Summary
This paper presents an analytical description of the fluid flow in a partially-filled cylinder rotating at a sufficiently high rate that the fluid forms a film of uniform thickness against the sidewall. Relative flow is induced by differential rotation of the upper endcap of the cylinder. When the film thickness is large enough, the main body of the fluid is in geostrophic balance, viscous effects being confined within thin shear layers at the flow boundaries. At the horizontal endcaps these layers are of Ekman type, while Stewartson layers arise at the sidewall and at the free surface. In contrast with the Stewartson layer at the sidewall, which has a sandwich structure consisting of layers of thicknesses E 1/4 and E 1/3, viscous effects at the free surface are concentrated in a single layer of thickness E 1/3 (E is the Ekman number). The theoretical velocity profiles are compared with numerical and experimental profiles presented by Shadday, Ribando and Kauzlarich [1] and the agreement is very good. The comparison is also made in the thin-film situation where the Stewartson layers partially overlap, and again the theoretical profiles agree fairly well with the numerical and experimental results.
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Van Heijst, G.J.F. Fluid flow in a partially-filled rotating cylinder. J Eng Math 20, 233–250 (1986). https://doi.org/10.1007/BF00038707
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DOI: https://doi.org/10.1007/BF00038707