Profiles of the local density, ρ, and the convective velocity, V_c, in the envelopes of the canonical TPAGB star (cyan solid line) and the modified TPAGB star with all three effects included and a = 10 R_⊙ (blue solid line), 20 R_⊙ (green dashed line), 40 R_⊙ (red dash-dot line), and 80 R_⊙ (black dotted line) at a time between two thermal pulses (t = 3500 yr). The magenta dashed curves labelled “MP17 value” are the average density, , and the convective velocity, defined as , used by MP17 (see their Eq. (6)).