The deepening of a shear-driven turbulent layer penetrating into stably stratified quiescent layer is studied using Direct Numerical Simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato and Phillips (J. Fluid Mech. 37, 643–655, 1969) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids inherent side wall and rotation effects of that experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as Ri−1/2 . In addition it is observed that all cases evolve in a self-similar fashion. A selfsimilarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.