Time evolution of the shell-averaged tracer concentration for β=10⁰ (panel a), 10² (panel b), and 10³ (panel c). Different colors correspond to different shell radii. The orange lines are given by Eq. (28). In panel b we set l_m=0.2 R_B (partially convective) and plot the decay rate at r=0.4 R_B (the solid line), r=0.6 R_B (the dotted line), and r=0.8 R_B (the dashed line), respectively. In panel c, we set l_m=R_B (fully convective).