minor at low excitation-flow intensities but substantial at large intensities. (C) 2017 The Author(s). Published by Elsevier Inc. on behalf of The Combustion Institute.