1. experiment of Merkli & Thomann (1975). The oscillating laminar velocity field is approximated with the planar analytic solution of the incompressible Navier-Stokes equations for parallel flow in a channel with imposed sinusoidal pressure gradient. The results show that a low pressure amplitude of H = 0.02 does not induce instability during the entire cycle at the given condition, however at higher amplitudes the growth rate increases substantially and the flow becomes unstable within portions of the cycle. This phenomenon corresponds to the experimental observation performed by Merkli and Thomann (1975), i.e., the flow can become highly turbulent and then nearly laminar within parts of a cycle. The appearance of two peaks in disturbance growth rate is to be expected, and demonstrates how the posed linear problem can display nonlinear, harmonic behavior of the growth rate. In the plateau regions, not only the variation of the growth rates but also the differences between the curves are very small and the curves appear to be almost identical in the presented scale.
2. AIAA-99-2508
3. the present numerical solution procedure yields the stability map verifying the critical Reynolds number of 5772.22. von Kerczek (1982) and others have stated that the symmetric eigenfunction is the only unstable mode of steady plane Poiseuille flow, and the present results consider the effects of modulation only on the symmetric modes.