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The time-dependent motion due to a cylinder moving in an unbounded rotating or stratified fluid

Published online by Cambridge University Press:  28 March 2006

F. P. Bretherton
F. P. Bretherton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

A rigid cylinder is initially at relative rest in a uniformly rotating, inviscid, incompressible fluid, with its generators perpendicular to the axis of rotation. The fluid is accelerated suddenly to a small constant velocity parallel to the axis of rotation, which is maintained thereafter. The growth of the subsequent disturbance due to the cylinder is interpreted in terms of plane inertial waves, the disturbance energy propagating with the local group velocity, which is in the plane of the wave front and proportional to the wavelength. Taylor columns, in which the fluid moves with the cylinder rather than round it, grow indefinitely in both directions parallel to the rotation axis, the head of the column moving with finite speed.

In a slightly viscous fluid, an ultimate steady state is reached, in which the columns are of finite length.

If a cylinder is moved horizontally in a non-rotating uniformly stratified Boussinesq liquid, an identical analysis may be applied with a similar interpretation in terms of internal gravity waves rather than inertial waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 3 , 26 May 1967 , pp. 545 - 570
Copyright
© 1967 Cambridge University Press

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