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Formation of a viscous boundary layer on the free surface of an imploding rotating liquid cylinder

Published online by Cambridge University Press:  19 April 2006

A. L. Cooper  and
D. L. Book
A. L. Cooper
Affiliation:
Plasma Physics Division, Naval Research Laboratory, Washington, D.C. 20375
D. L. Book
Affiliation:
Plasma Physics Division, Naval Research Laboratory, Washington, D.C. 20375
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Abstract

The effect of viscosity on the inner free surface of a rotating imploding cylindrical liquid shell compressing an ideal gas or magnetic flux load is analysed in the limit of high Reynolds number Re. The condition of vanishing tangential stress on the free surface leads to the formation of a boundary layer of thickness ∼ Re−½. Within this layer the zonal velocity v is reduced by an amount Δv such that Δ v/vRe−½. This results in a requirement of slightly increased rotation in order to satisfy the criterion for suppression of the Rayleigh-Taylor instability on the free surface. Calculations are presented for a model implosion trajectory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 93 , Issue 2 , 26 July 1979 , pp. 305 - 317
Copyright
© 1979 Cambridge University Press

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