Azimuthal velocity u_φ as a function of the normalized radius for λ = 10^-4, η = 0.15, and . The solid line is the numerical solution, dotted lines are the analytical solutions of the spin-up flow and the baroclinic flow, the dashed line is the sum of both. Downwards: E = 10^-5,10^-6,10^-7 and the transition value on the differential rotation is B = 10³,3 × 10³,10⁴, respectively. Beyond this threshold, the baroclinicity governs the differential rotation. Boundary conditions are no-slip on both sides r = η and r = 1. Note that as the Ekman number decreases, the discrepancy between the numerical and the analytical solutions decreases as well.