The connection between centrifugal instability and TollmienSchlichting-like instability for spiral Poiseuille flow

Abstract

For spiral Poiseuille flow with radius ratio η ≡ R i /R o = 0.5, we have computed complete linear stability boundaries for several values of the rotation rate ratio μ ≡ Ω o /Ω i , where R i and R o are the inner and outer cylinder radii, respectively, and Ω i and Ω o 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