| Abstract: | The small perturbation spectrum of a number of flows has recently been analyzed carefully [1–3]. At the same time, investigations for the boundary layer have been limited within the framework of linear perturbation theory to the neighborhood of the neutral curve although a spectrum analysis is of indubitable interest not only to find the stability criterion of a laminar stream, but also to solve a problem with initial data about the time development of an arbitrary small perturbation. In particular, the possibility of representing an arbitrary perturbation in terms of a system of basis functions is related to the question of the completeness of the system. The finiteness was proved [4] and an estimate was obtained of the domain of eigenvalue existence in an investigation of the boundary-layer stability and a deduction has been made about the finiteness of the small perturbations spectrum for boundary-layer flow on this basis. A sufficiently complete survey of the investigation of the neutral stability of a laminar boundary layer can be found in the monograph [5]. The small perturbations spectrum in a boundary layer flow is obtained in this paper by methods of the linear theory of hydrodynamic stability by using the complete boundary conditions on the outer boundary. It is shown that the small perturbations spectrum is finite for each fixed value of the wave number  . Singularities in the spectrum behavior are investigated for sufficiently small .Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 112–115, July–August, 1975.The author is grateful to M. A. Gol'dshtik and V. N. Shtern for useful discussions of the results of the research. |
