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The Flow Between Counter-Rotating Disks at High Reynolds Number

B. J. Matkowsky and W. L. Siegmann
SIAM Journal on Applied Mathematics
Vol. 30, No. 4 (Jun., 1976), pp. 720-727
Stable URL: http://www.jstor.org/stable/2100333
Page Count: 8
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The Flow Between Counter-Rotating Disks at High Reynolds Number
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Abstract

We investigate the von Karman similarity equations for fluid flow between two infinite coaxial disks that rotate with equal rotation rates and in opposite directions. The nonlinear singular perturbation problem for high Reynolds number is analyzed by formal asymptotic methods. We construct an asymptotic solution valid away from the boundary layers that occur on each disk. This solution requires that the fluid away from the boundary layers is essentially nonrotating, and thus confirms a conjecture of Stewartson. Moreover, its properties agree precisely with estimates for a solution whose existence has been proven by McLeod and Parter.

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