Abstract
While concentric cylinder flows exhibit Ekman pumping at small values of the Reynolds number, once the container symmetry is broken, fluid particles migrate toward the horizontal midplane within the diverging part of the flow domain, and they move away from the midplane within the converging part of the domain. Under this condition, Ekman pumping is evident only at the widest and at the narrowest sections of the gap. When gradually increasing the Reynolds number, the flow acquires a cellular structure in a manner reminiscent of Benjamin's symmetric flow data. The cells spread from the stationary end-plates and link up at the center. The cells persist round the cylinder with varying strength and thus are truly toroidal. We show evidence of solution multiplicity at higher values of the Reynolds number by calculating two qualitatively different flows. One flow contains four cells, the other contains six, and both are supported by identical steady-state conditions.
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