Shankar, PN (2007) *Three-dimensional flow in a cylinder with a stress-free sidewall.* Fluid dynamics research, 39 (7). pp. 569-589.

## Abstract

Stokes flow in a cylindrical column of fluid, with a stress-free cylindrical sidewall, is considered. The motion is assumed to be generated by the linear, uniform motion of either or both of the flat endwalls. The field is obtained by a vector eigenfunction expansion procedure. If the field is assumed to have a x3B8;- and z-dependence of the type exp(ix3B8; + kz), k has to satisfy the equation (1 x2212; k2)J13 + hat J1[2J12 x2212; hat J1{2hat J1 + (1 + k2)J1}] = 0, where hat J1 = kJ0 x2212; J1 and the argument of each Bessel function is k. This equation admits, unlike in the plane case and with important consequences, not just a real sequence {tilde lambdan} of eigenvalues but also a complex one {tilde mun}. Using a least squares procedure to satisfy the boundary conditions on the top and bottom walls, the three-dimensional velocity field in the column is determined for various values of column height h and wall speed ratio S. Detailed computations show that there are strong effects of both the stress-free boundary and three-dimensionality. The principal effect of the former is to permit motion on that boundary leading to large azimuthal motions and of the latter, unlike in the plane flow, to multiple primary eddies when h is sufficiently large. A number of new eddy structures are also found, which demonstrate that three-dimensionality often leads to the elimination of compactness found in plane flows. It is finally shown that the flow fields exhibit interesting bifurcations as S and h are varied.

Item Type: | Journal Article |
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Uncontrolled Keywords: | Three-dimensional stokes flow;Stress-free boundaries;Eddy structure;Meniscus roll coating;Vector eigenfunction expansions;Bifurcations |

Subjects: | AERONAUTICS > Aeronautics (General) |

Division/Department: | Computational and Theoretical Fluid Dynamics Division |

Depositing User: | Ms. Alphones Mary |

Date Deposited: | 18 May 2009 |

Last Modified: | 24 May 2010 09:56 |

URI: | http://nal-ir.nal.res.in/id/eprint/5105 |

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