Publication Date:
2004-06-25
Description:
For spiral Poiseuille flow with radius ratio η ≡ Ri/Ro = 0.5, we have computed complete linear stability boundaries for several values of the rotation rate ratio μ ≡ Ωo/Ωi, where Ri and Ro are the inner and outer cylinder radii, respectively, and Ωi and Ωo are the corresponding (signed) angular speeds. The analysis extends the previous range of Reynolds number Re studied computationally by more than eightyfold, and accounts for arbitrary disturbances of infinitesimal amplitude over the entire range of Re for which spiral Poiseuille flow is stable for some range of the Taylor number Ta. We show how the centrifugally driven instability (beginning with steady or azimuthally travelling-wave bifurcation of circular Couette flow at Re = 0 when μ 〈 η2) connects, as conjectured by Reid (1961) in the narrow-gap limit, to a non-axisymmetric Tollmien-Schlichting-like instability of non-rotating annular Poiseuille flow at Ta = 0. For μ 〉 η2, we show that there is no instability for 0 ≤ Re ≤ Remin. For μ = 0.5, Remin corresponds to a turning point, beyond which exists a range of Re for which there are two critical values of Ta, with spiral Poiseuille flow being stable below the lower one and above the upper one, and unstable in between. For the special case μ = 1, with the two cylinders having the same angular velocity, Remin corresponds to a vertical asymptote smaller than found by Meseguer & Marques (2002), whose results for μ 〉 η2 fail to account for disturbances with a sufficiently wide range of azimuthal wavenumbers. © 2004 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
