A laboratory study of the turbulence front initiated by the Rayleigh-Taylor instabilities was conducted by overturning a two-layer stratified flow in a tank. Dye was introduced to the upper layer and the concentration of the dye was determined using a video imaging method. The mass center of the heavier upper layer moved continuously to a lower elevation because of the intrusion of the heavier fluid into the lower layer and the lighter fluid into the upper layer. The downward movement of the mass center was accurately determined from the dye concentration profile. It is concluded that the initial advancement of the mass center follows a quadratic relation with time and the final advancement obeys a linear relation with time.