Spin-up of a two-layer rotating stratified fluid in a variable-depth container

We consider the spin-up of a two-layer, stably (density) stratified fluid i n a rotating container with an axisymmetric sloping base and cylindrical wa lls. Details of the spin-up readjustment mechanisms are presented under the assumption of small impulsive changes in the rotation rate of the containe r. It is shown that the relative positions of the density interface and the discontinuity in wall slope determine the qualitative large-time spin-up r esponse of the fluid. The density interface leads to a spin-up readjustment in each of the fluid layers that is essentially independent. However, when the density interface is below the boundary-slope discontinuity, a sub-reg ion of the upper layer is predicted to readjust in an algebraic rather than exponential manner. A detailed sequence of laboratory experiments have bee n performed to confirm the predictions of the linear spin-up analysis.