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 revealed 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 ratio of initial to final rotation rates, and the relative
importance of rotation and stratification.
In this paper we emphasize the experimental aspects of an investigation into the
initial readjustment process. We make comparisons with the previously presented
boundary-layer theory, showing good quantitative agreement for positive changes
in the rotation rate of the container (relative to the initial rotation sense). The
boundary-layer analysis is shown to be less successful in predicting the flow evolution
for nonlinear decelerations of the container. We discuss the qualitative features of
the spin-down experiments, which, in general, are dominated by non-axisymmetric
effects. The experiments are conducted using salt-stratified solutions, which have a
Schmidt number of approximately 700.
The latter sections of the paper present some stability results for the steady
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’
solutions are, in general, unstable.
The eigenvalue spectrum arising from the linear stability analysis is shown to have
both continuous and discrete components. Some analytical results concerning the
continuous spectrum are presented 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 singularity available
for a more general boundary-layer problem.