Computational assessment of subcritical and delayed onset in spiral Poiseuille flow experiments

For spiral Poiseuille flow with radius ratios η ≡ R_i/R_o = 0.77 and 0.95, we have computed complete linear stability boundaries, where R_i and R_o are the inner and outer cylinder radii, respectively. The analysis accounts for arbitrary disturbances of infinitesimal amplitude over the entire range of Reynolds numbers Re for which the flow is stable for some range of Taylor number Ta, and extends previous work to several non-zero rotation rate ratios μ ≡ Ω_o/Ω_i, where Ω_i and Ω_o are the (signed) angular speeds. For each combination of μ and η, there is a wide range of Re for which the critical Ta is nearly independent of Re, followed by a precipitous drop to Ta = 0 at the Re at which non-rotating annular Poiseuille flow becomes unstable with respect to a Tollmien-Schlichting-like disturbance. Comparison is also made to a wealth of experimental data for the onset of instability. For Re > 0, we compute critical values of Ta for most of the μ = 0 data, and for all of the non-zero-μ data. For μ = 0 and η = 0.955, agreement with data from an annulus with aspect ratio (length divided by gap) greater than 570 is within 3.2% for Re ≤ 325 (based on the gap and mean axial speed), strongly suggesting that no finite-amplitude instability occurs over this range of Re. At higher Re, onset is delayed, with experimental values of Ta_crit exceeding computed values. For μ = 0 and smaller η, comparison to experiment (with smaller aspect ratios) at low Re is slightly less good. For η = 0.77 and a range of μ, agreement with experiment is very good for Re < 135 except at the most positive or negative μ (where Ta^expt_crit > Ta^comp_crit), whereas for Re ≥ 166, Ta^expt_crit > Ta^comp_crit for all but the most positive μ. For η = 0.9497 and 0.959 and all but the most extreme values of μ, agreement is excellent (generally within 2%) up to the largest Re considered experimentally (200), again suggesting that finite-amplitude instability is unimportant.