The advection of an interface by a known transient periodic excitation flow is investigated in the present study, the results of which are relevant to the propagation of nearly isothermal premixed flames in turbulent flow. The relation between the corrugated-surface area and the intensity of the excitation flow is obtained numerically and compared with exact analytically derived solutions. The results elucidate the relation between the surface area and the intensity of spatial and temporal flow-field variations at low, moderate, and large intensities and highlight the stabilizing influence of Huygens surface propagation (e.g., of premixed flames) on the rate of surface-area increase, which is found to be otherwise unbounded in time.