Evolution of the azimuthal velocity for η = 0.15, , E = 10^-7, λ = 10^-4, and B = 0,10⁴,10⁵,10⁷ (downward). The solid line is the numerical solution, the dashed line is the full analytical solution, and the two dot lines are the solutions of each flow. The transition is at B = 10⁴, the differential rotation is then governed by baroclinicity as shown in Fig. 5. Boundary conditions are no-slip on both sides r = η and r = 1.