Time evolution of the major component of the azimuthal velocity w^{l = 1} normalized by its steady solution as a function of non-dimensional time with E = 10^-5,10^-6,10^-7 (the dot, the dashed, and the solid line, respectively) and Ro = 10^-6 at the radius r = 0.88. On the left side are the solutions with rigid boundary conditions on both sides and on the right side the solutions with stress-free boundary conditions on the outer. In the first case, the steady state is reached in a time smaller than the dimensionless time of contraction, while in the second case this time is longer and scales as E^-0.86.