Abstract
The problem of stability of an incompressible boundary layer relative to a localized disturbance is considered in a linear approximation. It is shown that the stability analysis reduces to the study of a discrete spectrum of eigenvalues of the corresponding boundary value problem. By means of numerical integration, analysis of the character of the emerging instability is carried out for an unstable mode for the Mach number M = 4.5.
Similar content being viewed by others
Literature cited
Lin Chia-Ch'iao, The Theory of Hydrodynamic Stability [Russian translation], IL, Moscow (1958).
R. Betchov and V. Kriminale, Problems of Hydrodynamic Stability [Russian translation], Mir, Moscow (1971).
M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1965).
L. D. Landau and E. M. Lifshits, Mechanics of Solids [in Russian], Gostekhizdat, Moscow (1954).
A. I. Akhiezer and R. V. Polovin, “Criteria of wave growth,” Usp. Fiz. Nauk,104, No. 2 (1971).
K. B. Dysthe, “Convective and absolute instability,” Nucl. Fusion,6, No. 3 (1966).
B. Nagel, “The saddle point method for multiple integrals with an application to the evaluation of radial Coulomb matrix elements for large multi-pole orders,” Arch. Phys.,27, No. 2 (1964).
S. V. Lordanskii and A. G. Kulikovskii, “On absolute stability of certain plane-parallel flows in the case of large Reynolds numbers,” Zh. Éksp. i Teor. Fiz.,49, No. 4 (1965).
A. A. Maslov, “A numerical investigation of stability of a supersonic laminar boundary layer,” Zh. Prikl. Mekhan i Tekh. Fiz., No. 5 (1972).
S. P. Hastings, “On the uniqueness and asymptotic behavior of a similarity solution for a compressible boundary layer,” Arch. Ration. Mech. and Analys.,42, No. 2 (1971).
E. A. Coddington and N. Levinson, The Theory of Ordinary Differential Equations [Russian translation], IL, Moscow (1958).
Author information
Authors and Affiliations
Additional information
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, pp. 107–114, May–June, 1973.
The author is grateful to V. V. Struminskii for his interest in this work; he is grateful to L. B. Aizin for useful discussion of the subjects broached, and to A. A. Maslov for the great help in carrying out the numerical calculations.
Rights and permissions
About this article
Cite this article
Dryzhov, A.S. Stability of a compressible boundary layer relative to a localized disturbance. J Appl Mech Tech Phys 14, 383–389 (1973). https://doi.org/10.1007/BF00850954
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00850954