Spin-up of homogeneous and stratified fluids

We consider the manner in which a container filled with viscous fluid adjus ts to changes in its rotation rate. We begin with homogeneous flows involvi ng small departures in rotation rate from an initial state of solid-body ro tation in an axisymmetric container. This is followed by a summary of other more recent developments, including weakly and fully nonlinear calculation s and comparison with experiment and the question of spin-down. The questio n of "spin-over" is addressed, followed by a brief synopsis of free-surface effects, and a discussion of nonaxisymmetric spin-up. The second part of t he review focuses on the effects of stratification on the spin-up process. Linearized (low Rossby number) spin-up within a cylindrical container is de scribed. Thereafter, both experimental and nonlinear computational results are described and compared. The final section focuses on stratified spin-up and spin-down in conical geometries, and a number of comparisons between t heory and experiment are given.