The von Karman similarity equations are investigated 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. An asymptotic solution is constructed that is 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 K. Stewartson. Moreover, its properties agree precisely with estimates for a solution whose existence has been proven by J. B. McLeod and S. V. Parter.
ASJC Scopus subject areas
- Applied Mathematics