Using the first perturbed vorticity equation, it is shown that the infinitesimal vorticies in water are rapidly amplified when the surface progressive wave has the density distribution of frequency spectrum of surface profile in the form of E(f)～f-n(n＞5). This amplication of vortices does not exist if n＜5. At n=5, the logarithmic infinity appears and may be physically considered as the equilibrium condition. This result may be interpreted that, if n＞5, some of the wave energy in the concerned part of the spectrum is transfered to the induced vortex motion.
　An experiment was added to clarify this property of progressive random waves. Wind waves are generated in a uni-directional air-water tunnel, and the wind is excluded from the water surface in a midway. After some passage in a calm condition, the effect of breaking disappears and capillary waves become weak. At this condition of stationary state, the decay of waves is examined. The result is agreeable with the above-mentioned analytical consideration.