History
Taylor columns were first observed by William Thomson, Lord Kelvin, in 1868. Taylor columns were featured in lecture demonstrations by Kelvin in 1881 and by John Perry in 1890. The phenomenon is explained via the Taylor–Proudman theorem, and it has been investigated by Taylor, Grace, Stewartson,Stewartson, K. (1952) "On the slow motion of a sphere along the axis of a rotating fluid," ''Proceedings of the Cambridge Philosophical Society'', vol. 48, pages 168–177. and MaxworthyMaxworthy, T. (1968) "The observed motion of a sphere through a short, rotating cylinder of fluid," ''Journal of Fluid Mechanics'', vol. 31, pages 643–655. See also: Maxworthy, T. (1970) "The flow created by a sphere moving along the axis of a rotating, slightly-viscous fluid," ''Journal of Fluid Mechanics'', vol. 40, pages 453–479.—among others.Theory
Taylor columns have been rigorously studied. For '' Re''<<1, '' Ek''<<1, '' Ro''<<1, the drag equation for a cylinder of radius, ''a'', the following relation has been found. To derive this, Moore and Saffman solved the linearised Navier–Stokes equation along in cylindrical coordinates, where some of the vertical and radial components of the viscous term are taken to be small relative to the Coriolis term: To solve these equations, we incorporate the volume conservation condition as well: We use the Ekman compatibility relation for this geometry to restrict the form of the velocity at the disk surface: The resultant velocity fields can be solved in terms of Bessel functions. whereby for '' Ek''<<1 the function ''A(k)'' is given by, Integrating the equation for the ''v'', we can find the pressure and thus the drag force given by the first equation.References
Further reading
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