Patterns of convection with different gravity profiles. (a) Normalized gravity profiles from stellar evolution code Cesam2k20 for a star of 0.8 M_⊙ at an early stage of stellar evolution (1 Myr, in light gray) and at the MS (4.9 ⋅ 10³ Myrs, dark gray). Example of imposed gravity profiles in DNS: g ∝ 1/r² for radii ratio ξ = 0.35 (in red), g ∝ r and ξ = 0.2 (in dashed light blue) and a typical profile from Cesam2k20 with ξ = 0.35 (in magenta, see Eq. (3) for detail). (b) Local convective Rossby number, normalized with its maximum, as a function of r/r_o for the runs gr2_2, gr_1, and gc_2, associated with the gravity profiles of panel (a) (same color code), and for the run gr2_3, with g ∝ 1/r² and ξ = 0.2 (in dashed red). Details of the runs are presented in Table B.1. (c) Equatorial cut of instantaneous radial velocity for g ∝ 1/r², ξ = 0.35 (run gr2_2). (d) Same as (c) but for g ∝ r, ξ = 0.2 (run gr_1). (e) Same as (c) but for g ∝ 1/r², ξ = 0.2 (run gr2_3). Velocities in panels (c-e) were normalized with ν/(r_o − r_i), i.e., kinematic viscosity, ν, and the thickness of convective zone.