Fig. 2.

Axisymmetric steady solutions of the differential rotation as a function of radius at the latitude θ = π/4 in the Taylor–Proudman regime. Left panel: analytical solution Eq. (45) is plotted in black dashed lines and compared with the numerical simulations obtained for fixed Pr(N0/Ω0)2 parameter (10−4) and contraction Reynolds number Rec (10−2) with various Ekman numbers: 10−2 (in grey), 10−3 (in cyan), 10−4 (in light blue), 10−5 (in dark blue), and 10−6 (in purple) respectively for runs 1.1–1.5 in Table 2. For E = 10−5 and E = 10−6, additional contraction Reynolds numbers are studied, namely 10−1 (runs 2.1 and 3.1 in Table 2), 1 (runs 2.2 and 3.2 in Table 2), and 10 (runs 2.3 and 3.3 in Table 2). All curves are rescaled by . Right panel: differential rotation between the inner and outer spheres ΔΩ = Ω(ri)−Ω(r0) at the same latitude and normalised with the rotation rate taken at the outer sphere Ω0, now plotted as a function of
. The previous numerical solutions obtained for E = 10−5 (runs 1.4 and 2.1–2.3 in Table 2) are plotted in dark blue, while the simulations performed for E = 10−6 (runs 1.5 and 3.1–3.3 in Table 2) are plotted in purple.
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