Abstract: | There have been many publications devoted to the investigation of the hydrodynamic stability of nonparallel flows on the basis of the modified Orr-Sommerfeld equation [1–4]. Taking into account the additional terms associated with the presence in the flow of a transverse component of velocity and acceleration can lead not only to a significant quantitative discrepancy as compared with calculations based on the usual Orr-Sommer-feld equation but also to qualitatively new results (nonclosure of the neutral curves for flow on a permeable surface in the presence of strong injection [4]). In this paper an asymptotic solution of the Orr-Sommer-feld equation, valid in the outer region of boundary layer flow, is constructed for self-similar gradient flow over a surface (Falkner-Skan flow). The continuity of the eigenvalue spectrum for an unbounded increase in the perturbation propagation velocity is demonstrated on the basis of the solution obtained. For the ordinary Orr-Sommerfeld equation a continuous transition of the spectrum through the value of the perturbation propagation velocity Cr=1 (which coincides with the velocity of the external flow) is impossible [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–173, January–February, 1987. |