Flow between rotating disks. Part 2. Stability

Abstract

Infinite-disk flows appear to possess multiple solutions at E −1 = 275 (Holodniok, Kubicek & Hlavacek 1977), where E = ν/ s 2 ω is the Ekman number. One of these solutions exhibits characteristics of Couette flow and is stable in the circular domain 0 < r / s < 50. The other two solutions, both Poiseuille-type flows, are unstable at all positions. The stable solution shows strong resemblance to experimental profiles obtained between finite disks. Stability of finite-disk flows is investigated in two cases: (i) one disk rotating and the other stationary, and (ii) counter-rotating disks. Photographs indicate presence of two instability types. Theoretical calculations are in fair agreement with experimental evidence on instability of type I.