Spinup of a stratified fluid in a sliced, circular cylinder

Experiments were performed in a linearly salt-stratified fluid in a circular cylindrical tank, with a planar bottom boundary sloped at a small angle $\alpha$ to the horizontal. The container rotated initially at an angular velocity $\Omega$, so that the Ekman number, $E$, was typically $10^{-5}$. We examined the adjustment when the container's angular speed is abruptly increased by $\epsilon \Omega$, with $\epsilon\sim .01$. Further, $\alpha \gg E^{1/2}$, and the Burger number $S$ is large. There are similarities and differences between this spinup and that in a sliced square cylinder (Munro \& Foster, {\it Phys.~Fluids} {\bf 26}, 2014, denoted by MF14). Unlike MF14, the axisymmetry of the initial core motion means there are no core eddies generated by boundary-layer eruption. In fact, since the core motion is nearly axisymmetric for all time at large $S$, eddy formation is confined to the region of height ${\cal{O}}(S^{-1/2})$ near the lower slope, within which the Rossby waves are confined. Just as in MF14, after several ``spinup times,'' the cross-container velocity profiles agree very well with a linear asymptotic theory for small $\epsilon, E$ and large $S$, provided one properly accounts for the Rayleigh layers on the cylinder's sidewall.