Stability of a compressible boundary layer relative to a localized disturbance
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.
KeywordsMathematical Modeling Boundary Layer Mechanical Engineer Stability Analysis Mach Number
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- 1.Lin Chia-Ch'iao, The Theory of Hydrodynamic Stability [Russian translation], IL, Moscow (1958).Google Scholar
- 2.R. Betchov and V. Kriminale, Problems of Hydrodynamic Stability [Russian translation], Mir, Moscow (1971).Google Scholar
- 3.M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1965).Google Scholar
- 4.L. D. Landau and E. M. Lifshits, Mechanics of Solids [in Russian], Gostekhizdat, Moscow (1954).Google Scholar
- 5.A. I. Akhiezer and R. V. Polovin, “Criteria of wave growth,” Usp. Fiz. Nauk,104, No. 2 (1971).Google Scholar
- 6.K. B. Dysthe, “Convective and absolute instability,” Nucl. Fusion,6, No. 3 (1966).Google Scholar
- 7.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).Google Scholar
- 8.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).Google Scholar
- 9.A. A. Maslov, “A numerical investigation of stability of a supersonic laminar boundary layer,” Zh. Prikl. Mekhan i Tekh. Fiz., No. 5 (1972).Google Scholar
- 10.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).Google Scholar
- 11.E. A. Coddington and N. Levinson, The Theory of Ordinary Differential Equations [Russian translation], IL, Moscow (1958).Google Scholar