Time evolution of the dimensionless penetration distance α = (r_cb − r_Sb)/H_p, Sb, where r_cb is the radius of the convective boundary, r_Sb the radius of the Schwarzschild boundary, and H_p, Sb the pressure scale height at r_Sb. The four example simulations are 2.5D with N_r = 512. The time axis shows the time as a fraction of the thermal timescale τ_th(b). The dotted vertical line at t = 0.3τ_th marks the end of the initial transient. Each data point corresponds to a time average over 0.05τ_th.