The transition Reynolds number for a plane duct

Recent calculations indicate that the two-dimensional self-oscillations branching off from the neutral curve of the linear theory exist up to a Reynolds number of 1650 but are unstable with respect to three-dimensional perturbations. The principal mechanism of the instability is the parametric resonance of half-frequency three-dimensional perturbations against the background of two-dimensional self-oscillations. A finite-amplitude resonance triplet of such perturbations is examined here, and it is shown that the minimum Reynolds number at which steady-state three-dimensional self-oscillations exist is 678. This is in agreement with experimental data on the transition Reynolds number.