Fluid flow in a partially-filled rotating cylinder
type: Item
instance of: scholarly article
title: Fluid flow in a partially-filled rotating cylinder
zbMATH Open document ID: 0605.76125
DOI: 10.1007/BF00038707
published in: Journal of Engineering Mathematics
publication date: 1986-01-01T00:00:00Z
review text: 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 earlier 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.
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3978717
zbMATH Keywords: partially-filled cylinder
zbMATH Keywords: differential rotation
zbMATH Keywords: film thickness
zbMATH Keywords: geostrophic balance
zbMATH Keywords: viscous effects
zbMATH Keywords: shear layers
zbMATH Keywords: flow boundaries
zbMATH Keywords: thin-film situation
zbMATH Keywords: Stewartson layers
author: G. J. F. Van Heijst
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3978717