  This is an entry for the Gallery of Fluid Motion of the 62nd Annual Meeting
of the APS-DFD (fluid dynamics videos). This video shows the three-dimensional
time-dependent incremental spin-up of a thermally stratified fluid in a
cylinder and in an annulus. The rigid bottom/side wall(s) are non-slip, and the
upper surface is stress-free. All the surfaces are thermally insulated. The
working fluid is water characterized by the kinematic viscosity $\nu$ and
thermal diffusivity $\kappa$. Initially, the fluid temperature varies linearly
with height and is characterized by a constant buoyancy frequency $N$, which is
proportional to the density gradient. The system undergoes an abrupt change in
the rotation rate from its initial value $\Omega_i $, when the fluid is in a
solid-body rotation state, to the final value $\Omega_f$. Our study reveals a
feasibility for transition from an axisymmetric initial circulation to
non-axisymmetric flow patterns at late spin-up times.
