Nonlinear spin-up of a thermally stratified fluid in cylindrical geometries

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.