Radial partial derivative of the ratio of the azimuthal velocity field U_ϕ to the radius r (left panel), cylindrical radial velocity field U_s = U_r sin θ + U_θ cos θ (middle panel), and vertical velocity field U_z = U_r cos θ − U_θ sin θ (right panel) as a function of radius. In each panel the top row corresponds to the latitude θ = π/4. In the left and middle panels the bottom row corresponds to the equator, but since the vertical velocity field U_z is zero at the equator, the bottom right panel is obtained close to this location, at about 85-degree angle with the vertical axis. In each case E = 10⁻⁵, P_r(N₀/Ω₀)² = 10⁻⁴ and Re_c = 10⁻². In all panels the plain blue curve corresponds to the Boussinesq case (run 1.4 in Table 2), while the other curves are obtained by varying the density contrast between the inner and outer spheres. Shown in the left panel are ρ_i/ρ₀ = 10.8 (dashed lines), 20.9 (dash-dotted lines), and 60.2 (dotted lines), corresponding to runs 2.2 to 2.4 in Table 6; in the middle and right panels the two black curves are respectively obtained for ρ_i/ρ₀ = 1.75 (plain curve) and ρ_i/ρ₀ = 20.9 (dashed lines), corresponding to runs 2.1 and 2.3 in Table 6.