Spin-up of stratified rotating flows at large Schmidt number: experiment and theory

We consider the nonlinear spin-up/down of a rotating stratified fluid in a conical container. An analysis of axisymmetric similarity-type solutions to the relevant boundary-layer problem, Duck, Foster & Hewitt (1997), has rev ealed three types of behaviour for this geometry. In general, the boundary layer evolves to either a steady state, or a gradually thickening boundary layer, or a finite-time singularity depending on the Schmidt number, the ra tio of initial to final rotation rates, and the relative importance of rota tion and stratification. In this paper we emphasize the experimental aspects of an investigation int o the initial readjustment process. We make comparisons with the previously presented boundary-layer theory, showing good quantitative agreement for p ositive changes in the rotation rate of the container (relative to the init ial rotation sense). The boundary-layer analysis is shown to be less succes sful in predicting the flow evolution for nonlinear decelerations of the co ntainer. We discuss the qualitative features of the spin-down experiments, which, in general, are dominated by non-axisymmetric effects. The experimen ts are conducted using salt-stratified solutions, which have a Schmidt numb er of approximately 700. The latter sections of the paper present some stability results for the ste ady boundary-layer states. A high degree of non-uniqueness is possible for the system of steady governing equations; however the experimental results are repeatable and stability calculations suggest that 'higher branch' solu tions are, in general, unstable. The eigenvalue spectrum arising from the l inear stability analysis is shown to have both continuous and discrete comp onents. Some analytical results concerning the continuous spectrum are pres ented in an appendix. A brief appendix completes the previous analysis of Duck, Foster & Hewitt ( 1997), presenting numerical evidence of a different form of finite-time sin gularity available for a more general boundary-layer problem.