On the flow induced by centrifugal buoyancy in a differentially-heated rotating cylinder

We consider the nature of thermally stratified flow in a closed cylinder rotating about the direction of gravity under conditions appropriate for terrestrial laboratory experiments. Motion is driven by centrifugal buoyancy, with outflow near the cold disk and inflow near the hot disk. Although similarity solutions for the infinite disk open-geometry problem exist and are easily found, even analytically in certain limits, there remain questions about the applicability of these spatially simplified models in a closed geometry with a vertical sidewall. This paper compares theoretical self-similar core solutions with computational simulations constructed to satisfy a wide range of sidewall thermal boundary conditions; insulating, conducting (with a linear temperature profile up the wall), hot (isothermal), or cold. The width of penetration of sidewall influence in toward the axis of rotation depends on the sidewall thermal boundary condition. However, as the cylinder radius is increased for a fixed height, a substantial region of the container about the axis is accurately described by the thermocline solutions of the theory. The non-self-similar region at large radius can include separation of the lower outflow boundary layer, a feature not evident in previous studies of this problem.