Results of the 3D simulations of an accretion-driven thermohaline front. Panels (a)–(c) and the 3D visualization correspond to the reference run with X_0,z = 10. Panel (a): horizontally averaged mass fraction of heavy elements X_Z as a function of depth z (measured from the top of the box), at different times (light to dark red). Panel (b): turbulent (solid) and molecular diffusion (dashed) composition fluxes at the same times. Panel (c): thermohaline layer depth h (blue, in units of H_box) and surface abundance X_surf (orange, in units of ΔX) as a function of time (in units of t_diff). Dashed lines are power-law fits, both consistent with t^1/2, as predicted by the shallow-layer model. Panel (d): composition gradient averaged over the thernohaline region, as a function of time for the five values of the imposed flux. The dashed line marks the critical gradient (dX/dz)_crit = R₀/Le = 0.25. Bottom right: 3D visualization of the heavy elements in the simulation box, showing the thermohaline fingers carrying heavy elements downward from the source at the top.