An oscillatory pipe flow with zero-mean components can be specified by two parameters ω' and R_eos, where ω'≡ R²ω'ν is the dimensionless frequency, R_eos≡| u_{m, os, 1}| D/ν the Reynolds number based on the amplitude | u_{m, os, 1}| of cross-sectional mean velocity u_m, D = 2R the pipe diameter, and ν the kinematic viscosity.
Reexamination of the authors' previous experimental results for such transitional oscillatory pipe flow revealed that two kinds of Reynolds numbers are reasonable to characterize the transition to turbulence in a half cycle of oscillation. The summary is as follows:
(1) The critical Reynolds number (u_mm D/ν)_c is well expressed by
(u_mm D/ν)_c=1.86R_eos0.02
(100000≥R_eos≥2300, (du_m/dt)_c≥ O)
where R_eos≥800 √ω for each dimensionless frequency in the present experimental range (2.63≤√ω≤23.37).
(2) Another critical Reynolds number (u^*δ₁/ν )_c is independent of R_eos, where u^* is the friction velocity, δ₁ the displacement thickness. It seems that (u^*δ₁/ν)_c approaches asymptotically the critical value of steady pipe flow 19.9 as ω'→0 and is almost equal to that of steady boundary layer on a flat plate 24.2 when √ω≥ 20.

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