The process by which a stratified, viscous fluid adjusts to small changes in the rotation rate of its container is studied. This paper treats the cases of homogeneous layers of different densities, as well as fluids which are continuously stratified.
It is shown that in several important cases the spin-up process, especially in the continuously stratified case, has a time scale which is very much longer than for homogeneous fluids, and that diffusion is the governing mechanism in the adjustment process.
In all cases the detailed problem, including a discussion of the side-wall boundary layers, is presented. Some novel features of the side-wall layers are discussed for the continuously stratified fluids, while in one case it is shown that no boundary layers appear during the transient approach to equilibrium.